Patent Publication Number: US-2022214522-A1

Title: Photographing optical system

Description:
RELATED APPLICATIONS 
     This application is a continuation patent application of U.S. application Ser. No. 16/734,132 filed on Jan. 3, 2020, which claims priority to Taiwan Application 108143234, filed on Nov. 27, 2019, which is incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     Technical Field 
     The present disclosure relates to a photographing optical system, an image capturing unit and an electronic device, more particularly to a photographing optical system and an image capturing unit applicable to an electronic device. 
     Description of Related Art 
     With the development of semiconductor manufacturing technology, the performance of image sensors has improved, and the pixel size thereof has been scaled down. Therefore, featuring high image quality becomes one of the indispensable features of an optical system nowadays. Furthermore, due to the rapid changes in technology, electronic devices equipped with optical systems are trending towards multi-functionality for various applications, and therefore the functionality requirements for the optical systems have been increasing. However, it is difficult for a conventional optical system to obtain a balance among the requirements such as high image quality, low sensitivity, a proper aperture size, miniaturization and a desirable field of view. 
     SUMMARY 
     According to one aspect of the present disclosure, a photographing optical system includes eight lens elements. The eight lens elements are, in order from an object side to an image side, a first lens element, a second lens element, a third lens element, a fourth lens element, a fifth lens element, a sixth lens element, a seventh lens element and an eighth lens element. Each of the eight lens elements has an object-side surface facing toward the object side and an image-side surface facing toward the image side. 
     The first lens element has positive refractive power. The fifth lens element has positive refractive power. The object-side surface of the seventh lens element is convex in a paraxial region thereof. The image-side surface of the eighth lens element is concave in a paraxial region thereof. At least one lens surface of at least one lens element of the photographing optical system has at least one critical point in an off-axis region thereof. 
     When an Abbe number of the second lens element is V 2 , a focal length of the first lens element is f 1 , a focal length of the fifth lens element is f 5 , a central thickness of the second lens element is CT 2 , a central thickness of the third lens element is CT 3 , a central thickness of the fifth lens element is CT 5 , and a central thickness of the seventh lens element is CT 7 , the following conditions are satisfied: 
       10.0&lt;V2&lt;50.0; 
       0 &lt;f 5 /f 1&lt;3.0; 
       0.10&lt;CT3/CT2&lt;1.5; and 
       0.10&lt;CT7/CT5&lt;1.3. 
     According to another aspect of the present disclosure, a photographing optical system includes eight lens elements. The eight lens elements are, in order from an object side to an image side, a first lens element, a second lens element, a third lens element, a fourth lens element, a fifth lens element, a sixth lens element, a seventh lens element and an eighth lens element. Each of the eight lens elements has an object-side surface facing toward the object side and an image-side surface facing toward the image side. The first lens element has positive refractive power. The object-side surface of the second lens element is convex in a paraxial region thereof. The fifth lens element has positive refractive power. The object-side surface of the seventh lens element is convex in a paraxial region thereof. The image-side surface of the eighth lens element is concave in a paraxial region thereof. At least one lens surface of at least one lens element of the photographing optical system has at least one critical point in an off-axis region thereof. When an Abbe number of the second lens element is V 2 , a focal length of the photographing optical system is f, a focal length of the first lens element is f 1 , a focal length of the fifth lens element is f 5 , a focal length of the seventh lens element is f 7 , a focal length of the eighth lens element is f 8 , and a curvature radius of the object-side surface of the second lens element is R 3 , the following conditions are satisfied: 
       10.0&lt;V2&lt;50.0; 
       0 &lt;f 5 /f 1&lt;9.5; 
       −7.5 &lt;f 8 /f 7&lt;−0.55; and
 
       0 &lt;R 3 /f&lt; 2.0. 
     According to another aspect of the present disclosure, a photographing optical system includes eight lens elements. The eight lens elements are, in order from an object side to an image side, a first lens element, a second lens element, a third lens element, a fourth lens element, a fifth lens element, a sixth lens element, a seventh lens element and an eighth lens element. Each of the eight lens elements has an object-side surface facing toward the object side and an image-side surface facing toward the image side. The first lens element has positive refractive power. The fifth lens element has positive refractive power. The object-side surface of the seventh lens element is convex in a paraxial region thereof. The image-side surface of the eighth lens element is concave in a paraxial region thereof. At least one lens surface of at least one lens element of the photographing optical system has at least one critical point in an off-axis region thereof. When an Abbe number of the second lens element is V 2 , a focal length of the first lens element is f 1 , a focal length of the fifth lens element is f 5 , a central thickness of the third lens element is CT 3 , a central thickness of the fifth lens element is CT 5 , and a central thickness of the seventh lens element is CT 7 , the following conditions are satisfied: 
       10.0&lt;V2&lt;50.0; 
       0 &lt;f 5 /f 1&lt;3.0; 
       1.8&lt;CT5/CT3; and 
       0.10&lt;CT7/CT5&lt;1.3. 
     According to another aspect of the present disclosure, an image capturing unit includes one of the aforementioned photographing optical systems and an image sensor, wherein the image sensor is disposed on an image surface of the photographing optical system. 
     According to another aspect of the present disclosure, an electronic device includes the aforementioned image capturing unit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure can be better understood by reading the following detailed description of the embodiments, with reference made to the accompanying drawings as follows: 
         FIG. 1  is a schematic view of an image capturing unit according to the 1st embodiment of the present disclosure; 
         FIG. 2  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 1st embodiment; 
         FIG. 3  is a schematic view of an image capturing unit according to the 2nd embodiment of the present disclosure; 
         FIG. 4  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 2nd embodiment; 
         FIG. 5  is a schematic view of an image capturing unit according to the 3rd embodiment of the present disclosure; 
         FIG. 6  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 3rd embodiment; 
         FIG. 7  is a schematic view of an image capturing unit according to the 4th embodiment of the present disclosure; 
         FIG. 8  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 4th embodiment; 
         FIG. 9  is a schematic view of an image capturing unit according to the 5th embodiment of the present disclosure; 
         FIG. 10  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 5th embodiment; 
         FIG. 11  is a schematic view of an image capturing unit according to the 6th embodiment of the present disclosure; 
         FIG. 12  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 6th embodiment; 
         FIG. 13  is a schematic view of an image capturing unit according to the 7th embodiment of the present disclosure; 
         FIG. 14  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 7th embodiment; 
         FIG. 15  is a schematic view of an image capturing unit according to the 8th embodiment of the present disclosure; 
         FIG. 16  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 8th embodiment; 
         FIG. 17  is a schematic view of an image capturing unit according to the 9th embodiment of the present disclosure; 
         FIG. 18  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 9th embodiment; 
         FIG. 19  is a schematic view of an image capturing unit according to the 10th embodiment of the present disclosure; 
         FIG. 20  shows spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 10th embodiment; 
         FIG. 21  is a perspective view of an image capturing unit according to the 11th embodiment of the present disclosure; 
         FIG. 22  is one perspective view of an electronic device according to the 12th embodiment of the present disclosure; 
         FIG. 23  is another perspective view of the electronic device in  FIG. 22 ; 
         FIG. 24  is a block diagram of the electronic device in  FIG. 22 ; and 
         FIG. 25  shows a schematic view of Y 11 , Y 82 , Yc 71 , Yc 72  and Yc 82 , as well as several inflection points and critical points of the lens elements according to the 1st embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     A photographing optical system includes eight lens elements. The eight lens elements are, in order from an object side to an image side, a first lens element, a second lens element, a third lens element, a fourth lens element, a fifth lens element, a sixth lens element, a seventh lens element and an eighth lens element. Each of the eight lens elements has an object-side surface facing toward the object side and an image-side surface facing toward the image side. 
     The first lens element has positive refractive power. Therefore, it is favorable for reducing the size of the photographing optical system. The object-side surface of the first lens element can be convex in a paraxial region thereof. Therefore, it is favorable for light from various regions within the field of view to enter the photographing optical system evenly so as to increase peripheral relative illuminance of the image surface. 
     The object-side surface of the second lens element can be convex in a paraxial region thereof. Therefore, it is favorable for correcting aberrations when collaborating with the first lens element. The image-side surface of the second lens element can be concave in a paraxial region thereof. Therefore, it is favorable for correcting aberrations such as astigmatism. 
     The fifth lens element has positive refractive power. Therefore, it is favorable for reducing the size of the photographing optical system. 
     The seventh lens element can have positive refractive power. Therefore, it is favorable for dispersing the positive refractive power distribution so as to reduce sensitivity of each lens elements while reducing the size of the photographing optical system. The object-side surface of the seventh lens element is convex in a paraxial region thereof. Therefore, it is favorable for adjusting the refractive power of the seventh lens element and correcting off-axis aberrations. 
     The eighth lens element can have negative refractive power. Therefore, it is favorable for balancing the refractive power distribution on the image side of the photographing optical system so as to reduce aberrations such as spherical aberration. The image-side surface of the eighth lens element is concave in a paraxial region thereof. Therefore, it is favorable for adjusting the back focal length and correcting off-axis aberrations such as field curvature. 
     According to the present disclosure, at least one of the object-side surface and the image-side surface of at least one lens element of the photographing optical system has at least one critical point in an off-axis region thereof. Therefore, it is favorable for increasing surface shape variation of the lens element so as to correct off-axis aberrations and increase peripheral illuminance of the image surface. Moreover, at least one of the object-side surface and the image-side surface of each of at least two lens elements of the photographing optical system can have at least one critical point in an off-axis region thereof. Moreover, at least one of the object-side surface and the image-side surface of each of at least three lens elements of the photographing optical system can have at least one critical point in an off-axis region thereof. Moreover, at least one of the object-side surface and the image-side surface of the sixth lens element can have at least one critical point in an off-axis region thereof. Therefore, it is favorable for adjusting the size distribution on the image-side of the photographing optical system. Moreover, the object-side surface of the seventh lens element can have at least one critical point in an off-axis region thereof. Therefore, it is favorable for adjusting the incident angle of light on the seventh lens element so as to reduce stray light. Moreover, the image-side surface of the seventh lens element can have at least one critical point in an off-axis region thereof. Therefore, it is favorable for further correcting off-axis aberrations when collaborating with the eighth lens element. Moreover, when a vertical distance between the critical point on the object-side surface of the seventh lens element and an optical axis is Yc 71 , and a vertical distance between the critical point on the image-side surface of the seventh lens element and the optical axis is Yc 72 , the at least one critical point in the off-axis region of the object-side surface and the at least one critical point in the off-axis region of the image-side surface of the seventh lens element can satisfy the following condition: 0.80&lt;Yc 72 /Yc 71 &lt;1.5. Therefore, it is favorable for adjusting the surface shape of the seventh lens element so as to further correct off-axis aberrations. Moreover, the at least one critical point in the off-axis region of the object-side surface and the at least one critical point in the off-axis region of the image-side surface of the seventh lens element can also satisfy the following condition: 0.90&lt;Yc 72 /Yc 71 &lt;1.4. Moreover, the image-side surface of the eighth lens element can have at least one critical point in an off-axis region thereof. Therefore, it is favorable for correcting off-axis aberrations and adjusting the incident angle on the image surface so as to increase image surface illuminance and the response efficiency of the image sensor. Moreover, when a vertical distance between the critical point on the image-side surface of the eighth lens element and the optical axis is Yc 82 , and a maximum effective radius of the image-side surface of the eighth lens element is Y 82 , the at least one critical point in the off-axis region of the image-side surface of the eighth lens element can satisfy the following condition: 0.20&lt;Yc 82 /Y 82 &lt;0.60. Therefore, it is favorable for adjusting the surface shape of the eighth lens element so as to further increase image quality. Moreover, the at least one critical point in the off-axis region of the image-side surface of the eighth lens element can also satisfy the following condition: 0.30&lt;Yc 82 /Y 82 &lt;0.50. Please refer to  FIG. 25 , which shows a schematic view of several critical points C of the third lens element  130 , the fourth lens element  140 , the sixth lens element  160 , the seventh lens element  170  and the eighth lens element  180 , as well as Yc 71 , Yc 72 , Yc 82  and Y 82  according to the 1st embodiment of the present disclosure. 
     According to the present disclosure, at least one of the object-side surface and the image-side surface of each of at least three lens elements of the photographing optical system can have at least one inflection point. Therefore, it is favorable for increasing the surface shape variation of the lens element so as to correct aberrations and reduce the system size. Moreover, at least one of the object-side surface and the image-side surface of each of at least four lens elements of the photographing optical system can have at least one inflection point. Moreover, at least one of the object-side surface and the image-side surface of each of at least five lens elements of the photographing optical system can have at least one inflection point. Moreover, each of the object-side surface and the image-side surface of each of all lens elements of the photographing optical system can have at least one inflection point. Therefore, it is favorable for further increasing the surface shape variation of the lens elements so as to correct aberrations and reduce the system size. Please refer to  FIG. 25 , which shows a schematic view of several inflection points P of all lens elements according to the 1st embodiment of the present disclosure. 
     An axial distance between the seventh lens element and the eighth lens element can be a maximum value among axial distances between each of all adjacent lens elements of the photographing optical system. Therefore, it is favorable for adjusting the lens elements distribution so as to increase the image surface area and correct off-axis aberrations. In the present disclosure, an axial distance between two adjacent lens elements is an axial distance between two adjacent lens surfaces of the two adjacent lens elements. 
     When an Abbe number of the second lens element is V 2 , the following condition is satisfied: 10.0&lt;V 2 &lt;50.0. Therefore, it is favorable for adjusting the material of the second lens element so as to correct aberrations such as chromatic aberration. Moreover, the following condition can also be satisfied: 11.0&lt;V 2 &lt;40.0. Moreover, the following condition can also be satisfied: 12.0&lt;V 2 &lt;30.0. Moreover, the following condition can also be satisfied: 13.0&lt;V 2 &lt;25.0. 
     When a focal length of the first lens element is f 1 , and a focal length of the fifth lens element is f 5 , the following condition is satisfied: 0&lt;f 5 /f 1 ; or f 5 /f 1 &lt;9.5. Therefore, it is favorable for adjusting the refractive power distribution of the photographing optical system so as to reduce the system size and adjust the system size distribution. Moreover, the following condition can also be satisfied: 0.10&lt;f 5 /f 1 . Moreover, the following condition can also be satisfied: 0.30&lt;f 5 /f 1 . Moreover, the following condition can also be satisfied: 0.50&lt;f 5 /f 1 . Moreover, the following condition can also be satisfied: f 5 /f 1 &lt;5.0. Moreover, the following condition can also be satisfied: f 5 /f 1 &lt;3.0. Moreover, the following condition can also be satisfied: f 5 /f 1 &lt;2.0. Moreover, the following condition can also be satisfied: 0&lt;f 5 /f 1 &lt;9.5. Moreover, the following condition can also be satisfied: 0&lt;f 5 /f 1 &lt;3.0. Moreover, the following condition can also be satisfied: 0.10&lt;f 5 /f 1 &lt;5.0. Moreover, the following condition can also be satisfied: 0.30&lt;f 5 /f 1 &lt;2.0. 
     When a central thickness of the fifth lens element is CTS, and a central thickness of the seventh lens element is CT 7 , the following condition can be satisfied: 0.10&lt;CT 7 /CT 5 &lt;1.3. Therefore, it is favorable for adjusting the lens elements distribution on the image side of the photographing optical system so as to reduce the size of the image side. Moreover, the following condition can also be satisfied: 0.20&lt;CT 7 /CT 5 &lt;1.0. Moreover, the following condition can also be satisfied: 0.40&lt;CT 7 /CT 5 &lt;0.70. 
     When a central thickness of the second lens element is CT 2 , and a central thickness of the third lens element is CT 3 , the following condition can be satisfied: 0.10&lt;CT 3 /CT 2 &lt;1.5. Therefore, it is favorable for the second and third lens elements to collaborate with each other so as to reduce the size on the object side of the photographing optical system. Moreover, the following condition can also be satisfied: 0.60&lt;CT 3 /CT 2 &lt;1.5. Moreover, the following condition can also be satisfied: 0.80&lt;CT 3 /CT 2 &lt;1.5. 
     When a focal length of the seventh lens element is f 7 , and a focal length of the eighth lens element is f 8 , the following condition can be satisfied: −7.5&lt;f 8 /f 7 &lt;−0.55. Therefore, it is favorable for the refractive power of the seventh and eighth lens elements to collaborate with each other so as to correct aberrations such as spherical aberration. Moreover, the following condition can also be satisfied: −4.0&lt;f 8 /f 7 &lt;−0.60. Moreover, the following condition can also be satisfied: −1.5&lt;f 8 /f 7 &lt;−0.65. 
     When a curvature radius of the object-side surface of the second lens element is R 3 , and a focal length of the photographing optical system is f, the following condition can be satisfied: 0&lt;R 3 /f&lt;2.0. Therefore, it is favorable for adjusting the surface shape and refractive power of the second lens element so as to correct aberrations. Moreover, the following condition can also be satisfied: 0.15&lt;R 3 /f&lt;1.4. Moreover, the following condition can also be satisfied: 0.30&lt;R 3 /f&lt;0.90. 
     When the central thickness of the third lens element is CT 3 , and the central thickness of the fifth lens element is CT 5 , the following condition can be satisfied: 1.0&lt;CT 5 /CT 3 ; or CT 5 /CT 3 &lt;10. Therefore, it is favorable for the third and fifth lens elements to collaborate with each other so as to obtain a balance between the size distribution on the object side and the image side of the photographing optical system. Moreover, the following condition can also be satisfied: 1.5&lt;CT 5 /CT 3 . Moreover, the following condition can also be satisfied: 1.8&lt;CT 5 /CT 3 . Moreover, the following condition can also be satisfied: 2.0&lt;CT 5 /CT 3 . Moreover, the following condition can also be satisfied: 2.2&lt;CT 5 /CT 3 . Moreover, the following condition can also be satisfied: CT 5 /CT 3 &lt;5.0. Moreover, the following condition can also be satisfied: CT 5 /CT 3 &lt;4.5. Moreover, the following condition can also be satisfied: 1.0&lt;CT 5 /CT 3 &lt;5.0. Moreover, the following condition can also be satisfied: 2.0&lt;CT 5 /CT 3 &lt;5.0. 
     When the Abbe number of the second lens element is V 2 , an Abbe number of the third lens element is V 3 , and an Abbe number of the fourth lens element is V 4 , the following condition can be satisfied: 30.0&lt;V 2 +V 3 +V 4 &lt;120.0. Therefore, it is favorable for the second, third, and fourth lens elements to collaborate with one another so as to further correct chromatic aberration. Moreover, the following condition can also be satisfied: 35.0&lt;V 2 +V 3 +V 4 &lt;110.0. Moreover, the following condition can also be satisfied: 40.0&lt;V 2 +V 3 +V 4 &lt;100.0. 
     When an Abbe number of the first lens element is V 1 , the Abbe number of the second lens element is V 2 , the Abbe number of the third lens element is V 3 , the Abbe number of the fourth lens element is V 4 , an Abbe number of the fifth lens element is V 5 , an Abbe number of the sixth lens element is V 6 , an Abbe number of the seventh lens element is V 7 , an Abbe number of the eighth lens element is V 8 , an Abbe number of the i-th lens element is Vi, a refractive index of the first lens element is N 1 , a refractive index of the second lens element is N 2 , a refractive index of the third lens element is N 3 , a refractive index of the fourth lens element is N 4 , a refractive index of the fifth lens element is N 5 , a refractive index of the sixth lens element is N 6 , a refractive index of the seventh lens element is N 7 , a refractive index of the eighth lens element is N 8 , a refractive index of the i-th lens element is Ni, and a minimum value of Vi/Ni is (Vi/Ni)min, the following condition can be satisfied: 6.0&lt;(Vi/Ni)min&lt;12.0, wherein i=1, 2, 3, 4, 5, 6, 7 or 8. Therefore, it is favorable for adjusting the material distribution of the photographing optical system so as to correct aberrations and reduce the system size. 
     When a curvature radius of the object-side surface of the fifth lens element is R 9 , and a curvature radius of the image-side surface of the fifth lens element is R 10 , the following condition can be satisfied: −1.5&lt;(R 9 +R 10 )/(R 9 −R 10 )&lt;1.5. Therefore, it is favorable for adjusting the surface shape of the fifth lens element so as to control the travelling direction of light, thereby obtaining a balance among the field of view, system size, and image surface size of the photographing optical system. Moreover, the following condition can also be satisfied: −1.1&lt;(R 9 +R 10 )/(R 9 −R 10 )&lt;1.1. 
     When an axial distance between the object-side surface of the first lens element and the image-side surface of the eighth lens element is TD, and the central thickness of the fifth lens element is CTS, the following condition can be satisfied: 3.0&lt;TD/CT 5 &lt;7.0. Therefore, it is favorable for adjusting the lens elements distribution so as to reduce the total track length of the photographing optical system. 
     When the focal length of the photographing optical system is f, a focal length of the second lens element is f 2 , and a focal length of the third lens element is f 3 , the following condition can be satisfied: |f/f 2 |+|f/f 3 |&lt;0.70. Therefore, it is favorable for the refractive power of the second and third lens elements to collaborate with each other so as to correct aberrations. 
     When the focal length of the photographing optical system is f, and a composite focal length of the first lens element and the second lens element is f 12 , the following condition can be satisfied: 0.35&lt;f/f 12 &lt;0.75. Therefore, it is favorable for the first and second lens elements to collaborate with each other so as to reduce the size on the object side of the photographing optical system. 
     When half of a maximum field of view of the photographing optical system is HFOV, the following condition can be satisfied: 30.0 [deg.]&lt;HFOV&lt;50.0 [deg.]. Therefore, it is favorable for the photographing optical system to feature wide field of view and for preventing distortion generated due to overly wide field of view. Moreover, the following condition can also be satisfied: 35.0 [deg.]&lt;HFOV&lt;45.0 [deg.]. 
     When the Abbe number of the second lens element is V 2 , and the refractive index of the second lens element is N 2 , the following condition can be satisfied: 6.0&lt;V 2 /N 2 &lt;15.0. Therefore, it is favorable for adjusting the material of the second lens element so as to correct aberrations such as chromatic aberration. 
     When the Abbe number of the sixth lens element is V 6 , the following condition can be satisfied: 15.0&lt;V 6 &lt;50.0. Therefore, it is favorable for adjusting the material of the sixth lens element so as to correct chromatic aberration. 
     When a central thickness of the first lens element is CT 1 , and the central thickness of the fifth lens element is CTS, the following condition can be satisfied: 1.1&lt;CT 5 /CT 1 &lt;2.0. Therefore, it is favorable for adjusting the lens elements distribution so as to reduce the system size. Moreover, the following condition can also be satisfied: 1.2&lt;CT 5 /CT 1 &lt;1.8. 
     When the axial distance between the object-side surface of the first lens element and the image-side surface of the eighth lens element is TD, and the focal length of the second lens element is f 2 , the following condition can be satisfied: −1.0&lt;TD/f 2 &lt;0.80. Therefore, it is favorable for adjusting the lens elements and the refractive power distribution so as to reduce the system size and correct aberrations. Moreover, the following condition can also be satisfied: −0.60&lt;TD/f 2 &lt;0.60. 
     When the focal length of the photographing optical system is f, the focal length of the second lens element is f 2 , the focal length of the third lens element is f 3 , and a focal length of the fourth lens element is f 4 , the following condition can be satisfied: −0.90&lt;f/f 2 +f/f 3 +f/f 4 &lt;0.20. Therefore, it is favorable for the refractive power of the second, third, and fourth lens elements to collaborate with one another so as to correct aberrations. 
     When the focal length of the fifth lens element is f 5 , and the central thickness of the fifth lens element is CT 5 , the following condition can be satisfied: 1.0&lt;f 5 /CT 5 &lt;30. Therefore, it is favorable for adjusting the refractive power of the fifth lens element so as to reduce the size of the photographing optical system. Moreover, the following condition can also be satisfied: 2.0&lt;f 5 /CT 5 &lt;20. Moreover, the following condition can also be satisfied: 3.0&lt;f 5 /CT 5 &lt;10. 
     When an f-number of the photographing optical system is Fno, the following condition can be satisfied: 1.0&lt;Fno&lt;2.2. Therefore, it is favorable for obtaining a balance between the aperture stop size and the depth of field. Moreover, the following condition can also be satisfied: 1.2&lt;Fno&lt;1.8. 
     When a maximum effective radius of the object-side surface of the first lens element is Y 11 , and the maximum effective radius of the image-side surface of the eighth lens element is Y 82 , the following condition can be satisfied: 1.8&lt;Y 82 /Y 11 &lt;3.0. Therefore, it is favorable for adjusting the outer diameters on the object and image sides of the photographing optical system so as to obtain a balance among the field of view, system size, and image surface size of the photographing optical system. Please refer to  FIG. 25 , which shows a schematic view of Y 11  and Y 82  according to the 1st embodiment of the present disclosure. 
     When a curvature radius of the object-side surface of the first lens element is R 1 , and a curvature radius of the image-side surface of the first lens element is R 2 , the following condition can be satisfied: −0.60&lt;R 1 /R 2 &lt;0.80. Therefore, it is favorable for adjusting the surface shape of the first lens element so as to adjust the travelling direction of light to provide a wide field of view configuration. Moreover, the following condition can also be satisfied: −0.30&lt;R 1 /R 2 &lt;0.70. 
     When the focal length of the photographing optical system is f, a curvature radius of the object-side surface of the sixth lens element is R 11 , and a curvature radius of the image-side surface of the sixth lens element is R 12 , the following condition can be satisfied: 2.5&lt;f/|R 11 |+f/|R 12 |&lt;7.5. Therefore, it is favorable for adjusting the surface shape and refractive power of the sixth lens element so as to correct aberrations when collaborating with the fifth lens element. 
     When the Abbe number of the second lens element is V 2 , and the Abbe number of the fourth lens element is V 4 , the following condition can be satisfied: 20.0&lt;V 2 +V 4 &lt;65.0. Therefore, it is favorable for the material of the second and fourth lens elements to collaborate with each other so as to further correct chromatic aberration. Moreover, the following condition can also be satisfied: 25.0&lt;V 2 +V 4 &lt;50.0. 
     When the central thickness of the first lens element is CT 1 , the central thickness of the second lens element is CT 2 , the central thickness of the third lens element is CT 3 , a central thickness of the fourth lens element is CT 4 , and the central thickness of the fifth lens element is CTS, the following condition can be satisfied: 0.10&lt;(CT 2 +CT 3 +CT 4 )/(CT 1 +CT 5 )&lt;1.0. Therefore, it is favorable for adjusting the lens elements distribution so as to reduce the size of the photographing optical system. Moreover, the following condition can also be satisfied: 0.20&lt;(CT 2 +CT 3 +CT 4 )/(CT 1 +CT 5 )&lt;0.75. 
     When a sum of central thicknesses of all lens elements of the photographing optical system is ΣCT, and the central thickness of the fifth lens element is CT 5 , the following condition can be satisfied: 2.5&lt;ΣCT/CT 5 &lt;6.0. Therefore, it is favorable for adjusting the lens elements distribution so as to reduce the size of the photographing optical system and provide a wide field of view configuration. Moreover, the following condition can also be satisfied: 3.0&lt;ΣCT/CT 5 &lt;5.0. 
     When an axial distance between the object-side surface of the first lens element and the image surface is TL, the following condition can be satisfied: 3.0 [mm]&lt;TL&lt;15.0 [mm]. Therefore, it is favorable for the photographing optical system to have a proper length for various applications. 
     When the axial distance between the object-side surface of the first lens element and the image surface is TL, and the focal length of the photographing optical system is f, the following condition can be satisfied: 1.0&lt;TL/f&lt;1.6. Therefore, it is favorable for obtaining a balance between the field of view and total track length. 
     When the axial distance between the object-side surface of the first lens element and the image surface is TL, and a maximum image height of the photographing optical system (half of a diagonal length of an effective photosensitive area of the image sensor) is ImgH, the following condition can be satisfied: 1.0&lt;TL/ImgH&lt;2.0. Therefore, it is favorable for obtaining a balance between the total track length and image surface size. 
     When the focal length of the photographing optical system is f, the focal length of the first lens element is f 1 , the focal length of the second lens element is f 2 , the focal length of the third lens element is f 3 , the focal length of the fourth lens element is f 4 , the focal length of the fifth lens element is f 5 , a focal length of the sixth lens element is f 6 , the focal length of the seventh lens element is f 7 , and the focal length of the eighth lens element is f 8 , at least one of the following conditions can be satisfied: 0.20&lt;f/f 1 &lt;1.0; −1.2&lt;f/f 2 &lt;1.2; −0.40&lt;f/f 3 &lt;0.40; −1.0&lt;f/f 4 &lt;1.0; 0.20&lt;f/f 5 &lt;1.0; −1.2&lt;f/f 6 &lt;1.0; 0&lt;f/f 7 &lt;2.0; and −2.0&lt;f/f 8 &lt;0. Therefore, it is favorable for adjusting the refractive power of the lens elements so as to correct aberrations, reduce the system size, and adjust field of view. Moreover, at least one of the following conditions can also be satisfied: 0.30&lt;f/f 1 &lt;0.90; −0.40&lt;f/f 2 &lt;0.40; −0.30&lt;f/f 3 &lt;0.30; −0.80 &lt;f/f 4 &lt;0.40; 0.35&lt;f/f 5 &lt;0.90; −1.0&lt;f/f 6 &lt;0.50; 0.20&lt;f/f 7 &lt;1.8; and −1.7&lt;f/f 8 &lt;−0.30. 
     When the focal length of the photographing optical system is f, and a composite focal length of the second lens element and the third lens element is f 23 , the following condition can be satisfied: −0.40&lt;f/f 23 &lt;0.20. Therefore, it is favorable for the second and third lens elements to collaborate with each other so as to correct aberrations. 
     When the curvature radius of the object-side surface of the second lens element is R 3 , and a curvature radius of the image-side surface of the second lens element is R 4 , the following condition can be satisfied: 0.50&lt;R 3 /R 4 &lt;2.0. Therefore, it is favorable for adjusting the surface shape of the second lens element so as to correct aberrations such as astigmatism. Moreover, the following condition can also be satisfied: 0.70&lt;R 3 /R 4 &lt;1.5. 
     According to the present disclosure, the aforementioned features and conditions can be utilized in numerous combinations so as to achieve corresponding effects. 
     According to the present disclosure, the lens elements of the photographing optical system can be made of either glass or plastic material. When the lens elements are made of glass material, the refractive power distribution of the photographing optical system may be more flexible, and the influence on imaging caused by external environment temperature change may be reduced. The glass lens element can either be made by grinding or molding. When the lens elements are made of plastic material, the manufacturing costs can be effectively reduced. Furthermore, surfaces of each lens element can be arranged to be spherical or aspheric, wherein the former reduces manufacturing difficulty, and the latter allows more control variables for eliminating aberrations thereof, the required number of the lens elements can be reduced, and the total track length of the photographing optical system can be effectively shortened. Furthermore, the aspheric surfaces may be formed by plastic injection molding or glass molding. 
     According to the present disclosure, when a lens surface is aspheric, it means that the lens surface has an aspheric shape throughout its optically effective area, or a portion(s) thereof. 
     According to the present disclosure, one or more of the lens elements&#39; material may optionally include an additive which alters the lens elements&#39; transmittance in a specific range of wavelength for a reduction in unwanted stray light or colour deviation. For example, the additive may optionally filter out light in the wavelength range of 600 nm to 800 nm to reduce excessive red light and/or near infrared light; or may optionally filter out light in the wavelength range of 350 nm to 450 nm to reduce excessive blue light and/or near ultraviolet light from interfering the final image. The additive may be homogeneously mixed with a plastic material to be used in manufacturing a mixed-material lens element by injection molding. 
     According to the present disclosure, each of an object-side surface and an image-side surface has a paraxial region and an off-axis region. The paraxial region refers to the region of the surface where light rays travel close to the optical axis, and the off-axis region refers to the region of the surface away from the paraxial region. Particularly, unless otherwise stated, when the lens element has a convex surface, it indicates that the surface is convex in the paraxial region thereof; when the lens element has a concave surface, it indicates that the surface is concave in the paraxial region thereof. Moreover, when a region of refractive power or focus of a lens element is not defined, it indicates that the region of refractive power or focus of the lens element is in the paraxial region thereof. 
     According to the present disclosure, an inflection point is a point on the surface of the lens element at which the surface changes from concave to convex, or vice versa. A critical point is a non-axial point of the lens surface where its tangent is perpendicular to the optical axis. 
     According to the present disclosure, the image surface of the photographing optical system, based on the corresponding image sensor, can be flat or curved, especially a curved surface being concave facing towards the object side of the photographing optical system. 
     According to the present disclosure, an image correction unit, such as a field flattener, can be optionally disposed between the lens element closest to the image side of the photographing optical system and the image surface for correction of aberrations such as field curvature. The optical properties of the image correction unit, such as curvature, thickness, index of refraction, position and surface shape (convex or concave surface with spherical, aspheric, diffractive or Fresnel types), can be adjusted according to the design of the image capturing unit. In general, a preferable image correction unit is, for example, a thin transparent element having a concave object-side surface and a planar image-side surface, and the thin transparent element is disposed near the image surface. 
     According to the present disclosure, the photographing optical system can include at least one stop, such as an aperture stop, a glare stop or a field stop. Said glare stop or said field stop is set for eliminating the stray light and thereby improving image quality thereof. 
     According to the present disclosure, an aperture stop can be configured as a front stop or a middle stop. A front stop disposed between an imaged object and the first lens element can provide a longer distance between an exit pupil of the photographing optical system and the image surface to produce a telecentric effect, and thereby improves the image-sensing efficiency of an image sensor (for example, CCD or CMOS). A middle stop disposed between the first lens element and the image surface is favorable for enlarging the viewing angle of the photographing optical system and thereby provides a wider field of view for the same. 
     According to the present disclosure, the photographing optical system can include an aperture control unit. The aperture control unit may be a mechanical component or a light modulator, which can control the size and shape of the aperture through electricity or electrical signals. The mechanical component can include a movable member, such as a blade assembly or a light baffle. The light modulator can include a shielding element, such as a filter, an electrochromic material or a liquid-crystal layer. The aperture control unit controls the amount of incident light or exposure time to enhance the capability of image quality adjustment. In addition, the aperture control unit can be the aperture stop of the present disclosure, which changes the f-number to obtain different image effects, such as the depth of field or lens speed. 
     According to the above description of the present disclosure, the following specific embodiments are provided for further explanation. 
     1st Embodiment 
       FIG. 1  is a schematic view of an image capturing unit according to the 1st embodiment of the present disclosure.  FIG. 2  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 1st embodiment. In  FIG. 1 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  199 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  100 , a first lens element  110 , a second lens element  120 , a third lens element  130 , a stop  101 , a fourth lens element  140 , a fifth lens element  150 , a sixth lens element  160 , a seventh lens element  170 , an eighth lens element  180 , a filter  190  and an image surface  195 . The photographing optical system includes eight lens elements ( 110 ,  120 ,  130 ,  140 ,  150 ,  160 ,  170  and  180 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  110  with positive refractive power has an object-side surface  111  being convex in a paraxial region thereof and an image-side surface  112  being concave in a paraxial region thereof. The first lens element  110  is made of plastic material and has the object-side surface  111  and the image-side surface  112  being both aspheric. The image-side surface  112  of the first lens element  110  has two inflection points. 
     The second lens element  120  with positive refractive power has an object-side surface  121  being convex in a paraxial region thereof and an image-side surface  122  being concave in a paraxial region thereof. The second lens element  120  is made of plastic material and has the object-side surface  121  and the image-side surface  122  being both aspheric. The object-side surface  121  of the second lens element  120  has two inflection points. The image-side surface  122  of the second lens element  120  has one inflection point. 
     The third lens element  130  with negative refractive power has an object-side surface  131  being convex in a paraxial region thereof and an image-side surface  132  being concave in a paraxial region thereof. The third lens element  130  is made of plastic material and has the object-side surface  131  and the image-side surface  132  being both aspheric. The object-side surface  131  of the third lens element  130  has one inflection point. The image-side surface  132  of the third lens element  130  has one inflection point. The object-side surface  131  of the third lens element  130  has one critical point in an off-axis region thereof. The image-side surface  132  of the third lens element  130  has one critical point in an off-axis region thereof. 
     The fourth lens element  140  with positive refractive power has an object-side surface  141  being convex in a paraxial region thereof and an image-side surface  142  being concave in a paraxial region thereof. The fourth lens element  140  is made of plastic material and has the object-side surface  141  and the image-side surface  142  being both aspheric. The object-side surface  141  of the fourth lens element  140  has one inflection point. The image-side surface  142  of the fourth lens element  140  has one inflection point. The object-side surface  141  of the fourth lens element  140  has one critical point in an off-axis region thereof. The image-side surface  142  of the fourth lens element  140  has one critical point in an off-axis region thereof. 
     The fifth lens element  150  with positive refractive power has an object-side surface  151  being concave in a paraxial region thereof and an image-side surface  152  being convex in a paraxial region thereof. The fifth lens element  150  is made of plastic material and has the object-side surface  151  and the image-side surface  152  being both aspheric. The object-side surface  151  of the fifth lens element  150  has one inflection point. The image-side surface  152  of the fifth lens element  150  has one inflection point. 
     The sixth lens element  160  with negative refractive power has an object-side surface  161  being concave in a paraxial region thereof and an image-side surface  162  being convex in a paraxial region thereof. The sixth lens element  160  is made of plastic material and has the object-side surface  161  and the image-side surface  162  being both aspheric. The object-side surface  161  of the sixth lens element  160  has two inflection points. The image-side surface  162  of the sixth lens element  160  has two inflection points. The image-side surface  162  of the sixth lens element  160  has one critical point in an off-axis region thereof. 
     The seventh lens element  170  with positive refractive power has an object-side surface  171  being convex in a paraxial region thereof and an image-side surface  172  being concave in a paraxial region thereof. The seventh lens element  170  is made of plastic material and has the object-side surface  171  and the image-side surface  172  being both aspheric. The object-side surface  171  of the seventh lens element  170  has two inflection points. The image-side surface  172  of the seventh lens element  170  has one inflection point. The object-side surface  171  of the seventh lens element  170  has one critical point in an off-axis region thereof. The image-side surface  172  of the seventh lens element  170  has one critical point in an off-axis region thereof. 
     The eighth lens element  180  with negative refractive power has an object-side surface  181  being convex in a paraxial region thereof and an image-side surface  182  being concave in a paraxial region thereof. The eighth lens element  180  is made of plastic material and has the object-side surface  181  and the image-side surface  182  being both aspheric. The object-side surface  181  of the eighth lens element  180  has two inflection points. The image-side surface  182  of the eighth lens element  180  has three inflection points. The object-side surface  181  of the eighth lens element  180  has one critical point in an off-axis region thereof. The image-side surface  182  of the eighth lens element  180  has one critical point in an off-axis region thereof. 
     The filter  190  is made of glass material and located between the eighth lens element  180  and the image surface  195 , and will not affect the focal length of the photographing optical system. The image sensor  199  is disposed on or near the image surface  195  of the photographing optical system. 
     The equation of the aspheric surface profiles of the aforementioned lens elements of the 1st embodiment is expressed as follows: 
     
       
         
           
             
               
                 X 
                 ⁡ 
                 
                   ( 
                   Y 
                   ) 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         Y 
                         2 
                       
                       / 
                       R 
                     
                     ) 
                   
                   / 
                   
                     ( 
                     
                       1 
                       + 
                       
                         s 
                         ⁢ 
                         q 
                         ⁢ 
                         r 
                         ⁢ 
                         
                           t 
                           ⁡ 
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                                 × 
                                 
                                   
                                     ( 
                                     
                                       Y 
                                       / 
                                       R 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                 
                 + 
                 
                   
                     ∑ 
                     i 
                   
                   ⁢ 
                   
                     
                       ( 
                       Ai 
                       ) 
                     
                     × 
                     
                       ( 
                       
                         Y 
                         i 
                       
                       ) 
                     
                   
                 
               
             
             , 
           
         
       
     
     where, 
     X is a displacement in parallel with an optical axis from an axial vertex on the aspheric surface to a point at a distance of Y from the optical axis on the aspheric surface; 
     Y is a vertical distance from the point on the aspheric surface to the optical axis; 
     R is the curvature radius; 
     k is the conic coefficient; and 
     Ai is the i-th aspheric coefficient, and in the embodiments, i may be, but is not limited to, 4, 6, 8, 10, 12, 14, 16, 18 and 20. 
     In the photographing optical system of the image capturing unit according to the 1st embodiment, when a focal length of the photographing optical system is f, an f-number of the photographing optical system is Fno, and half of a maximum field of view of the photographing optical system is HFOV, these parameters have the following values: f=5.69 millimeters (mm), Fno=1.51, HFOV=39.4 degrees (deg.). 
     When an Abbe number of the first lens element  110  is V 1 , an Abbe number of the second lens element  120  is V 2 , an Abbe number of the third lens element  130  is V 3 , an Abbe number of the fourth lens element  140  is V 4 , an Abbe number of the fifth lens element  150  is V 5 , an Abbe number of the sixth lens element  160  is V 6 , an Abbe number of the seventh lens element  170  is V 7 , an Abbe number of the eighth lens element  180  is V 8 , an Abbe number of the i-th lens element is Vi, a refractive index of the first lens element  110  is N 1 , a refractive index of the second lens element  120  is N 2 , a refractive index of the third lens element  130  is N 3 , a refractive index of the fourth lens element  140  is N 4 , a refractive index of the fifth lens element  150  is N 5 , a refractive index of the sixth lens element  160  is N 6 , a refractive index of the seventh lens element  170  is N 7 , a refractive index of the eighth lens element  180  is N 8 , a refractive index of the i-th lens element is Ni, and a minimum value of Vi/Ni is (Vi/Ni)min, the following condition is satisfied: (Vi/Ni)min=10.90. In this embodiment, (Vi/Ni)min is equal to V 3 /N 3 , V 4 /N 4  and V 6 /N 6 . 
     When the Abbe number of the second lens element  120  is V 2 , the following condition is satisfied: V 2 =20.4. 
     When the Abbe number of the second lens element  120  is V 2 , the Abbe number of the third lens element  130  is V 3 , and the Abbe number of the fourth lens element  140  is V 4 , the following condition is satisfied: V 2 +V 3 +V 4 =57.2. 
     When the Abbe number of the second lens element  120  is V 2 , and the Abbe number of the fourth lens element  140  is V 4 , the following condition is satisfied: V 2 +V 4 =38.8. 
     When the Abbe number of the second lens element  120  is V 2 , and the refractive index of the second lens element  120  is N 2 , the following condition is satisfied: V 2 /N 2 =12.29. 
     When the Abbe number of the sixth lens element  160  is V 6 , the following condition is satisfied: V 6 =18.4. 
     When a sum of central thicknesses of all lens elements of the photographing optical system is ΣCT, and a central thickness of the fifth lens element  150  is CTS, the following condition is satisfied: ΣCT/CT 5 =3.56. In this embodiment, ΣCT is a sum of central thicknesses of the first lens element  110 , the second lens element  120 , the third lens element  130 , the fourth lens element  140 , the fifth lens element  150 , the sixth lens element  160 , the seventh lens element  170  and the eighth lens element  180 . 
     When the central thickness of the first lens element  110  is CT 1 , the central thickness of the second lens element  120  is CT 2 , the central thickness of the third lens element  130  is CT 3 , the central thickness of the fourth lens element  140  is CT 4 , and the central thickness of the fifth lens element  150  is CT 5 , the following condition is satisfied: (CT 2 +CT 3 +CT 4 )/(CT 1 +CT 5 )=0.41. 
     When the central thickness of the second lens element  120  is CT 2 , and the central thickness of the third lens element  130  is CT 3 , the following condition is satisfied: CT 3 /CT 2 =1.00. 
     When the central thickness of the first lens element  110  is CT 1 , and the central thickness of the fifth lens element  150  is CT 5 , the following condition is satisfied: CT 5 /CT 1 =1.50. 
     When the central thickness of the third lens element  130  is CT 3 , and the central thickness of the fifth lens element  150  is CT 5 , the following condition is satisfied: CT 5 /CT 3 =4.25. 
     When the central thickness of the fifth lens element  150  is CT 5 , and the central thickness of the seventh lens element  170  is CT 7 , the following condition is satisfied: CT 7 /CT 5 =0.49. 
     When an axial distance between the object-side surface  111  of the first lens element  110  and the image-side surface  182  of the eighth lens element  180  is TD, and the central thickness of the fifth lens element  150  is CT 5 , the following condition is satisfied: TD/CT 5 =5.64. 
     When the axial distance between the object-side surface  111  of the first lens element  110  and the image-side surface  182  of the eighth lens element  180  is TD, and a focal length of the second lens element  120  is f 2 , the following condition is satisfied: TD/f 2 =0.23. 
     When an axial distance between the object-side surface  111  of the first lens element  110  and the image surface  195  is TL, the following condition is satisfied: TL=7.85 [mm]. 
     When the axial distance between the object-side surface  111  of the first lens element  110  and the image surface  195  is TL, and the focal length of the photographing optical system is f, the following condition is satisfied: TL/f=1.38. 
     When the axial distance between the object-side surface  111  of the first lens element  110  and the image surface  195  is TL, and a maximum image height of the photographing optical system is ImgH, the following condition is satisfied: TL/ImgH=1.64. 
     When a curvature radius of the object-side surface  111  of the first lens element  110  is R 1 , and a curvature radius of the image-side surface  112  of the first lens element  110  is R 2 , the following condition is satisfied: R 1 /R 2 =0.55. 
     When a curvature radius of the object-side surface  121  of the second lens element  120  is R 3 , and the focal length of the photographing optical system is f, the following condition is satisfied: R 3 /f=0.47. 
     When the curvature radius of the object-side surface  121  of the second lens element  120  is R 3 , and a curvature radius of the image-side surface  122  of the second lens element  120  is R 4 , the following condition is satisfied: R 3 /R 4 =0.90. 
     When a curvature radius of the object-side surface  151  of the fifth lens element  150  is R 9 , and a curvature radius of the image-side surface  152  of the fifth lens element  150  is R 10 , the following condition is satisfied: (R 9 +R 10 )/(R 9 −R 10 )=1.03. 
     When the focal length of the photographing optical system is f, and a focal length of the first lens element  110  is f 1 , the following condition is satisfied: f/f 1 =0.42. 
     When the focal length of the photographing optical system is f, and the focal length of the first lens element  120  is f 2 , the following condition is satisfied: f/f 2 =0.20. 
     When the focal length of the photographing optical system is f, the focal length of the second lens element  120  is f 2 , and a focal length of the third lens element  130  is f 3 , the following condition is satisfied: |f/f 2 |+|f/f 3 |=0.40. 
     When the focal length of the photographing optical system is f, the focal length of the second lens element  120  is f 2 , the focal length of the third lens element  130  is f 3 , and a focal length of the fourth lens element  140  is f 4 , the following condition is satisfied: f/f 2 +f/f 3 +f/f 4 =0.02. 
     When the focal length of the photographing optical system is f, and the focal length of the third lens element  130  is f 3 , the following condition is satisfied: f/f 3 =−0.20. 
     When the focal length of the photographing optical system is f, and the focal length of the fourth lens element  140  is f 4 , the following condition is satisfied: f/f 4 =0.02. 
     When the focal length of the photographing optical system is f, and a focal length of the fifth lens element  150  is f 5 , the following condition is satisfied: f/f 5 =0.73. 
     When the focal length of the photographing optical system is f, and a focal length of the sixth lens element  160  is f 6 , the following condition is satisfied: f/f 6 =−0.27. 
     When the focal length of the photographing optical system is f, and a focal length of the seventh lens element  170  is f 7 , the following condition is satisfied: f/f 7 =0.48. 
     When the focal length of the photographing optical system is f, and a focal length of the eighth lens element  180  is f 8 , the following condition is satisfied: f/f 8 =−0.66. 
     When the focal length of the photographing optical system is f, and a composite focal length of the first lens element  110  and the second lens element  120  is f 12 , the following condition is satisfied: f/f 12 =0.62. 
     When the focal length of the photographing optical system is f, and a composite focal length of the second lens element  120  and the third lens element  130  is f 23 , the following condition is satisfied: f/f 23 =0.02. 
     When the focal length of the photographing optical system is f, a curvature radius of the object-side surface  161  of the sixth lens element  160  is R 11 , and a curvature radius of the image-side surface  162  of the sixth lens element  160  is R 12 , the following condition is satisfied: f/|R 11 |+f/|R 12 |=5.69. 
     When the focal length of the fifth lens element  150  is f 5 , and the central thickness of the fifth lens element  150  is CT 5 , the following condition is satisfied: f 5 /CT 5 =6.84. 
     When the focal length of the first lens element  110  is f 1 , and the focal length of the fifth lens element  150  is f 5 , the following condition is satisfied: f 5 /f 1 =0.58. 
     When the focal length of the seventh lens element  170  is f 7 , and the focal length of the eighth lens element  180  is f 8 , the following condition is satisfied: f 8 /f 7 =−0.73. 
     When a maximum effective radius of the object-side surface  111  of the first lens element  110  is Y 11 , and a maximum effective radius of the image-side surface  182  of the eighth lens element  180  is Y 82 , the following condition is satisfied: Y 82 /Y 11 =2.12. 
     When a vertical distance between the critical point on the object-side surface  171  of the seventh lens element  170  and the optical axis is Yc 71 , and a vertical distance between the critical point on the image-side surface  172  of the seventh lens element  170  and the optical axis is Yc 72 , the following condition is satisfied: Yc 72 /Yc 71 =1.24. 
     When a vertical distance between the critical point on the image-side surface  182  of the eighth lens element  180  and the optical axis is Yc 82 , and the maximum effective radius of the image-side surface  182  of the eighth lens element  180  is Y 82 , the following condition is satisfied: Yc 82 /Y 82 =0.42. 
     The detailed optical data of the 1st embodiment are shown in Table 1 and the aspheric surface data are shown in Table 2 below. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 1st Embodiment 
               
               
                 f = 5.69 mm, Fno = 1.51, HFOV = 39.4 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.538  
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 3.600 
                 (ASP) 
                 0.763 
                 Plastic 
                 1.545 
                 56.1 
                 13.42 
               
               
                 3 
                   
                 6.560 
                 (ASP) 
                 0.021 
               
               
                 4 
                 Lens 2 
                 2.661 
                 (ASP) 
                 0.269 
                 Plastic 
                 1.660 
                 20.4 
                 28.68 
               
               
                 5 
                   
                 2.972 
                 (ASP) 
                 0.493 
               
               
                 6 
                 Lens 3 
                 7.188 
                 (ASP) 
                 0.270 
                 Plastic 
                 1.686 
                 18.4 
                 −28.78 
               
               
                 7 
                   
                 5.189 
                 (ASP) 
                 0.054 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 8 
                 Stop 
                 Plano 
                 0.181 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 9 
                 Lens 4 
                 7.478 
                 (ASP) 
                 0.247 
                 Plastic 
                 1.686 
                 18.4 
                 319.11 
               
               
                 10 
                   
                 7.639 
                 (ASP) 
                 0.189 
               
               
                 11 
                 Lens 5 
                 −263.852 
                 (ASP) 
                 1.148 
                 Plastic 
                 1.544 
                 56.0 
                 7.85 
               
               
                 12 
                   
                 −4.210 
                 (ASP) 
                 0.344 
               
               
                 13 
                 Lens 6 
                 −1.812 
                 (ASP) 
                 0.352 
                 Plastic 
                 1.686 
                 18.4 
                 −20.88 
               
               
                 14 
                   
                 −2.238 
                 (ASP) 
                 0.020 
               
               
                 15 
                 Lens 7 
                 2.013 
                 (ASP) 
                 0.559 
                 Plastic 
                 1.544 
                 56.0 
                 11.87 
               
               
                 16 
                   
                 2.638 
                 (ASP) 
                 1.087 
               
               
                 17 
                 Lens 8 
                 3.611 
                 (ASP) 
                 0.476 
                 Plastic 
                 1.566 
                 37.4 
                 −8.69 
               
               
                 18 
                   
                 1.983 
                 (ASP) 
                 0.600 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 19 
                 Filter 
                 Plano 
                 0.210 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 20 
                   
                 Plano 
                 0.568 
               
               
                 21 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 101 (Surface 8) is 1.690 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 k = 
                 −1.5316E+00 
                 −2.0505E+01 
                 −1.9707E+00 
                 3.7561E−01 
                 −1.7851E+00 
                 −1.1918E+00 
               
               
                 A4 = 
                  5.4169E−03 
                 −7.7415E−02 
                 −5.3318E−02 
                 1.0895E−02 
                 −1.6493E−02 
                 −2.4401E−02 
               
               
                 A6 = 
                  3.8998E−04 
                  6.9237E−02 
                  1.1593E−02 
                 −6.4746E−02  
                 −1.2145E−02 
                 −8.7196E−03 
               
               
                 A8 = 
                 −2.1802E−04 
                 −3.9281E−02 
                  3.8612E−03 
                 5.3696E−02 
                  6.7648E−03 
                  5.7511E−03 
               
               
                 A10 = 
                 −2.9994E−05 
                  1.4653E−02 
                 −4.9672E−03 
                 −2.8295E−02  
                 −4.9306E−03 
                 −4.5213E−03 
               
               
                 A12 = 
                  7.8712E−05 
                 −3.3898E−03 
                  2.2673E−03 
                 9.2818E−03 
                  2.3840E−03 
                  2.8551E−03 
               
               
                 A14 = 
                 −2.6512E−05 
                  4.3082E−04 
                 −5.2284E−04 
                 −1.7469E−03  
                 −6.0868E−04 
                 −8.6126E−04 
               
               
                 A16 = 
                  2.7861E−06 
                 −2.2144E−05 
                  5.0703E−05 
                 1.4354E−04 
                  6.2505E−05 
                  9.5014E−05 
               
               
                   
               
               
                 Surface # 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
               
               
                   
               
               
                 k = 
                 −1.0361E+01 
                 −4.7713E−01 
                 −9.9000E+01 
                 −5.0143E−01 
                 −1.0728E+00 
                 −1.0268E+00 
               
               
                 A4 = 
                 −3.0066E−02 
                 −2.8807E−02 
                 −1.4560E−02 
                 −3.5684E−02 
                  6.2857E−02 
                  3.1129E−02 
               
               
                 A6 = 
                 −3.4948E−03 
                  6.6803E−03 
                  1.3312E−02 
                  8.7087E−03 
                 −6.1731E−02 
                 −3.4892E−02 
               
               
                 A8 = 
                  2.1358E−03 
                 −4.4427E−03 
                 −8.9300E−03 
                  5.6746E−03 
                  5.7559E−02 
                  3.2445E−02 
               
               
                 A10 = 
                 −5.0234E−03 
                  1.1418E−03 
                  5.0014E−03 
                 −6.3903E−03 
                 −3.3452E−02 
                 −1.7643E−02 
               
               
                 A12 = 
                  5.0826E−03 
                  8.0097E−04 
                 −2.0569E−03 
                  2.8278E−03 
                  1.2189E−02 
                  5.9527E−03 
               
               
                 A14 = 
                 −2.1194E−03 
                 −6.7523E−04 
                  3.2985E−04 
                 −7.8636E−04 
                 −2.7249E−03 
                 −1.2147E−03 
               
               
                 A16 = 
                  3.7624E−04 
                  1.6995E−04 
                  3.5672E−05 
                  1.4768E−04 
                  3.5929E−04 
                  1.4537E−04 
               
               
                 A18 = 
                 −2.4028E−05 
                 −1.4523E−05 
                 −1.6208E−05 
                 −1.7067E−05 
                 −2.5386E−05 
                 −9.4402E−06 
               
               
                 A20 = 
                 — 
                 — 
                  1.2987E−06 
                  9.0200E−07 
                  7.2451E−07 
                  2.5865E−07 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface # 
                 15 
                 16 
                 17 
                 18 
               
               
                   
                   
               
               
                   
                 k = 
                 −9.9019E−01 
                 −9.8729E−01 
                 −8.1861E−01 
                 −1.0033E+00 
               
               
                   
                 A4 = 
                 −4.7196E−02 
                 −2.6213E−03 
                 −9.6059E−02 
                 −1.0522E−01 
               
               
                   
                 A6 = 
                  1.3953E−02 
                 −6.3230E−03 
                  1.8905E−02 
                  2.8532E−02 
               
               
                   
                 A8 = 
                 −6.5658E−03 
                  1.1805E−03 
                 −2.1049E−03 
                 −6.3526E−03 
               
               
                   
                 A10 = 
                  2.0216E−03 
                 −1.1298E−04 
                  1.4038E−04 
                  1.0530E−03 
               
               
                   
                 A12 = 
                 −4.4199E−04 
                  8.8467E−06 
                 −4.6316E−06 
                 −1.2285E−04 
               
               
                   
                 A14 = 
                  6.8761E−05 
                 −1.0998E−06 
                 −1.2279E−08 
                  9.5584E−06 
               
               
                   
                 A16 = 
                 −7.1569E−06 
                  1.2458E−07 
                  4.6079E−09 
                 −4.6428E−07 
               
               
                   
                 A18 = 
                  4.3612E−07 
                 −7.5401E−09 
                 −8.4513E−12 
                  1.2622E−08 
               
               
                   
                 A20 = 
                 −1.1450E−08 
                  1.7866E−10 
                 −3.0769E−12 
                 −1.4603E−10 
               
               
                   
                   
               
            
           
         
       
     
     In Table 1, the curvature radius, the thickness and the focal length are shown in millimeters (mm). Surface numbers 0-21 represent the surfaces sequentially arranged from the object side to the image side along the optical axis. In Table 2, k represents the conic coefficient of the equation of the aspheric surface profiles. A4-20 represent the aspheric coefficients ranging from the 4th order to the 20th order. The tables presented below for each embodiment are the corresponding schematic parameter and aberration curves, and the definitions of the tables are the same as Table 1 and Table 2 of the 1st embodiment. Therefore, an explanation in this regard will not be provided again. 
     2nd Embodiment 
       FIG. 3  is a schematic view of an image capturing unit according to the 2nd embodiment of the present disclosure.  FIG. 4  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 2nd embodiment. In  FIG. 3 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  299 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  200 , a first lens element  210 , a second lens element  220 , a stop  201 , a third lens element  230 , a stop  202 , a fourth lens element  240 , a fifth lens element  250 , a sixth lens element  260 , a seventh lens element  270 , an eighth lens element  280 , a filter  290  and an image surface  295 . The photographing optical system includes eight lens elements ( 210 ,  220 ,  230 ,  240 ,  250 ,  260 ,  270  and  280 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  210  with positive refractive power has an object-side surface  211  being convex in a paraxial region thereof and an image-side surface  212  being convex in a paraxial region thereof. The first lens element  210  is made of plastic material and has the object-side surface  211  and the image-side surface  212  being both aspheric. The image-side surface  212  of the first lens element  210  has three inflection points. The image-side surface  212  of the first lens element  210  has one critical point in an off-axis region thereof. 
     The second lens element  220  with negative refractive power has an object-side surface  221  being convex in a paraxial region thereof and an image-side surface  222  being concave in a paraxial region thereof. The second lens element  220  is made of plastic material and has the object-side surface  221  and the image-side surface  222  being both aspheric. The object-side surface  221  of the second lens element  220  has one inflection point. The image-side surface  222  of the second lens element  220  has one inflection point. The object-side surface  221  of the second lens element  220  has one critical point in an off-axis region thereof. 
     The third lens element  230  with positive refractive power has an object-side surface  231  being convex in a paraxial region thereof and an image-side surface  232  being concave in a paraxial region thereof. The third lens element  230  is made of plastic material and has the object-side surface  231  and the image-side surface  232  being both aspheric. The object-side surface  231  of the third lens element  230  has two inflection points. The image-side surface  232  of the third lens element  230  has two inflection points. 
     The fourth lens element  240  with positive refractive power has an object-side surface  241  being convex in a paraxial region thereof and an image-side surface  242  being concave in a paraxial region thereof. The fourth lens element  240  is made of plastic material and has the object-side surface  241  and the image-side surface  242  being both aspheric. The object-side surface  241  of the fourth lens element  240  has one inflection point. The image-side surface  242  of the fourth lens element  240  has one inflection point. The object-side surface  241  of the fourth lens element  240  has one critical point in an off-axis region thereof. The image-side surface  242  of the fourth lens element  240  has one critical point in an off-axis region thereof. 
     The fifth lens element  250  with positive refractive power has an object-side surface  251  being concave in a paraxial region thereof and an image-side surface  252  being convex in a paraxial region thereof. The fifth lens element  250  is made of plastic material and has the object-side surface  251  and the image-side surface  252  being both aspheric. The object-side surface  251  of the fifth lens element  250  has one inflection point. The image-side surface  252  of the fifth lens element  250  has one inflection point. 
     The sixth lens element  260  with negative refractive power has an object-side surface  261  being concave in a paraxial region thereof and an image-side surface  262  being convex in a paraxial region thereof. The sixth lens element  260  is made of plastic material and has the object-side surface  261  and the image-side surface  262  being both aspheric. The object-side surface  261  of the sixth lens element  260  has two inflection points. The image-side surface  262  of the sixth lens element  260  has two inflection points. The image-side surface  262  of the sixth lens element  260  has one critical point in an off-axis region thereof. 
     The seventh lens element  270  with positive refractive power has an object-side surface  271  being convex in a paraxial region thereof and an image-side surface  272  being concave in a paraxial region thereof. The seventh lens element  270  is made of plastic material and has the object-side surface  271  and the image-side surface  272  being both aspheric. The object-side surface  271  of the seventh lens element  270  has two inflection points. The image-side surface  272  of the seventh lens element  270  has four inflection points. The object-side surface  271  of the seventh lens element  270  has one critical point in an off-axis region thereof. The image-side surface  272  of the seventh lens element  270  has one critical point in an off-axis region thereof. 
     The eighth lens element  280  with negative refractive power has an object-side surface  281  being convex in a paraxial region thereof and an image-side surface  282  being concave in a paraxial region thereof. The eighth lens element  280  is made of plastic material and has the object-side surface  281  and the image-side surface  282  being both aspheric. The object-side surface  281  of the eighth lens element  280  has three inflection points. The image-side surface  282  of the eighth lens element  280  has one inflection point. The object-side surface  281  of the eighth lens element  280  has two critical points in an off-axis region thereof. The image-side surface  282  of the eighth lens element  280  has one critical point in an off-axis region thereof. 
     The filter  290  is made of glass material and located between the eighth lens element  280  and the image surface  295 , and will not affect the focal length of the photographing optical system. The image sensor  299  is disposed on or near the image surface  295  of the photographing optical system. 
     The detailed optical data of the 2nd embodiment are shown in Table 3 and the aspheric surface data are shown in Table 4 below. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 2nd Embodiment 
               
               
                 f = 7.51 mm, Fno = 1.40, HFOV = 39.0 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.742 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 5.317 
                 (ASP) 
                 1.181 
                 Plastic 
                 1.545 
                 56.1 
                 9.58 
               
               
                 3 
                   
                 −260.138 
                 (ASP) 
                 0.015 
               
               
                 4 
                 Lens 2 
                 4.142 
                 (ASP) 
                 0.386 
                 Plastic 
                 1.701 
                 14.8 
                 −20.05 
               
               
                 5 
                   
                 3.076 
                 (ASP) 
                 0.671 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 6 
                 Stop 
                 Plano 
                 −0.181 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 Lens 3 
                 7.553 
                 (ASP) 
                 0.547 
                 Plastic 
                 1.679 
                 18.4 
                 146.33 
               
               
                 8 
                   
                 7.935 
                 (ASP) 
                 0.217 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 9 
                 Stop 
                 Plano 
                 0.283 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 10 
                 Lens 4 
                 9.151 
                 (ASP) 
                 0.452 
                 Plastic 
                 1.701 
                 14.8 
                 357.82 
               
               
                 11 
                   
                 9.305 
                 (ASP) 
                 0.192 
               
               
                 12 
                 Lens 5 
                 −224.800 
                 (ASP) 
                 1.854 
                 Plastic 
                 1.529 
                 58.1 
                 8.51 
               
               
                 13 
                   
                 −4.428 
                 (ASP) 
                 0.198 
               
               
                 14 
                 Lens 6 
                 −2.477 
                 (ASP) 
                 0.487 
                 Plastic 
                 1.639 
                 23.3 
                 −8.83 
               
               
                 15 
                   
                 −4.756 
                 (ASP) 
                 0.015 
               
               
                 16 
                 Lens 7 
                 2.762 
                 (ASP) 
                 0.920 
                 Plastic 
                 1.582 
                 30.2 
                 8.09 
               
               
                 17 
                   
                 5.862 
                 (ASP) 
                 1.103 
               
               
                 18 
                 Lens 8 
                 6.115 
                 (ASP) 
                 0.742 
                 Plastic 
                 1.562 
                 44.6 
                 −9.21 
               
               
                 19 
                   
                 2.681 
                 (ASP) 
                 1.160 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 20 
                 Filter 
                 Plano 
                 0.145 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 21 
                   
                 Plano 
                 0.393 
               
               
                 22 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 201 (Surface 6) is 2.327 mm. 
               
               
                 active radius of the stop 202 (Surface 9) is 2.197 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                 −4.2387E−01 
                 3.6069E−07 
                 −6.5312E−02 
                 −1.2296E−04 
                 −1.4590E+01 
                 −1.1188E+01 
               
               
                 A4 = 
                  1.1046E−03 
                 1.0617E−02 
                 −7.2459E−03 
                 −2.0747E−02 
                 −4.8566E−03 
                 −1.0705E−02 
               
               
                 A6 = 
                 −5.4784E−05 
                 −7.0047E−03  
                 −1.3240E−03 
                  5.7793E−03 
                  2.3956E−03 
                  9.8640E−04 
               
               
                 A8 = 
                  1.3739E−05 
                 2.8654E−03 
                 −5.2433E−04 
                 −4.2536E−03 
                 −8.2257E−04 
                  1.0677E−03 
               
               
                 A10 = 
                  4.6754E−06 
                 −7.3218E−04  
                  3.3685E−04 
                  1.4547E−03 
                 −2.8540E−05 
                 −9.8270E−04 
               
               
                 A12 = 
                 −1.9760E−06 
                 1.1635E−04 
                 −7.1903E−05 
                 −2.9874E−04 
                  3.8202E−05 
                  3.2282E−04 
               
               
                 A14 = 
                  3.3785E−07 
                 −1.0365E−05  
                  6.6162E−06 
                  3.4337E−05 
                 −3.0007E−06 
                 −4.6687E−05 
               
               
                 A16 = 
                 −1.8923E−08 
                 3.8899E−07 
                 −2.1207E−07 
                 −1.6365E−06 
                 — 
                  2.5835E−06 
               
               
                   
               
               
                 Surface # 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 k = 
                  1.1643E+01 
                  3.2859E−01 
                  9.0000E+01 
                 −5.4352E−01 
                 −9.6866E−01 
                 −6.7041E−01 
               
               
                 A4 = 
                 −1.8441E−02 
                 −1.0217E−02 
                 −2.1875E−03 
                 −1.4989E−02 
                  2.7318E−02 
                  3.7977E−03 
               
               
                 A6 = 
                 −4.8440E−03 
                 −7.6415E−03 
                 −4.3883E−03 
                 −5.1236E−03 
                 −1.4206E−02 
                 −4.3452E−03 
               
               
                 A8 = 
                  4.4350E−03 
                  6.1277E−03 
                  1.9688E−03 
                  6.0111E−03 
                  6.3816E−03 
                  1.7038E−03 
               
               
                 A10 = 
                 −2.2525E−03 
                 −2.6920E−03 
                 −2.7812E−04 
                 −2.4399E−03 
                 −1.7331E−03 
                 −3.2716E−04 
               
               
                 A12 = 
                  5.9516E−04 
                  7.0304E−04 
                 −1.0019E−04 
                  5.8136E−04 
                  2.9189E−04 
                  3.3374E−05 
               
               
                 A14 = 
                 −7.7784E−05 
                 −1.0580E−04 
                  5.0803E−05 
                 −8.9818E−05 
                 −2.9978E−05 
                 −1.0505E−06 
               
               
                 A16 = 
                  3.8510E−06 
                  8.3919E−06 
                 −9.4496E−06 
                  8.8948E−06 
                  1.7909E−06 
                 −9.7746E−08 
               
               
                 A18 = 
                 — 
                 −2.7056E−07 
                  8.4941E−07 
                 −5.1421E−07 
                 −5.5567E−08 
                  9.1429E−09 
               
               
                 A20 = 
                 — 
                 — 
                 −3.0361E−08 
                  1.3215E−08 
                  6.4700E−10 
                 −2.1629E−10 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface # 
                 16 
                 17 
                 18 
                 19 
               
               
                   
                   
               
               
                   
                 k = 
                 −1.0382E+00 
                 −9.4254E−01 
                 −2.6935E+00 
                 −9.1653E−01 
               
               
                   
                 A4 = 
                 −1.2092E−02 
                  3.0652E−02 
                 −3.4492E−02 
                 −4.4028E−02 
               
               
                   
                 A6 = 
                 −7.8531E−04 
                 −1.4098E−02 
                  2.0654E−03 
                  6.0916E−03 
               
               
                   
                 A8 = 
                 −2.4697E−04 
                  2.8759E−03 
                  1.7082E−04 
                 −7.0450E−04 
               
               
                   
                 A10 = 
                  1.4113E−04 
                 −3.7594E−04 
                 −2.9240E−05 
                  6.3487E−05 
               
               
                   
                 A12 = 
                 −2.7389E−05 
                  3.2208E−05 
                  1.7337E−06 
                 −3.9713E−06 
               
               
                   
                 A14 = 
                  2.7069E−06 
                 −1.7693E−06 
                 −5.3907E−08 
                  1.6049E−07 
               
               
                   
                 A16 = 
                 −1.4235E−07 
                  5.9719E−08 
                  8.8210E−10 
                 −3.9595E−09 
               
               
                   
                 A18 = 
                  3.7582E−09 
                 −1.1266E−09 
                 −6.1047E−12 
                  5.4063E−11 
               
               
                   
                 A20 = 
                 −3.8709E−11 
                  9.0964E−12 
                  2.2779E−15 
                 −3.1273E−13 
               
               
                   
                   
               
            
           
         
       
     
     In the 2nd embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 2nd embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 3 and Table 4 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 2nd Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 7.51 
                 R3/R4 
                 1.35 
               
               
                 Fno 
                 1.40 
                 (R9 + R10)/(R9 − R10) 
                 1.04 
               
               
                 HFOV [deg.] 
                 39.0 
                 f/f1 
                 0.78 
               
               
                 (Vi/Ni)min 
                 8.70 
                 f/f2 
                 −0.37 
               
               
                 V2 
                 14.8 
                 |f/f2| + |f/f3| 
                 0.43 
               
               
                 V2 + V3 + V4 
                 48.0 
                 f/f2 + f/f3 + f/f4 
                 −0.30 
               
               
                 V2 + V4 
                 29.6 
                 f/f3 
                 0.05 
               
               
                 V2/N2 
                 8.70 
                 f/f4 
                 0.02 
               
               
                 V6 
                 23.3 
                 f/f5 
                 0.88 
               
               
                 ΣCT/CT5 
                 3.54 
                 f/f6 
                 −0.85 
               
               
                 (CT2 + CT3 + CT4)/ 
                 0.46 
                 f/f7 
                 0.93 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 1.42 
                 f/f8 
                 −0.82 
               
               
                 CT5/CT1 
                 1.57 
                 f/f12 
                 0.48 
               
               
                 CT5/CT3 
                 3.39 
                 f/f23 
                 −0.33 
               
               
                 CT7/CT5 
                 0.50 
                 f/|R11| + f/|R12| 
                 4.61 
               
               
                 TD/CT5 
                 4.90 
                 f5/CT5 
                 4.59 
               
               
                 TD/f2 
                 −0.45 
                 f5/f1 
                 0.89 
               
               
                 TL [mm] 
                 10.78 
                 f8/f7 
                 −1.14 
               
               
                 TL/f 
                 1.43 
                 Y82/Y11 
                 2.01 
               
               
                 TL/ImgH 
                 1.74 
                 Yc72/Yc71 
                 1.13 
               
               
                 R1/R2 
                 −0.02 
                 Yc82/Y82 
                 0.40 
               
               
                 R3/f 
                 0.55 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     3rd Embodiment 
       FIG. 5  is a schematic view of an image capturing unit according to the 3rd embodiment of the present disclosure.  FIG. 6  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 3rd embodiment. In  FIG. 5 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  399 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  300 , a first lens element  310 , a second lens element  320 , a third lens element  330 , a fourth lens element  340 , a fifth lens element  350 , a sixth lens element  360 , a stop  301 , a seventh lens element  370 , an eighth lens element  380 , a filter  390  and an image surface  395 . The photographing optical system includes eight lens elements ( 310 ,  320 ,  330 ,  340 ,  350 ,  360 ,  370  and  380 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  310  with positive refractive power has an object-side surface  311  being convex in a paraxial region thereof and an image-side surface  312  being concave in a paraxial region thereof. The first lens element  310  is made of plastic material and has the object-side surface  311  and the image-side surface  312  being both aspheric. 
     The second lens element  320  with positive refractive power has an object-side surface  321  being convex in a paraxial region thereof and an image-side surface  322  being concave in a paraxial region thereof. The second lens element  320  is made of plastic material and has the object-side surface  321  and the image-side surface  322  being both aspheric. The image-side surface  322  of the second lens element  320  has one inflection point. 
     The third lens element  330  with negative refractive power has an object-side surface  331  being convex in a paraxial region thereof and an image-side surface  332  being concave in a paraxial region thereof. The third lens element  330  is made of plastic material and has the object-side surface  331  and the image-side surface  332  being both aspheric. The object-side surface  331  of the third lens element  330  has one inflection point. The image-side surface  332  of the third lens element  330  has two inflection points. The object-side surface  331  of the third lens element  330  has one critical point in an off-axis region thereof. The image-side surface  332  of the third lens element  330  has two critical points in an off-axis region thereof. 
     The fourth lens element  340  with negative refractive power has an object-side surface  341  being concave in a paraxial region thereof and an image-side surface  342  being convex in a paraxial region thereof. The fourth lens element  340  is made of plastic material and has the object-side surface  341  and the image-side surface  342  being both aspheric. The image-side surface  342  of the fourth lens element  340  has three inflection points. The image-side surface  342  of the fourth lens element  340  has two critical points in an off-axis region thereof. 
     The fifth lens element  350  with positive refractive power has an object-side surface  351  being convex in a paraxial region thereof and an image-side surface  352  being convex in a paraxial region thereof. The fifth lens element  350  is made of glass material and has the object-side surface  351  and the image-side surface  352  being both aspheric. The object-side surface  351  of the fifth lens element  350  has two inflection points. The image-side surface  352  of the fifth lens element  350  has one inflection point. The object-side surface  351  of the fifth lens element  350  has one critical point in an off-axis region thereof. 
     The sixth lens element  360  with positive refractive power has an object-side surface  361  being concave in a paraxial region thereof and an image-side surface  362  being convex in a paraxial region thereof. The sixth lens element  360  is made of plastic material and has the object-side surface  361  and the image-side surface  362  being both aspheric. The object-side surface  361  of the sixth lens element  360  has two inflection points. The image-side surface  362  of the sixth lens element  360  has two inflection points. The image-side surface  362  of the sixth lens element  360  has one critical point in an off-axis region thereof. 
     The seventh lens element  370  with positive refractive power has an object-side surface  371  being convex in a paraxial region thereof and an image-side surface  372  being concave in a paraxial region thereof. The seventh lens element  370  is made of plastic material and has the object-side surface  371  and the image-side surface  372  being both aspheric. The object-side surface  371  of the seventh lens element  370  has three inflection points. The image-side surface  372  of the seventh lens element  370  has one inflection point. The object-side surface  371  of the seventh lens element  370  has one critical point in an off-axis region thereof. The image-side surface  372  of the seventh lens element  370  has one critical point in an off-axis region thereof. 
     The eighth lens element  380  with negative refractive power has an object-side surface  381  being convex in a paraxial region thereof and an image-side surface  382  being concave in a paraxial region thereof. The eighth lens element  380  is made of plastic material and has the object-side surface  381  and the image-side surface  382  being both aspheric. The object-side surface  381  of the eighth lens element  380  has four inflection points. The image-side surface  382  of the eighth lens element  380  has two inflection points. The object-side surface  381  of the eighth lens element  380  has one critical point in an off-axis region thereof. The image-side surface  382  of the eighth lens element  380  has one critical point in an off-axis region thereof. 
     The filter  390  is made of glass material and located between the eighth lens element  380  and the image surface  395 , and will not affect the focal length of the photographing optical system. The image sensor  399  is disposed on or near the image surface  395  of the photographing optical system. 
     The detailed optical data of the 3rd embodiment are shown in Table 5 and the aspheric surface data are shown in Table 6 below. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 3rd Embodiment 
               
               
                 f = 9.54 mm, Fno = 2.00, HFOV = 40.0 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.689 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 4.425 
                 (ASP) 
                 0.932 
                 Plastic 
                 1.545 
                 56.1 
                 14.57 
               
               
                 3 
                   
                 9.250 
                 (ASP) 
                 0.103 
               
               
                 4 
                 Lens 2 
                 4.628 
                 (ASP) 
                 0.316 
                 Plastic 
                 1.660 
                 20.4 
                 540.04 
               
               
                 5 
                   
                 4.562 
                 (ASP) 
                 0.767 
               
               
                 6 
                 Lens 3 
                 13.308 
                 (ASP) 
                 0.353 
                 Plastic 
                 1.686 
                 18.4 
                 −69.80 
               
               
                 7 
                   
                 10.301 
                 (ASP) 
                 0.473 
               
               
                 8 
                 Lens 4 
                 −37.267 
                 (ASP) 
                 0.300 
                 Plastic 
                 1.686 
                 18.4 
                 −81.05 
               
               
                 9 
                   
                 −113.361 
                 (ASP) 
                 0.020 
               
               
                 10 
                 Lens 5 
                 33.431 
                 (ASP) 
                 1.180 
                 Glass 
                 1.522 
                 62.2 
                 19.92 
               
               
                 11 
                   
                 −14.926 
                 (ASP) 
                 0.921 
               
               
                 12 
                 Lens 6 
                 −4.409 
                 (ASP) 
                 0.500 
                 Plastic 
                 1.686 
                 18.4 
                 133.28 
               
               
                 13 
                   
                 −4.400 
                 (ASP) 
                 −0.281 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 14 
                 Stop 
                 Plano 
                 0.301 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 15 
                 Lens 7 
                 3.262 
                 (ASP) 
                 0.683 
                 Plastic 
                 1.562 
                 44.6 
                 24.05 
               
               
                 16 
                   
                 3.976 
                 (ASP) 
                 2.711 
               
               
                 17 
                 Lens 8 
                 15.486 
                 (ASP) 
                 0.600 
                 Plastic 
                 1.582 
                 30.2 
                 −9.46 
               
               
                 18 
                   
                 4.005 
                 (ASP) 
                 1.000 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 19 
                 Filter 
                 Plano 
                 0.170 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 20 
                   
                 Plano 
                 0.458 
               
               
                 21 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 301 (Surface 14) is 4.046 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 k = 
                 −1.2367E+00  
                 −1.6065E+01 
                 −9.2460E−01 
                  3.1206E−01 
                 −4.5855E+01 
                  1.5211E+00 
               
               
                 A4 = 
                 1.7440E−03 
                 −1.5332E−02 
                 −1.8156E−02 
                 −5.2127E−03 
                 −5.4129E−03 
                 −8.4180E−03 
               
               
                 A6 = 
                 4.4393E−05 
                  6.4677E−03 
                  4.5492E−03 
                 −9.7079E−04 
                 −7.5981E−04 
                 −8.6287E−04 
               
               
                 A8 = 
                 2.5039E−05 
                 −1.9054E−03 
                 −9.9599E−04 
                  5.5239E−04 
                  3.0438E−05 
                  3.3014E−04 
               
               
                 A10 = 
                 −1.6161E−05  
                  3.9134E−04 
                  1.6740E−04 
                 −1.7321E−04 
                 −6.6168E−05 
                 −1.8490E−04 
               
               
                 A12 = 
                 4.7207E−06 
                 −5.0477E−05 
                 −1.5303E−05 
                  3.2272E−05 
                  2.0557E−05 
                  5.2671E−05 
               
               
                 A14 = 
                 −6.9892E−07  
                  3.6088E−06 
                  5.6640E−07 
                 −3.3755E−06 
                 −2.3067E−06 
                 −5.9524E−06 
               
               
                 A16 = 
                 4.4634E−08 
                 −9.9422E−08 
                  8.4122E−09 
                  1.4404E−07 
                  9.5954E−08 
                  2.3942E−07 
               
               
                   
               
               
                 Surface # 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
               
               
                   
               
               
                 k = 
                  3.0680E+01 
                 9.0000E+01 
                 −9.9000E+01 
                 5.4086E+00 
                 −7.9118E−01 
                 −1.2475E+00 
               
               
                 A4 = 
                 −1.5592E−03 
                 1.5834E−02 
                  1.9309E−02 
                 −6.4954E−03  
                  1.2804E−02 
                  2.9456E−03 
               
               
                 A6 = 
                 −5.4576E−03 
                 −1.8156E−02  
                 −1.7157E−02 
                 2.9081E−03 
                  6.6261E−04 
                  2.2626E−03 
               
               
                 A8 = 
                  2.5428E−03 
                 7.4926E−03 
                  7.0032E−03 
                 −1.2264E−03  
                 −1.1605E−03 
                 −1.1130E−03 
               
               
                 A10 = 
                 −7.6838E−04 
                 −1.7592E−03  
                 −1.6547E−03 
                 2.6099E−04 
                  3.5409E−04 
                  2.7912E−04 
               
               
                 A12 = 
                  1.5602E−04 
                 2.4631E−04 
                  2.3182E−04 
                 −2.7716E−05  
                 −6.2401E−05 
                 −4.3803E−05 
               
               
                 A14 = 
                 −1.8866E−05 
                 −1.9917E−05  
                 −1.8441E−05 
                 5.7284E−07 
                  7.1689E−06 
                  4.4773E−06 
               
               
                 A16 = 
                  1.1895E−06 
                 8.0428E−07 
                  6.6755E−07 
                 1.8475E−07 
                 −5.1840E−07 
                 −2.8144E−07 
               
               
                 A18 = 
                 −3.0498E−08 
                 −1.0224E−08  
                  2.6690E−09 
                 −1.8792E−08  
                  2.1138E−08 
                  9.6832E−09 
               
               
                 A20 = 
                 — 
                 — 
                 −6.3507E−10 
                 5.7839E−10 
                 −3.7013E−10 
                 −1.3840E−10 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface # 
                 15 
                 16 
                 17 
                 18 
               
               
                   
                   
               
               
                   
                 k = 
                 −1.1200E+00 
                 −1.3169E+00 
                  1.7580E+00 
                 −1.0917E+00 
               
               
                   
                 A4 = 
                 −9.6758E−03 
                  2.0007E−03 
                 −2.5336E−02 
                 −2.6457E−02 
               
               
                   
                 A6 = 
                  8.4460E−04 
                 −2.2602E−03 
                  3.2655E−03 
                  3.5164E−03 
               
               
                   
                 A8 = 
                 −4.2216E−04 
                  3.7777E−04 
                 −3.3965E−04 
                 −3.7128E−04 
               
               
                   
                 A10 = 
                  1.1298E−04 
                 −4.1739E−05 
                  2.6851E−05 
                  2.7761E−05 
               
               
                   
                 A12 = 
                 −1.8414E−05 
                  3.1912E−06 
                 −1.4296E−06 
                 −1.4134E−06 
               
               
                   
                 A14 = 
                  1.8669E−06 
                 −1.6495E−07 
                  4.8282E−08 
                  4.7350E−08 
               
               
                   
                 A16 = 
                 −1.1556E−07 
                  5.4390E−09 
                 −9.8613E−10 
                 −9.9034E−10 
               
               
                   
                 A18 = 
                  3.9714E−09 
                 −1.0229E−10 
                  1.1104E−11 
                  1.1650E−11 
               
               
                   
                 A20 = 
                 −5.7480E−11 
                  8.2950E−13 
                 −5.2956E−14 
                 −5.8565E−14 
               
               
                   
                   
               
            
           
         
       
     
     In the 3rd embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 3rd embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 5 and Table 6 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 3rd Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 9.54 
                 R3/R4 
                 1.01 
               
               
                 Fno 
                 2.00 
                 (R9 + R10)/(R9 − R10) 
                 0.38 
               
               
                 HFOV [deg.] 
                 40.0 
                 f/f1 
                 0.65 
               
               
                 (Vi/Ni)min 
                 10.90 
                 f/f2 
                 0.02 
               
               
                 V2 
                 20.4 
                 |f/f2| + |f/f3| 
                 0.15 
               
               
                 V2 + V3 + V4 
                 57.2 
                 f/f2 + f/f3 + f/f4 
                 −0.24 
               
               
                 V2 + V4 
                 38.8 
                 f/f3 
                 −0.14 
               
               
                 V2/N2 
                 12.29 
                 f/f4 
                 −0.12 
               
               
                 V6 
                 18.4 
                 f/f5 
                 0.48 
               
               
                 ΣCT/CT5 
                 4.12 
                 f/f6 
                 0.07 
               
               
                 (CT2 + CT3 + CT4)/ 
                 0.46 
                 f/f7 
                 0.40 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 1.12 
                 f/f8 
                 −1.01 
               
               
                 CT5/CT1 
                 1.27 
                 f/f12 
                 0.69 
               
               
                 CT5/CT3 
                 3.34 
                 f/f23 
                 −0.11 
               
               
                 CT7/CT5 
                 0.58 
                 f/|R11| + f/|R12| 
                 4.33 
               
               
                 TD/CT5 
                 8.37 
                 f5/CT5 
                 16.88 
               
               
                 TD/f2 
                 0.02 
                 f5/f1 
                 1.37 
               
               
                 TL [mm] 
                 11.51 
                 f8/f7 
                 −0.39 
               
               
                 TL/f 
                 1.21 
                 Y82/Y11 
                 2.58 
               
               
                 TL/ImgH 
                 1.41 
                 Yc72/Yc71 
                 1.20 
               
               
                 R1/R2 
                 0.48 
                 Yc82/Y82 
                 0.37 
               
               
                 R3/f 
                 0.49 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     4th Embodiment 
       FIG. 7  is a schematic view of an image capturing unit according to the 4th embodiment of the present disclosure.  FIG. 8  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 4th embodiment. In  FIG. 7 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  499 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  400 , a first lens element  410 , a second lens element  420 , a stop  401 , a third lens element  430 , a fourth lens element  440 , a stop  402 , a fifth lens element  450 , a sixth lens element  460 , a seventh lens element  470 , an eighth lens element  480 , a filter  490  and an image surface  495 . The photographing optical system includes eight lens elements ( 410 ,  420 ,  430 ,  440 ,  450 ,  460 ,  470  and  480 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  410  with positive refractive power has an object-side surface  411  being convex in a paraxial region thereof and an image-side surface  412  being convex in a paraxial region thereof. The first lens element  410  is made of plastic material and has the object-side surface  411  and the image-side surface  412  being both aspheric. The image-side surface  412  of the first lens element  410  has two inflection points. The image-side surface  412  of the first lens element  410  has one critical point in an off-axis region thereof. 
     The second lens element  420  with negative refractive power has an object-side surface  421  being convex in a paraxial region thereof and an image-side surface  422  being concave in a paraxial region thereof. The second lens element  420  is made of plastic material and has the object-side surface  421  and the image-side surface  422  being both aspheric. The object-side surface  421  of the second lens element  420  has two inflection points. The image-side surface  422  of the second lens element  420  has one inflection point. 
     The third lens element  430  with positive refractive power has an object-side surface  431  being convex in a paraxial region thereof and an image-side surface  432  being concave in a paraxial region thereof. The third lens element  430  is made of plastic material and has the object-side surface  431  and the image-side surface  432  being both aspheric. The object-side surface  431  of the third lens element  430  has one inflection point. The image-side surface  432  of the third lens element  430  has two inflection points. The object-side surface  431  of the third lens element  430  has one critical point in an off-axis region thereof. The image-side surface  432  of the third lens element  430  has one critical point in an off-axis region thereof. 
     The fourth lens element  440  with negative refractive power has an object-side surface  441  being convex in a paraxial region thereof and an image-side surface  442  being concave in a paraxial region thereof. The fourth lens element  440  is made of plastic material and has the object-side surface  441  and the image-side surface  442  being both aspheric. The object-side surface  441  of the fourth lens element  440  has three inflection points. The image-side surface  442  of the fourth lens element  440  has three inflection points. The object-side surface  441  of the fourth lens element  440  has three critical points in an off-axis region thereof. The image-side surface  442  of the fourth lens element  440  has one critical point in an off-axis region thereof. 
     The fifth lens element  450  with positive refractive power has an object-side surface  451  being convex in a paraxial region thereof and an image-side surface  452  being convex in a paraxial region thereof. The fifth lens element  450  is made of plastic material and has the object-side surface  451  and the image-side surface  452  being both aspheric. The image-side surface  452  of the fifth lens element  450  has one inflection point. 
     The sixth lens element  460  with negative refractive power has an object-side surface  461  being convex in a paraxial region thereof and an image-side surface  462  being concave in a paraxial region thereof. The sixth lens element  460  is made of plastic material and has the object-side surface  461  and the image-side surface  462  being both aspheric. The object-side surface  461  of the sixth lens element  460  has one inflection point. The image-side surface  462  of the sixth lens element  460  has two inflection points. The object-side surface  461  of the sixth lens element  460  has one critical point in an off-axis region thereof. The image-side surface  462  of the sixth lens element  460  has one critical point in an off-axis region thereof. 
     The seventh lens element  470  with positive refractive power has an object-side surface  471  being convex in a paraxial region thereof and an image-side surface  472  being concave in a paraxial region thereof. The seventh lens element  470  is made of plastic material and has the object-side surface  471  and the image-side surface  472  being both aspheric. The object-side surface  471  of the seventh lens element  470  has three inflection points. The image-side surface  472  of the seventh lens element  470  has three inflection points. The object-side surface  471  of the seventh lens element  470  has one critical point in an off-axis region thereof. The image-side surface  472  of the seventh lens element  470  has one critical point in an off-axis region thereof. 
     The eighth lens element  480  with negative refractive power has an object-side surface  481  being concave in a paraxial region thereof and an image-side surface  482  being concave in a paraxial region thereof. The eighth lens element  480  is made of plastic material and has the object-side surface  481  and the image-side surface  482  being both aspheric. The object-side surface  481  of the eighth lens element  480  has one inflection point. The image-side surface  482  of the eighth lens element  480  has one inflection point. The object-side surface  481  of the eighth lens element  480  has one critical point in an off-axis region thereof. The image-side surface  482  of the eighth lens element  480  has one critical point in an off-axis region thereof. 
     The filter  490  is made of glass material and located between the eighth lens element  480  and the image surface  495 , and will not affect the focal length of the photographing optical system. The image sensor  499  is disposed on or near the image surface  495  of the photographing optical system. 
     The detailed optical data of the 4th embodiment are shown in Table 7 and the aspheric surface data are shown in Table 8 below. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 4th Embodiment 
               
               
                 f = 5.16 mm, Fno = 1.41, HFOV = 39.7 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.578 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 3.616 
                 (ASP) 
                 0.788 
                 Plastic 
                 1.545 
                 56.1 
                 6.58 
               
               
                 3 
                   
                 −441.899 
                 (ASP) 
                 0.050 
               
               
                 4 
                 Lens 2 
                 2.639 
                 (ASP) 
                 0.280 
                 Plastic 
                 1.669 
                 19.5 
                 −17.28 
               
               
                 5 
                   
                 2.057 
                 (ASP) 
                 0.366 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 6 
                 Stop 
                 Plano 
                 0.249 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 Lens 3 
                 15.083 
                 (ASP) 
                 0.290 
                 Plastic 
                 1.669 
                 19.5 
                 29.47 
               
               
                 8 
                   
                 63.676 
                 (ASP) 
                 0.050 
               
               
                 9 
                 Lens 4 
                 95.335 
                 (ASP) 
                 0.300 
                 Plastic 
                 1.662 
                 20.0 
                 −8.44 
               
               
                 10 
                   
                 5.268 
                 (ASP) 
                 0.101 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 11 
                 Stop 
                 Plano 
                 −0.058 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 12 
                 Lens 5 
                 9.356 
                 (ASP) 
                 1.129 
                 Plastic 
                 1.544 
                 56.0 
                 9.96 
               
               
                 13 
                   
                 −12.315 
                 (ASP) 
                 0.212 
               
               
                 14 
                 Lens 6 
                 4.603 
                 (ASP) 
                 0.520 
                 Plastic 
                 1.555 
                 46.7 
                 −14.15 
               
               
                 15 
                   
                 2.785 
                 (ASP) 
                 0.119 
               
               
                 16 
                 Lens 7 
                 1.665 
                 (ASP) 
                 0.518 
                 Plastic 
                 1.544 
                 56.0 
                 3.35 
               
               
                 17 
                   
                 17.241 
                 (ASP) 
                 0.768 
               
               
                 18 
                 Lens 8 
                 −11.677 
                 (ASP) 
                 0.430 
                 Plastic 
                 1.534 
                 55.9 
                 −3.91 
               
               
                 19 
                   
                 2.573 
                 (ASP) 
                 0.500 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 20 
                 Filter 
                 Plano 
                 0.210 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 21 
                   
                 Plano 
                 0.478 
               
               
                 22 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 401 (Surface 6) is 1.550 mm. 
               
               
                 active radius of the stop 402 (Surface 11) is 1.850 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                 −2.6519E−02 
                 −9.9000E+01 
                 −5.9466E+00 
                 −4.5336E+00 
                 4.8994E+01 
                 0.0000E+00 
               
               
                 A4 = 
                  2.6894E−03 
                  4.2721E−03 
                 −6.2726E−03 
                  1.4806E−03 
                 1.2128E−02 
                 6.9446E−02 
               
               
                 A6 = 
                  4.6335E−03 
                  3.4587E−03 
                 −1.5104E−02 
                 −1.9432E−02 
                 −4.0352E−02  
                 −8.3295E−02  
               
               
                 A8 = 
                 −6.2205E−03 
                 −1.6987E−03 
                  2.3011E−02 
                  1.3742E−02 
                 2.9880E−03 
                 3.3598E−02 
               
               
                 A10 = 
                  4.6607E−03 
                  5.7709E−04 
                 −1.7891E−02 
                 −5.4534E−03 
                 −2.3333E−03  
                 −6.6360E−03  
               
               
                 A12 = 
                 −1.8506E−03 
                 −8.1603E−05 
                  8.2740E−03 
                  8.5600E−04 
                 3.0819E−03 
                 5.8919E−04 
               
               
                 A14 = 
                  3.9136E−04 
                 −3.0153E−06 
                 −2.1524E−03 
                 −2.8154E−05 
                 −6.8927E−04  
                 — 
               
               
                 A16 = 
                 −3.4043E−05 
                 — 
                  2.3636E−04 
                 — 
                 — 
                 — 
               
               
                   
               
               
                 surface # 
                 9 
                 10 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 k = 
                 −9.9000E+01 
                  4.1306E+00 
                 7.8608E+00 
                  2.2030E+01 
                 −6.2016E+01  
                 −5.0806E+00 
               
               
                 A4 = 
                 −2.9498E−03 
                 −6.1994E−02 
                 4.1759E−03 
                 −2.0986E−02 
                 8.1004E−03 
                 −1.9209E−01 
               
               
                 A6 = 
                 −3.5249E−02 
                  8.9070E−03 
                 −2.4472E−02  
                 −5.0104E−03 
                 4.9346E−03 
                  1.4016E−01 
               
               
                 A8 = 
                  4.9610E−02 
                  1.0122E−02 
                 2.1278E−02 
                  2.2583E−03 
                 −1.7958E−02  
                 −7.5469E−02 
               
               
                 A10 = 
                 −2.4833E−02 
                 −3.9634E−03 
                 −8.3443E−03  
                 −8.7975E−04 
                 1.1303E−02 
                  2.6357E−02 
               
               
                 A12 = 
                  5.3400E−03 
                 −3.1863E−04 
                 1.6894E−03 
                  4.3014E−04 
                 −4.3596E−03  
                 −6.0659E−03 
               
               
                 A14 = 
                 −4.2561E−04 
                  3.1296E−04 
                 −1.7006E−04  
                 −1.1375E−04 
                 1.0638E−03 
                  9.0863E−04 
               
               
                 A16 = 
                 — 
                 −3.7362E−05 
                 6.8725E−06 
                  1.1390E−05 
                 −1.4391E−04  
                 −7.9150E−05 
               
               
                 A18 = 
                 — 
                 — 
                 — 
                 — 
                 7.9921E−06 
                  2.9778E−06 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 surface # 
                 16 
                 17 
                 18 
                 19 
               
               
                   
                   
               
               
                   
                 k = 
                 −7.0799E−01 
                  7.0623E+00 
                  9.3687E+00 
                 −1.5501E+00 
               
               
                   
                 A4 = 
                 −9.2597E−02 
                  1.3218E−01 
                 −8.8703E−02 
                 −1.1052E−01 
               
               
                   
                 A6 = 
                  2.0038E−02 
                 −1.0891E−01 
                 −3.9230E−03 
                  3.2182E−02 
               
               
                   
                 A8 = 
                 −1.2230E−02 
                  4.0161E−02 
                  1.7040E−02 
                 −5.0862E−03 
               
               
                   
                 A10 = 
                  2.7647E−03 
                 −8.7531E−03 
                 −5.9077E−03 
                  3.3324E−04 
               
               
                   
                 A12 = 
                  1.8258E−04 
                  1.0802E−03 
                  1.0355E−03 
                  2.3243E−05 
               
               
                   
                 A14 = 
                 −2.1230E−04 
                 −5.2813E−05 
                 −1.0717E−04 
                 −6.5473E−06 
               
               
                   
                 A16 = 
                  3.8066E−05 
                 −3.1462E−06 
                  6.6372E−06 
                  5.5635E−07 
               
               
                   
                 A18 = 
                 −2.2151E−06 
                  5.1803E−07 
                 −2.2828E−07 
                 −2.2452E−08 
               
               
                   
                 A20 = 
                 — 
                 −1.8784E−08 
                  3.3650E−09 
                  3.6254E−10 
               
               
                   
                   
               
            
           
         
       
     
     In the 4th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 4th embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 7 and Table 8 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 4th Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 5.16 
                 R3/R4 
                 1.28 
               
               
                 Fno 
                 1.41 
                 (R9 + R10)/(R9 − R10) 
                 −0.14 
               
               
                 HFOV [deg.] 
                 39.7 
                 f/f1 
                 0.78 
               
               
                 (Vi/Ni)min 
                 11.65 
                 f/f2 
                 −0.30 
               
               
                 V2 
                 19.5 
                 |f/f2| + |f/f3| 
                 0.47 
               
               
                 V2 + V3 + V4 
                 58.9 
                 f/f2 + f/f3 + f/f4 
                 −0.74 
               
               
                 V2 + V4 
                 39.4 
                 f/f3 
                 0.18 
               
               
                 V2/N2 
                 11.65 
                 f/f4 
                 −0.61 
               
               
                 V6 
                 46.7 
                 f/f5 
                 0.52 
               
               
                 ΣCT/CT5 
                 3.77 
                 f/f6 
                 −0.36 
               
               
                 (CT2 + CT3 + CT4)/ 
                 0.45 
                 f/f7 
                 1.54 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 1.04 
                 f/f8 
                 −1.32 
               
               
                 CT5/CT1 
                 1.43 
                 f/f12 
                 0.55 
               
               
                 CT5/CT3 
                 3.89 
                 f/f23 
                 −0.13 
               
               
                 CT7/CT5 
                 0.46 
                 f/|R11| + f/|R12| 
                 2.98 
               
               
                 TD/CT5 
                 5.41 
                 f5/CT5 
                 8.82 
               
               
                 TD/f2 
                 −0.35 
                 f5/f1 
                 1.51 
               
               
                 TL [mm] 
                 7.30 
                 f8/f7 
                 −1.17 
               
               
                 TL/f 
                 1.41 
                 Y82/Y11 
                 2.00 
               
               
                 TL/ImgH 
                 1.70 
                 Yc72/Yc71 
                 1.04 
               
               
                 R1/R2 
                 −0.01 
                 Yc82/Y82 
                 0.36 
               
               
                 R3/f 
                 0.51 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     5th Embodiment 
       FIG. 9  is a schematic view of an image capturing unit according to the 5th embodiment of the present disclosure.  FIG. 10  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 5th embodiment. In  FIG. 9 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  599 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  500 , a first lens element  510 , a second lens element  520 , a stop  501 , a third lens element  530 , a stop  502 , a fourth lens element  540 , a fifth lens element  550 , a sixth lens element  560 , a seventh lens element  570 , an eighth lens element  580 , a filter  590  and an image surface  595 . The photographing optical system includes eight lens elements ( 510 ,  520 ,  530 ,  540 ,  550 ,  560 ,  570  and  580 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  510  with positive refractive power has an object-side surface  511  being convex in a paraxial region thereof and an image-side surface  512  being convex in a paraxial region thereof. The first lens element  510  is made of plastic material and has the object-side surface  511  and the image-side surface  512  being both aspheric. The image-side surface  512  of the first lens element  510  has one inflection point. The image-side surface  512  of the first lens element  510  has one critical point in an off-axis region thereof. 
     The second lens element  520  with negative refractive power has an object-side surface  521  being convex in a paraxial region thereof and an image-side surface  522  being concave in a paraxial region thereof. The second lens element  520  is made of plastic material and has the object-side surface  521  and the image-side surface  522  being both aspheric. The object-side surface  521  of the second lens element  520  has one inflection point. The image-side surface  522  of the second lens element  520  has one inflection point. The object-side surface  521  of the second lens element  520  has one critical point in an off-axis region thereof. 
     The third lens element  530  with positive refractive power has an object-side surface  531  being convex in a paraxial region thereof and an image-side surface  532  being concave in a paraxial region thereof. The third lens element  530  is made of plastic material and has the object-side surface  531  and the image-side surface  532  being both aspheric. The object-side surface  531  of the third lens element  530  has two inflection points. The image-side surface  532  of the third lens element  530  has two inflection points. The image-side surface  532  of the third lens element  530  has two critical points in an off-axis region thereof. 
     The fourth lens element  540  with negative refractive power has an object-side surface  541  being convex in a paraxial region thereof and an image-side surface  542  being concave in a paraxial region thereof. The fourth lens element  540  is made of plastic material and has the object-side surface  541  and the image-side surface  542  being both aspheric. The object-side surface  541  of the fourth lens element  540  has one inflection point. The image-side surface  542  of the fourth lens element  540  has one inflection point. The object-side surface  541  of the fourth lens element  540  has one critical point in an off-axis region thereof. The image-side surface  542  of the fourth lens element  540  has one critical point in an off-axis region thereof. 
     The fifth lens element  550  with positive refractive power has an object-side surface  551  being convex in a paraxial region thereof and an image-side surface  552  being convex in a paraxial region thereof. The fifth lens element  550  is made of plastic material and has the object-side surface  551  and the image-side surface  552  being both aspheric. The object-side surface  551  of the fifth lens element  550  has three inflection points. The image-side surface  552  of the fifth lens element  550  has one inflection point. The object-side surface  551  of the fifth lens element  550  has one critical point in an off-axis region thereof. 
     The sixth lens element  560  with negative refractive power has an object-side surface  561  being concave in a paraxial region thereof and an image-side surface  562  being convex in a paraxial region thereof. The sixth lens element  560  is made of plastic material and has the object-side surface  561  and the image-side surface  562  being both aspheric. The object-side surface  561  of the sixth lens element  560  has one inflection point. The image-side surface  562  of the sixth lens element  560  has two inflection points. The object-side surface  561  of the sixth lens element  560  has one critical point in an off-axis region thereof. The image-side surface  562  of the sixth lens element  560  has one critical point in an off-axis region thereof. 
     The seventh lens element  570  with positive refractive power has an object-side surface  571  being convex in a paraxial region thereof and an image-side surface  572  being concave in a paraxial region thereof. The seventh lens element  570  is made of plastic material and has the object-side surface  571  and the image-side surface  572  being both aspheric. The object-side surface  571  of the seventh lens element  570  has two inflection points. The image-side surface  572  of the seventh lens element  570  has four inflection points. The object-side surface  571  of the seventh lens element  570  has one critical point in an off-axis region thereof. The image-side surface  572  of the seventh lens element  570  has one critical point in an off-axis region thereof. 
     The eighth lens element  580  with negative refractive power has an object-side surface  581  being convex in a paraxial region thereof and an image-side surface  582  being concave in a paraxial region thereof. The eighth lens element  580  is made of plastic material and has the object-side surface  581  and the image-side surface  582  being both aspheric. The object-side surface  581  of the eighth lens element  580  has three inflection points. The image-side surface  582  of the eighth lens element  580  has one inflection point. The object-side surface  581  of the eighth lens element  580  has two critical points in an off-axis region thereof. The image-side surface  582  of the eighth lens element  580  has one critical point in an off-axis region thereof. 
     The filter  590  is made of glass material and located between the eighth lens element  580  and the image surface  595 , and will not affect the focal length of the photographing optical system. The image sensor  599  is disposed on or near the image surface  595  of the photographing optical system. 
     The detailed optical data of the 5th embodiment are shown in Table 9 and the aspheric surface data are shown in Table 10 below. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 5th Embodiment 
               
               
                 f = 5.18 mm, Fno = 1.40, HFOV = 39.0 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.543 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 3.682 
                 (ASP) 
                 0.804 
                 Plastic 
                 1.545 
                 56.1 
                 6.58 
               
               
                 3 
                   
                 −122.745 
                 (ASP) 
                 0.035 
               
               
                 4 
                 Lens 2 
                 2.901 
                 (ASP) 
                 0.320 
                 Plastic 
                 1.669 
                 19.5 
                 −14.19 
               
               
                 5 
                   
                 2.124 
                 (ASP) 
                 0.477 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 6 
                 Stop 
                 Plano 
                 −0.111 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 Lens 3 
                 6.193 
                 (ASP) 
                 0.367 
                 Plastic 
                 1.544 
                 56.0 
                 65.33 
               
               
                 8 
                   
                 7.343 
                 (ASP) 
                 0.115 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 9 
                 Stop 
                 Plano 
                 0.195 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 10 
                 Lens 4 
                 7.026 
                 (ASP) 
                 0.350 
                 Plastic 
                 1.669 
                 19.5 
                 −31.50 
               
               
                 11 
                   
                 5.164 
                 (ASP) 
                 0.097 
               
               
                 12 
                 Lens 5 
                 18.400 
                 (ASP) 
                 1.100 
                 Plastic 
                 1.544 
                 56.0 
                 6.34 
               
               
                 13 
                   
                 −4.152 
                 (ASP) 
                 0.108 
               
               
                 14 
                 Lens 6 
                 −1.834 
                 (ASP) 
                 0.420 
                 Plastic 
                 1.584 
                 28.2 
                 −9.22 
               
               
                 15 
                   
                 −3.017 
                 (ASP) 
                 0.035 
               
               
                 16 
                 Lens 7 
                 1.949 
                 (ASP) 
                 0.614 
                 Plastic 
                 1.544 
                 56.0 
                 6.00 
               
               
                 17 
                   
                 4.293 
                 (ASP) 
                 0.673 
               
               
                 18 
                 Lens 8 
                 3.739 
                 (ASP) 
                 0.500 
                 Plastic 
                 1.534 
                 55.9 
                 −6.56 
               
               
                 19 
                   
                 1.725 
                 (ASP) 
                 0.800 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 20 
                 Filter 
                 Plano 
                 0.210 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 21 
                   
                 Plano 
                 0.325 
               
               
                 22 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 501 (Surface 6) is 1.605 mm. 
               
               
                 active radius of the stop 502 (Surface 9) is 1.515 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                 −3.8301E−01  
                 0.0000E+00 
                  0.0000E+00 
                  0.0000E+00 
                 −1.2701E+01 
                 −9.9618E+00 
               
               
                 A4 = 
                 3.3457E−03 
                 3.1080E−02 
                 −1.1795E−02 
                 −4.7194E−02 
                 −9.3118E−03 
                 −3.2069E−02 
               
               
                 A6 = 
                 5.3209E−04 
                 −4.0668E−02  
                 −2.8434E−02 
                  3.9451E−03 
                  1.4574E−02 
                  8.7149E−03 
               
               
                 A8 = 
                 5.5213E−05 
                 3.1959E−02 
                  8.4738E−03 
                 −2.7541E−02 
                 −2.1030E−02 
                  3.4697E−03 
               
               
                 A10 = 
                 −4.2169E−04  
                 −1.5322E−02  
                  4.2272E−03 
                  2.6183E−02 
                  8.5561E−03 
                 −1.9207E−02 
               
               
                 A12 = 
                 2.8564E−04 
                 4.5562E−03 
                 −3.9783E−03 
                 −1.3431E−02 
                 −9.1632E−04 
                  1.7476E−02 
               
               
                 A14 = 
                 −6.9022E−05  
                 −7.7228E−04  
                  1.0982E−03 
                  3.6485E−03 
                  1.3193E−05 
                 −6.0516E−03 
               
               
                 A16 = 
                 6.1250E−06 
                 5.6791E−05 
                 −1.0458E−04 
                 −3.9543E−04 
                 — 
                  7.4493E−04 
               
               
                   
               
               
                 Surface # 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 k = 
                  1.2423E+01 
                 1.3203E−01 
                 8.8600E+01 
                 −8.8185E−01 
                 −9.6984E−01 
                 −8.0226E−01 
               
               
                 A4 = 
                 −6.7989E−02 
                 −6.6548E−02  
                 −4.5475E−02  
                 −2.8815E−02 
                  9.9388E−02 
                  9.8134E−04 
               
               
                 A6 = 
                  1.6834E−02 
                 2.7006E−02 
                 1.6774E−02 
                 −3.8965E−02 
                 −1.1724E−01 
                 −1.5649E−02 
               
               
                 A8 = 
                 −6.9501E−03 
                 1.2512E−02 
                 1.7014E−02 
                  3.4192E−02 
                  9.7748E−02 
                  2.2429E−02 
               
               
                 A10 = 
                 −1.7436E−02 
                 −3.8760E−02  
                 −2.3155E−02  
                 −5.4432E−04 
                 −4.9187E−02 
                 −1.5236E−02 
               
               
                 A12 = 
                  1.9061E−02 
                 2.8809E−02 
                 7.1384E−03 
                 −1.1288E−02 
                  1.6068E−02 
                  6.0710E−03 
               
               
                 A14 = 
                 −7.0389E−03 
                 −1.0334E−02  
                 1.3147E−03 
                  6.5272E−03 
                 −3.3711E−03 
                 −1.3937E−03 
               
               
                 A16 = 
                  8.6756E−04 
                 1.8573E−03 
                 −1.2739E−03  
                 −1.7663E−03 
                  4.2950E−04 
                  1.8129E−04 
               
               
                 A18 = 
                 — 
                 −1.3525E−04  
                 2.8460E−04 
                  2.4374E−04 
                 −2.9663E−05 
                 −1.2446E−05 
               
               
                 A20 = 
                 — 
                 — 
                 −2.2209E−05  
                 −1.3710E−05 
                  8.3048E−07 
                  3.5052E−07 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface # 
                 16 
                 17 
                 18 
                 19 
               
               
                   
                   
               
               
                   
                 k = 
                 −1.0014E+00 
                 −7.5632E−01 
                 −2.6306E+00 
                 −9.2400E−01 
               
               
                   
                 A4 = 
                 −3.5806E−02 
                  8.9864E−02 
                 −1.0128E−01 
                 −1.3840E−01 
               
               
                   
                 A6 = 
                 −1.2874E−03 
                 −8.4239E−02 
                  1.1717E−02 
                  4.1232E−02 
               
               
                   
                 A8 = 
                 −5.6061E−03 
                  3.5938E−02 
                  2.5804E−03 
                 −1.0109E−02 
               
               
                   
                 A10 = 
                  4.6488E−03 
                 −1.0054E−02 
                 −8.5251E−04 
                  1.8994E−03 
               
               
                   
                 A12 = 
                 −1.7886E−03 
                  1.8590E−03 
                  1.0234E−04 
                 −2.4794E−04 
               
               
                   
                 A14 = 
                  3.7546E−04 
                 −2.2030E−04 
                 −6.2547E−06 
                  2.1003E−05 
               
               
                   
                 A16 = 
                 −4.3285E−05 
                  1.5989E−05 
                  1.7796E−07 
                 −1.0886E−06 
               
               
                   
                 A18 = 
                  2.5712E−06 
                 −6.4628E−07 
                 −7.1276E−10 
                  3.1204E−08 
               
               
                   
                 A20 = 
                 −6.1554E−08 
                  1.1144E−08 
                 −4.7919E−11 
                 −3.7790E−10 
               
               
                   
                   
               
            
           
         
       
     
     In the 5th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 5th embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 9 and Table 10 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 5th Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 5.18 
                 R3/R4 
                 1.37 
               
               
                 Fno 
                 1.40 
                 (R9 + R10)/(R9 − R10) 
                 0.63 
               
               
                 HFOV [deg.] 
                 39.0 
                 f/f1 
                 0.79 
               
               
                 (Vi/Ni)min 
                 11.65 
                 f/f2 
                 −0.36 
               
               
                 V2 
                 19.5 
                 |f/f2| + |f/f3| 
                 0.44 
               
               
                 V2 + V3 + V4 
                 94.9 
                 f/f2 + f/f3 + f/f4 
                 −0.45 
               
               
                 V2 + V4 
                 38.9 
                 f/f3 
                 0.08 
               
               
                 V2/N2 
                 11.65 
                 f/f4 
                 −0.16 
               
               
                 V6 
                 28.2 
                 f/f5 
                 0.82 
               
               
                 ΣCT/CT5 
                 4.07 
                 f/f6 
                 −0.56 
               
               
                 (CT2 + CT3 + CT4)/ 
                 0.54 
                 f/f7 
                 0.86 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 1.15 
                 f/f8 
                 −0.79 
               
               
                 CT5/CT1 
                 1.37 
                 f/f12 
                 0.50 
               
               
                 CT5/CT3 
                 3.00 
                 f/f23 
                 −0.29 
               
               
                 CT7/CT5 
                 0.56 
                 f/|R11| + f/|R12| 
                 4.54 
               
               
                 TD/CT5 
                 5.54 
                 f5/CT5 
                 5.76 
               
               
                 TD/f2 
                 −0.43 
                 f5/f1 
                 0.96 
               
               
                 TL [mm] 
                 7.43 
                 f8/f7 
                 −1.09 
               
               
                 TL/f 
                 1.44 
                 Y82/Y11 
                 2.02 
               
               
                 TL/ImgH 
                 1.74 
                 Yc72/Yc71 
                 1.12 
               
               
                 R1/R2 
                 −0.03 
                 Yc82/Y82 
                 0.44 
               
               
                 R3/f 
                 0.56 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     6th Embodiment 
       FIG. 11  is a schematic view of an image capturing unit according to the 6th embodiment of the present disclosure.  FIG. 12  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 6th embodiment. In  FIG. 11 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  699 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  600 , a first lens element  610 , a second lens element  620 , a stop  601 , a third lens element  630 , a stop  602 , a fourth lens element  640 , a fifth lens element  650 , a sixth lens element  660 , a seventh lens element  670 , an eighth lens element  680 , a filter  690  and an image surface  695 . The photographing optical system includes eight lens elements ( 610 ,  620 ,  630 ,  640 ,  650 ,  660 ,  670  and  680 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  610  with positive refractive power has an object-side surface  611  being convex in a paraxial region thereof and an image-side surface  612  being concave in a paraxial region thereof. The first lens element  610  is made of plastic material and has the object-side surface  611  and the image-side surface  612  being both aspheric. 
     The second lens element  620  with negative refractive power has an object-side surface  621  being convex in a paraxial region thereof and an image-side surface  622  being concave in a paraxial region thereof. The second lens element  620  is made of plastic material and has the object-side surface  621  and the image-side surface  622  being both aspheric. The object-side surface  621  of the second lens element  620  has one inflection point. The image-side surface  622  of the second lens element  620  has one inflection point. The object-side surface  621  of the second lens element  620  has one critical point in an off-axis region thereof. 
     The third lens element  630  with positive refractive power has an object-side surface  631  being convex in a paraxial region thereof and an image-side surface  632  being concave in a paraxial region thereof. The third lens element  630  is made of plastic material and has the object-side surface  631  and the image-side surface  632  being both aspheric. The object-side surface  631  of the third lens element  630  has two inflection points. The image-side surface  632  of the third lens element  630  has two inflection points. The image-side surface  632  of the third lens element  630  has two critical points in an off-axis region thereof. 
     The fourth lens element  640  with negative refractive power has an object-side surface  641  being convex in a paraxial region thereof and an image-side surface  642  being concave in a paraxial region thereof. The fourth lens element  640  is made of plastic material and has the object-side surface  641  and the image-side surface  642  being both aspheric. The object-side surface  641  of the fourth lens element  640  has one inflection point. The image-side surface  642  of the fourth lens element  640  has one inflection point. The object-side surface  641  of the fourth lens element  640  has one critical point in an off-axis region thereof. The image-side surface  642  of the fourth lens element  640  has one critical point in an off-axis region thereof. 
     The fifth lens element  650  with positive refractive power has an object-side surface  651  being convex in a paraxial region thereof and an image-side surface  652  being convex in a paraxial region thereof. The fifth lens element  650  is made of plastic material and has the object-side surface  651  and the image-side surface  652  being both aspheric. The object-side surface  651  of the fifth lens element  650  has two inflection points. The image-side surface  652  of the fifth lens element  650  has one inflection point. The object-side surface  651  of the fifth lens element  650  has one critical point in an off-axis region thereof. 
     The sixth lens element  660  with negative refractive power has an object-side surface  661  being concave in a paraxial region thereof and an image-side surface  662  being convex in a paraxial region thereof. The sixth lens element  660  is made of plastic material and has the object-side surface  661  and the image-side surface  662  being both aspheric. The object-side surface  661  of the sixth lens element  660  has two inflection points. The image-side surface  662  of the sixth lens element  660  has one inflection point. The image-side surface  662  of the sixth lens element  660  has one critical point in an off-axis region thereof. 
     The seventh lens element  670  with positive refractive power has an object-side surface  671  being convex in a paraxial region thereof and an image-side surface  672  being concave in a paraxial region thereof. The seventh lens element  670  is made of plastic material and has the object-side surface  671  and the image-side surface  672  being both aspheric. The object-side surface  671  of the seventh lens element  670  has two inflection points. The image-side surface  672  of the seventh lens element  670  has two inflection points. The object-side surface  671  of the seventh lens element  670  has one critical point in an off-axis region thereof. The image-side surface  672  of the seventh lens element  670  has one critical point in an off-axis region thereof. 
     The eighth lens element  680  with negative refractive power has an object-side surface  681  being convex in a paraxial region thereof and an image-side surface  682  being concave in a paraxial region thereof. The eighth lens element  680  is made of plastic material and has the object-side surface  681  and the image-side surface  682  being both aspheric. The object-side surface  681  of the eighth lens element  680  has three inflection points. The image-side surface  682  of the eighth lens element  680  has three inflection points. The object-side surface  681  of the eighth lens element  680  has two critical points in an off-axis region thereof. The image-side surface  682  of the eighth lens element  680  has one critical point in an off-axis region thereof. 
     The filter  690  is made of glass material and located between the eighth lens element  680  and the image surface  695 , and will not affect the focal length of the photographing optical system. The image sensor  699  is disposed on or near the image surface  695  of the photographing optical system. 
     The detailed optical data of the 6th embodiment are shown in Table 11 and the aspheric surface data are shown in Table 12 below. 
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 6th Embodiment 
               
               
                 f = 5.18 mm, Fno = 1.40, HFOV = 39.1 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.529 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 3.764 
                 (ASP) 
                 0.775 
                 Plastic 
                 1.545 
                 56.1 
                 7.28 
               
               
                 3 
                   
                 68.551 
                 (ASP) 
                 0.035 
               
               
                 4 
                 Lens 2 
                 2.738 
                 (ASP) 
                 0.320 
                 Plastic 
                 1.660 
                 20.4 
                 −16.48 
               
               
                 5 
                   
                 2.086 
                 (ASP) 
                 0.471 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 6 
                 Stop 
                 Plano 
                 −0.111 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 Lens 3 
                 4.782 
                 (ASP) 
                 0.416 
                 Plastic 
                 1.544 
                 56.0 
                 41.54 
               
               
                 8 
                   
                 5.879 
                 (ASP) 
                 0.097 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 9 
                 Stop 
                 Plano 
                 0.182 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 10 
                 Lens 4 
                 6.442 
                 (ASP) 
                 0.350 
                 Plastic 
                 1.669 
                 19.5 
                 −75.39 
               
               
                 11 
                   
                 5.588 
                 (ASP) 
                 0.124 
               
               
                 12 
                 Lens 5 
                 25.044 
                 (ASP) 
                 1.015 
                 Plastic 
                 1.544 
                 56.0 
                 6.25 
               
               
                 13 
                   
                 −3.878 
                 (ASP) 
                 0.129 
               
               
                 14 
                 Lens 6 
                 −1.758 
                 (ASP) 
                 0.420 
                 Plastic 
                 1.669 
                 19.5 
                 −13.05 
               
               
                 15 
                   
                 −2.412 
                 (ASP) 
                 0.035 
               
               
                 16 
                 Lens 7 
                 2.057 
                 (ASP) 
                 0.575 
                 Plastic 
                 1.544 
                 56.0 
                 10.05 
               
               
                 17 
                   
                 2.972 
                 (ASP) 
                 0.700 
               
               
                 18 
                 Lens 8 
                 3.593 
                 (ASP) 
                 0.500 
                 Plastic 
                 1.534 
                 55.9 
                 −7.75 
               
               
                 19 
                   
                 1.830 
                 (ASP) 
                 0.800 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 20 
                 Filter 
                 Plano 
                 0.210 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 21 
                   
                 Plano 
                 0.300 
               
               
                 22 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 601 (Surface 6) is 1.635 mm. 
               
               
                 active radius of the stop 602 (Surface 9) is 1.538 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                 −4.0891E−01  
                 0.0000E+00 
                  0.0000E+00 
                  0.0000E+00 
                 −1.2943E+01 
                 −2.0093E+01 
               
               
                 A4 = 
                 3.3195E−03 
                 1.1113E−02 
                 −3.1787E−02 
                 −5.2038E−02 
                  7.4506E−04 
                 −2.9018E−02 
               
               
                 A6 = 
                 2.3048E−04 
                 −1.2629E−02  
                 −2.3498E−03 
                  7.1476E−03 
                  1.7014E−03 
                  3.5472E−03 
               
               
                 A8 = 
                 9.2968E−05 
                 6.8236E−03 
                 −1.5974E−02 
                 −3.1423E−02 
                 −3.4432E−03 
                  1.5803E−02 
               
               
                 A10 = 
                 −4.1752E−04  
                 −1.4854E−03  
                  1.8235E−02 
                  2.8751E−02 
                 −6.1897E−03 
                 −3.1635E−02 
               
               
                 A12 = 
                 2.8403E−04 
                 7.3721E−05 
                 −8.5165E−03 
                 −1.4138E−02 
                  4.3604E−03 
                  2.1525E−02 
               
               
                 A14 = 
                 −6.6596E−05  
                 2.1025E−05 
                  1.8663E−03 
                  3.7086E−03 
                 −6.5709E−04 
                 −6.3492E−03 
               
               
                 A16 = 
                 5.7722E−06 
                 −2.7842E−06  
                 −1.5903E−04 
                 −3.9415E−04 
                 — 
                  7.1335E−04 
               
               
                   
               
               
                 Surface # 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 k = 
                  1.3233E+01 
                 −2.5167E+00 
                  1.0121E−01 
                 −8.9563E−01 
                 −8.5916E−01 
                 0.0000E+00 
               
               
                 A4 = 
                 −7.1216E−02 
                 −3.9539E−02 
                 −8.0866E−03 
                 −2.3398E−02 
                  8.7465E−02 
                 3.4160E−02 
               
               
                 A6 = 
                 −1.0634E−02 
                 −5.0461E−02 
                 −3.5113E−02 
                  1.3687E−03 
                 −8.0707E−02 
                 −3.9157E−02  
               
               
                 A8 = 
                  4.3691E−02 
                  9.9711E−02 
                  2.8499E−02 
                 −6.4786E−02 
                  3.1387E−02 
                 5.1769E−02 
               
               
                 A10 = 
                 −5.3195E−02 
                 −9.0819E−02 
                  9.7406E−03 
                  1.1358E−01 
                  2.7140E−02 
                 −3.9031E−02  
               
               
                 A12 = 
                  3.0481E−02 
                  4.5424E−02 
                 −3.2342E−02 
                 −8.5813E−02 
                 −3.5137E−02 
                 1.8658E−02 
               
               
                 A14 = 
                 −8.4208E−03 
                 −1.2662E−02 
                  2.2513E−02 
                  3.5080E−02 
                  1.6729E−02 
                 −5.5982E−03  
               
               
                 A16 = 
                  8.7183E−04 
                  1.8326E−03 
                 −7.4694E−03 
                 −8.1304E−03 
                 −4.1734E−03 
                 1.0194E−03 
               
               
                 A18 = 
                 — 
                 −1.0704E−04 
                  1.2358E−03 
                  1.0077E−03 
                  5.4359E−04 
                 −1.0275E−04  
               
               
                 A20 = 
                 — 
                 — 
                 −8.2057E−05 
                 −5.1815E−05 
                 −2.9299E−05 
                 4.3939E−06 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface # 
                 16 
                 17 
                 18 
                 19 
               
               
                   
                   
               
               
                   
                 k = 
                 −1.2443E+00 
                 −4.1178E+00 
                 −4.4446E+00 
                 −9.0845E−01 
               
               
                   
                 A4 = 
                 −3.7578E−02 
                  4.8746E−02 
                 −1.0795E−01 
                 −1.3566E−01 
               
               
                   
                 A6 = 
                  2.0103E−03 
                 −4.9650E−02 
                  2.5107E−02 
                  4.3019E−02 
               
               
                   
                 A8 = 
                 −6.4992E−03 
                  2.1366E−02 
                 −4.8027E−03 
                 −1.1804E−02 
               
               
                   
                 A10 = 
                  5.2574E−03 
                 −6.5848E−03 
                  1.0710E−03 
                  2.3715E−03 
               
               
                   
                 A12 = 
                 −2.5081E−03 
                  1.4491E−03 
                 −1.8713E−04 
                 −3.1460E−04 
               
               
                   
                 A14 = 
                  7.4977E−04 
                 −2.1962E−04 
                  2.0772E−05 
                  2.6461E−05 
               
               
                   
                 A16 = 
                 −1.3611E−04 
                  2.1496E−05 
                 −1.3840E−06 
                 −1.3558E−06 
               
               
                   
                 A18 = 
                  1.3422E−05 
                 −1.2053E−06 
                  5.0918E−08 
                  3.8661E−08 
               
               
                   
                 A20 = 
                 −5.4142E−07 
                  2.9095E−08 
                 −7.9904E−10 
                 −4.7173E−10 
               
               
                   
                   
               
            
           
         
       
     
     In the 6th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 6th embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 11 and Table 12 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 6th Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 5.18 
                 R3/R4 
                 1.31 
               
               
                 Fno 
                 1.40 
                 (R9 + R10)/(R9 − R10) 
                 0.73 
               
               
                 HFOV [deg.] 
                 39.1 
                 f/f1 
                 0.71 
               
               
                 (Vi/Ni)min 
                 11.65 
                 f/f2 
                 −0.31 
               
               
                 V2 
                 20.4 
                 |f/f2| + |f/f3| 
                 0.44 
               
               
                 V2 + V3 + V4 
                 95.8 
                 f/f2 + f/f3 + f/f4 
                 −0.26 
               
               
                 V2 + V4 
                 39.9 
                 f/f3 
                 0.12 
               
               
                 V2/N2 
                 12.29 
                 f/f4 
                 −0.07 
               
               
                 V6 
                 19.5 
                 f/f5 
                 0.83 
               
               
                 ΣCT/CT5 
                 4.31 
                 f/f6 
                 −0.40 
               
               
                 (CT2 + CT3 + CT4)/ 
                 0.61 
                 f/f7 
                 0.52 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 1.30 
                 f/f8 
                 −0.67 
               
               
                 CT5/CT1 
                 1.31 
                 f/f12 
                 0.46 
               
               
                 CT5/CT3 
                 2.44 
                 f/f23 
                 −0.20 
               
               
                 CT7/CT5 
                 0.57 
                 f/|R11| + f/|R12| 
                 5.09 
               
               
                 TD/CT5 
                 5.94 
                 f5/CT5 
                 6.16 
               
               
                 TD/f2 
                 −0.37 
                 f5/f1 
                 0.86 
               
               
                 TL [mm] 
                 7.34 
                 f8/f7 
                 −0.77 
               
               
                 TL/f 
                 1.42 
                 Y82/Y11 
                 1.99 
               
               
                 TL/ImgH 
                 1.71 
                 Yc72/Yc71 
                 1.11 
               
               
                 R1/R2 
                 0.05 
                 Yc82/Y82 
                 0.41 
               
               
                 R3/f 
                 0.53 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     7th Embodiment 
       FIG. 13  is a schematic view of an image capturing unit according to the 7th embodiment of the present disclosure.  FIG. 14  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 7th embodiment. In  FIG. 13 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  799 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  700 , a first lens element  710 , a second lens element  720 , a third lens element  730 , a stop  701 , a fourth lens element  740 , a fifth lens element  750 , a sixth lens element  760 , a seventh lens element  770 , an eighth lens element  780 , a filter  790  and an image surface  795 . The photographing optical system includes eight lens elements ( 710 ,  720 ,  730 ,  740 ,  750 ,  760 ,  770  and  780 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  710  with positive refractive power has an object-side surface  711  being convex in a paraxial region thereof and an image-side surface  712  being concave in a paraxial region thereof. The first lens element  710  is made of plastic material and has the object-side surface  711  and the image-side surface  712  being both aspheric. The object-side surface  711  of the first lens element  710  has one inflection point. The image-side surface  712  of the first lens element  710  has one inflection point. The image-side surface  712  of the first lens element  710  has one critical point in an off-axis region thereof. 
     The second lens element  720  with negative refractive power has an object-side surface  721  being convex in a paraxial region thereof and an image-side surface  722  being concave in a paraxial region thereof. The second lens element  720  is made of plastic material and has the object-side surface  721  and the image-side surface  722  being both aspheric. The object-side surface  721  of the second lens element  720  has two inflection points. The image-side surface  722  of the second lens element  720  has one inflection point. 
     The third lens element  730  with negative refractive power has an object-side surface  731  being convex in a paraxial region thereof and an image-side surface  732  being concave in a paraxial region thereof. The third lens element  730  is made of plastic material and has the object-side surface  731  and the image-side surface  732  being both aspheric. The object-side surface  731  of the third lens element  730  has one inflection point. The image-side surface  732  of the third lens element  730  has one inflection point. The object-side surface  731  of the third lens element  730  has one critical point in an off-axis region thereof. The image-side surface  732  of the third lens element  730  has one critical point in an off-axis region thereof. 
     The fourth lens element  740  with positive refractive power has an object-side surface  741  being convex in a paraxial region thereof and an image-side surface  742  being concave in a paraxial region thereof. The fourth lens element  740  is made of plastic material and has the object-side surface  741  and the image-side surface  742  being both aspheric. The object-side surface  741  of the fourth lens element  740  has one inflection point. The image-side surface  742  of the fourth lens element  740  has one inflection point. The object-side surface  741  of the fourth lens element  740  has one critical point in an off-axis region thereof. The image-side surface  742  of the fourth lens element  740  has one critical point in an off-axis region thereof. The fifth lens element  750  with positive refractive power has an object-side surface  751  being convex in a paraxial region thereof and an image-side surface  752  being convex in a paraxial region thereof. The fifth lens element  750  is made of plastic material and has the object-side surface  751  and the image-side surface  752  being both aspheric. The object-side surface  751  of the fifth lens element  750  has two inflection points. The image-side surface  752  of the fifth lens element  750  has one inflection point. The object-side surface  751  of the fifth lens element  750  has one critical point in an off-axis region thereof. 
     The sixth lens element  760  with negative refractive power has an object-side surface  761  being concave in a paraxial region thereof and an image-side surface  762  being convex in a paraxial region thereof. The sixth lens element  760  is made of plastic material and has the object-side surface  761  and the image-side surface  762  being both aspheric. The object-side surface  761  of the sixth lens element  760  has two inflection points. The image-side surface  762  of the sixth lens element  760  has one inflection point. The image-side surface  762  of the sixth lens element  760  has one critical point in an off-axis region thereof. 
     The seventh lens element  770  with positive refractive power has an object-side surface  771  being convex in a paraxial region thereof and an image-side surface  772  being concave in a paraxial region thereof. The seventh lens element  770  is made of plastic material and has the object-side surface  771  and the image-side surface  772  being both aspheric. The object-side surface  771  of the seventh lens element  770  has two inflection points. The image-side surface  772  of the seventh lens element  770  has two inflection points. The object-side surface  771  of the seventh lens element  770  has one critical point in an off-axis region thereof. The image-side surface  772  of the seventh lens element  770  has one critical point in an off-axis region thereof. 
     The eighth lens element  780  with negative refractive power has an object-side surface  781  being convex in a paraxial region thereof and an image-side surface  782  being concave in a paraxial region thereof. The eighth lens element  780  is made of plastic material and has the object-side surface  781  and the image-side surface  782  being both aspheric. The object-side surface  781  of the eighth lens element  780  has four inflection points. The image-side surface  782  of the eighth lens element  780  has three inflection points. The object-side surface  781  of the eighth lens element  780  has one critical point in an off-axis region thereof. The image-side surface  782  of the eighth lens element  780  has one critical point in an off-axis region thereof. 
     The filter  790  is made of glass material and located between the eighth lens element  780  and the image surface  795 , and will not affect the focal length of the photographing optical system. The image sensor  799  is disposed on or near the image surface  795  of the photographing optical system. 
     The detailed optical data of the 7th embodiment are shown in Table 13 and the aspheric surface data are shown in Table 14 below. 
     
       
         
           
               
             
               
                 TABLE 13 
               
             
            
               
                   
               
               
                 7th Embodiment 
               
               
                 f = 5.67 mm, Fno = 1.51, HFOV = 39.5 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.533  
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 3.415 
                 (ASP) 
                 0.888 
                 Plastic 
                 1.545 
                 56.1 
                 7.50 
               
               
                 3 
                   
                 18.869 
                 (ASP) 
                 0.035 
               
               
                 4 
                 Lens 2 
                 3.701 
                 (ASP) 
                 0.310 
                 Plastic 
                 1.669 
                 19.5 
                 −20.59 
               
               
                 5 
                   
                 2.819 
                 (ASP) 
                 0.386 
               
               
                 6 
                 Lens 3 
                 5.625 
                 (ASP) 
                 0.324 
                 Plastic 
                 1.669 
                 19.5 
                 −278.48 
               
               
                 7 
                   
                 5.334 
                 (ASP) 
                 0.048 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 8 
                 Stop 
                 Plano 
                 0.195 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 9 
                 Lens 4 
                 8.799 
                 (ASP) 
                 0.340 
                 Plastic 
                 1.669 
                 19.5 
                 3093.10 
               
               
                 10 
                   
                 8.700 
                 (ASP) 
                 0.090 
               
               
                 11 
                 Lens 5 
                 57.035 
                 (ASP) 
                 1.144 
                 Plastic 
                 1.544 
                 56.0 
                 7.95 
               
               
                 12 
                   
                 −4.646 
                 (ASP) 
                 0.198 
               
               
                 13 
                 Lens 6 
                 −1.695 
                 (ASP) 
                 0.390 
                 Plastic 
                 1.669 
                 19.5 
                 −17.41 
               
               
                 14 
                   
                 −2.166 
                 (ASP) 
                 0.035 
               
               
                 15 
                 Lens 7 
                 1.985 
                 (ASP) 
                 0.556 
                 Plastic 
                 1.544 
                 56.0 
                 11.83 
               
               
                 16 
                   
                 2.587 
                 (ASP) 
                 1.016 
               
               
                 17 
                 Lens 8 
                 3.616 
                 (ASP) 
                 0.510 
                 Plastic 
                 1.545 
                 56.1 
                 −9.44 
               
               
                 18 
                   
                 2.018 
                 (ASP) 
                 0.600 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 19 
                 Filter 
                 Plano 
                 0.210 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 20 
                   
                 Plano 
                 0.578 
               
               
                 21 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 701 (Surface 8) is 1.685 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 14 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 k = 
                 −1.7504E+00 
                  0.0000E+00 
                 −1.0965E+00 
                  1.3351E−01 
                 −3.3437E−01 
                 −1.9277E+00 
               
               
                 A4 = 
                  4.9695E−03 
                 −1.6207E−02 
                 −2.8445E−02 
                 −2.2187E−02 
                 −2.3183E−02 
                 −3.5738E−02 
               
               
                 A6 = 
                  1.8340E−03 
                  7.8154E−03 
                  2.0141E−03 
                 −9.6625E−03 
                  5.8441E−03 
                  9.5618E−03 
               
               
                 A8 = 
                 −1.8037E−03 
                 −3.6175E−03 
                 −1.6842E−03 
                  4.3351E−03 
                 −7.3937E−03 
                 −7.3112E−03 
               
               
                 A10 = 
                  8.7042E−04 
                  1.4743E−03 
                  2.2951E−03 
                 −1.5205E−03 
                  2.5521E−03 
                  2.0227E−03 
               
               
                 A12 = 
                 −2.3479E−04 
                 −4.2717E−04 
                 −9.7879E−04 
                  4.5373E−04 
                 −6.4085E−04 
                  2.3595E−04 
               
               
                 A14 = 
                  3.1579E−05 
                  6.5190E−05 
                  1.7159E−04 
                 −1.4707E−04 
                  9.8782E−05 
                 −1.8020E−04 
               
               
                 A16 = 
                 −1.9360E−06 
                 −3.7468E−06 
                 −8.3518E−06 
                  2.3364E−05 
                 −4.8487E−06 
                  1.6476E−05 
               
               
                   
               
               
                 Surface # 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
               
               
                   
               
               
                 k = 
                 0.0000E+00 
                  6.4462E−01 
                  0.0000E+00 
                 −1.1099E−01 
                 −1.0000E+00 
                 −1.0000E+00 
               
               
                 A4 = 
                 −3.5647E−02  
                 −2.9396E−02 
                 −2.0362E−02 
                 −3.8398E−02 
                  7.0280E−02 
                  3.2205E−02 
               
               
                 A6 = 
                 2.0027E−03 
                  1.9626E−02 
                  2.7805E−02 
                  1.4928E−02 
                 −5.4183E−02 
                 −2.6309E−02 
               
               
                 A8 = 
                 −4.3317E−03  
                 −2.7609E−02 
                 −3.0796E−02 
                 −2.5175E−03 
                  3.7564E−02 
                  1.8723E−02 
               
               
                 A10 = 
                 9.4333E−04 
                  1.9168E−02 
                  1.6077E−02 
                 −4.7988E−03 
                 −2.0107E−02 
                 −8.4381E−03 
               
               
                 A12 = 
                 2.1208E−03 
                 −6.8961E−03 
                 −2.7614E−03 
                  4.2828E−03 
                  7.9536E−03 
                  2.6480E−03 
               
               
                 A14 = 
                 −1.3869E−03  
                  1.2421E−03 
                 −1.1717E−03 
                 −1.6293E−03 
                 −2.0365E−03 
                 −5.5793E−04 
               
               
                 A16 = 
                 3.1895E−04 
                 −8.7541E−05 
                  6.8926E−04 
                  3.2872E−04 
                  3.0698E−04 
                  7.6730E−05 
               
               
                 A18 = 
                 −2.8389E−05  
                 −3.9294E−07 
                 −1.2876E−04 
                 −3.4638E−05 
                 −2.4027E−05 
                 −6.3825E−06 
               
               
                 A20 = 
                 — 
                 — 
                  8.5004E−06 
                  1.5362E−06 
                  6.9831E−07 
                  2.4385E−07 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 surface # 
                 15 
                 16 
                 17 
                 18 
               
               
                   
                   
               
               
                   
                 k = 
                 −1.0000E+00 
                 −1.0000E+00 
                 −1.00000E+00  
                 −1.0000E+00 
               
               
                   
                 A4 = 
                 −4.6607E−02 
                  2.3749E−03 
                 −9.2672E−02 
                 −1.0166E−01 
               
               
                   
                 A6 = 
                  1.3183E−02 
                 −8.8938E−03 
                  2.1419E−02 
                  2.8558E−02 
               
               
                   
                 A8 = 
                 −6.8213E−03 
                  1.5920E−03 
                 −3.8325E−03 
                 −6.7977E−03 
               
               
                   
                 A10 = 
                  2.1927E−03 
                 −9.2175E−05 
                  6.4837E−04 
                  1.2148E−03 
               
               
                   
                 A12 = 
                 −4.8423E−04 
                 −9.2374E−06 
                 −9.2158E−05 
                 −1.5413E−04 
               
               
                   
                 A14 = 
                  7.4023E−05 
                  1.8687E−06 
                  9.2698E−06 
                  1.3100E−05 
               
               
                   
                 A16 = 
                 −7.5083E−06 
                 −1.1342E−07 
                 −5.9028E−07 
                 −6.9446E−07 
               
               
                   
                 A18 = 
                  4.5360E−07 
                  1.9103E−09 
                  2.1104E−08 
                  2.0531E−08 
               
               
                   
                 A20 = 
                 −1.2119E−08 
                  3.4886E−11 
                 −3.2117E−10 
                 −2.5726E−10 
               
               
                   
                   
               
            
           
         
       
     
     In the 7th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 7th embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 13 and Table 14 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 7th Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 5.67 
                 R3/R4 
                 1.31 
               
               
                 Fno 
                 1.51 
                 (R9 + R10)/(R9 − R10) 
                 0.85 
               
               
                 HFOV [deg.] 
                 39.5 
                 f/f1 
                 0.76 
               
               
                 (Vi/Ni)min 
                 11.65 
                 f/f2 
                 −0.28 
               
               
                 V2 
                 19.5 
                 |f/f2| + |f/f3| 
                 0.30 
               
               
                 V2 + V3 + V4 
                 58.4 
                 f/f2 + f/f3 + f/f4 
                 −0.29 
               
               
                 V2 + V4 
                 38.9 
                 f/f3 
                 −0.02 
               
               
                 V2/N2 
                 11.65 
                 f/f4 
                 0.002 
               
               
                 V6 
                 19.5 
                 f/f5 
                 0.71 
               
               
                 ΣCT/CT5 
                 3.90 
                 f/f6 
                 −0.33 
               
               
                 (CT2 + CT3 + CT4)/ 
                 0.48 
                 f/f7 
                 0.48 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 1.05 
                 f/f8 
                 −0.60 
               
               
                 CT5/CT1 
                 1.29 
                 f/f12 
                 0.54 
               
               
                 CT5/CT3 
                 3.53 
                 f/f23 
                 −0.30 
               
               
                 CT7/CT5 
                 0.49 
                 f/|R11| + f/|R12| 
                 5.97 
               
               
                 TD/CT5 
                 5.65 
                 f5/CT5 
                 6.95 
               
               
                 TD/f2 
                 −0.31 
                 f5/f1 
                 1.06 
               
               
                 TL [mm] 
                 7.85 
                 f8/f7 
                 −0.80 
               
               
                 TL/f 
                 1.38 
                 Y82/Y11 
                 2.08 
               
               
                 TL/ImgH 
                 1.64 
                 Yc72/Yc71 
                 1.28 
               
               
                 R1/R2 
                 0.18 
                 Yc82/Y82 
                 0.44 
               
               
                 R3/f 
                 0.65 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     8th Embodiment 
       FIG. 15  is a schematic view of an image capturing unit according to the 8th embodiment of the present disclosure.  FIG. 16  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 8th embodiment. In  FIG. 15 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  899 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  800 , a first lens element  810 , a second lens element  820 , a third lens element  830 , a stop  801 , a fourth lens element  840 , a fifth lens element  850 , a sixth lens element  860 , a seventh lens element  870 , an eighth lens element  880 , a filter  890  and an image surface  895 . The photographing optical system includes eight lens elements ( 810 ,  820 ,  830 ,  840 ,  850 ,  860 ,  870  and  880 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  810  with positive refractive power has an object-side surface  811  being convex in a paraxial region thereof and an image-side surface  812  being concave in a paraxial region thereof. The first lens element  810  is made of plastic material and has the object-side surface  811  and the image-side surface  812  being both aspheric. The object-side surface  811  of the first lens element  810  has one inflection point. The image-side surface  812  of the first lens element  810  has one inflection point. The image-side surface  812  of the first lens element  810  has one critical point in an off-axis region thereof. 
     The second lens element  820  with negative refractive power has an object-side surface  821  being convex in a paraxial region thereof and an image-side surface  822  being concave in a paraxial region thereof. The second lens element  820  is made of plastic material and has the object-side surface  821  and the image-side surface  822  being both aspheric. The object-side surface  821  of the second lens element  820  has two inflection points. The image-side surface  822  of the second lens element  820  has one inflection point. 
     The third lens element  830  with negative refractive power has an object-side surface  831  being convex in a paraxial region thereof and an image-side surface  832  being concave in a paraxial region thereof. The third lens element  830  is made of plastic material and has the object-side surface  831  and the image-side surface  832  being both aspheric. The object-side surface  831  of the third lens element  830  has one inflection point. The image-side surface  832  of the third lens element  830  has one inflection point. The object-side surface  831  of the third lens element  830  has one critical point in an off-axis region thereof. The image-side surface  832  of the third lens element  830  has one critical point in an off-axis region thereof. 
     The fourth lens element  840  with negative refractive power has an object-side surface  841  being convex in a paraxial region thereof and an image-side surface  842  being concave in a paraxial region thereof. The fourth lens element  840  is made of plastic material and has the object-side surface  841  and the image-side surface  842  being both aspheric. The object-side surface  841  of the fourth lens element  840  has one inflection point. The image-side surface  842  of the fourth lens element  840  has one inflection point. The object-side surface  841  of the fourth lens element  840  has one critical point in an off-axis region thereof. The image-side surface  842  of the fourth lens element  840  has one critical point in an off-axis region thereof. 
     The fifth lens element  850  with positive refractive power has an object-side surface  851  being convex in a paraxial region thereof and an image-side surface  852  being convex in a paraxial region thereof. The fifth lens element  850  is made of plastic material and has the object-side surface  851  and the image-side surface  852  being both aspheric. The object-side surface  851  of the fifth lens element  850  has two inflection points. The image-side surface  852  of the fifth lens element  850  has one inflection point. The object-side surface  851  of the fifth lens element  850  has one critical point in an off-axis region thereof. 
     The sixth lens element  860  with negative refractive power has an object-side surface  861  being concave in a paraxial region thereof and an image-side surface  862  being convex in a paraxial region thereof. The sixth lens element  860  is made of plastic material and has the object-side surface  861  and the image-side surface  862  being both aspheric. The object-side surface  861  of the sixth lens element  860  has two inflection points. The image-side surface  862  of the sixth lens element  860  has one inflection point. The image-side surface  862  of the sixth lens element  860  has one critical point in an off-axis region thereof. 
     The seventh lens element  870  with positive refractive power has an object-side surface  871  being convex in a paraxial region thereof and an image-side surface  872  being concave in a paraxial region thereof. The seventh lens element  870  is made of plastic material and has the object-side surface  871  and the image-side surface  872  being both aspheric. The object-side surface  871  of the seventh lens element  870  has two inflection points. The image-side surface  872  of the seventh lens element  870  has two inflection points. The object-side surface  871  of the seventh lens element  870  has one critical point in an off-axis region thereof. The image-side surface  872  of the seventh lens element  870  has one critical point in an off-axis region thereof. 
     The eighth lens element  880  with negative refractive power has an object-side surface  881  being convex in a paraxial region thereof and an image-side surface  882  being concave in a paraxial region thereof. The eighth lens element  880  is made of plastic material and has the object-side surface  881  and the image-side surface  882  being both aspheric. The object-side surface  881  of the eighth lens element  880  has four inflection points. The image-side surface  882  of the eighth lens element  880  has four inflection points. The object-side surface  881  of the eighth lens element  880  has one critical point in an off-axis region thereof. The image-side surface  882  of the eighth lens element  880  has one critical point in an off-axis region thereof. 
     The filter  890  is made of glass material and located between the eighth lens element  880  and the image surface  895 , and will not affect the focal length of the photographing optical system. The image sensor  899  is disposed on or near the image surface  895  of the photographing optical system. 
     The detailed optical data of the 8th embodiment are shown in Table 15 and the aspheric surface data are shown in Table 16 below. 
     
       
         
           
               
             
               
                 TABLE 15 
               
             
            
               
                   
               
               
                 8th Embodiment 
               
               
                 f = 5.67 mm, Fno = 1.51, HFOV = 39.6 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.534  
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 3.428 
                 (ASP) 
                 0.883 
                 Plastic 
                 1.545 
                 56.1 
                 7.79 
               
               
                 3 
                   
                 16.214 
                 (ASP) 
                 0.035 
               
               
                 4 
                 Lens 2 
                 3.600 
                 (ASP) 
                 0.310 
                 Plastic 
                 1.669 
                 19.5 
                 −24.99 
               
               
                 5 
                   
                 2.860 
                 (ASP) 
                 0.397 
               
               
                 6 
                 Lens 3 
                 6.292 
                 (ASP) 
                 0.320 
                 Plastic 
                 1.669 
                 19.5 
                 −237.44 
               
               
                 7 
                   
                 5.929 
                 (ASP) 
                 0.037 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 8 
                 Stop 
                 Plano 
                 0.188 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 9 
                 Lens 4 
                 9.244 
                 (ASP) 
                 0.340 
                 Plastic 
                 1.669 
                 19.5 
                 −237.72 
               
               
                 10 
                   
                 8.608 
                 (ASP) 
                 0.096 
               
               
                 11 
                 Lens 5 
                 50.195 
                 (ASP) 
                 1.164 
                 Plastic 
                 1.544 
                 56.0 
                 8.19 
               
               
                 12 
                   
                 −4.848 
                 (ASP) 
                 0.193 
               
               
                 13 
                 Lens 6 
                 −1.740 
                 (ASP) 
                 0.378 
                 Plastic 
                 1.669 
                 19.5 
                 −19.06 
               
               
                 14 
                   
                 −2.191 
                 (ASP) 
                 0.035 
               
               
                 15 
                 Lens 7 
                 1.984 
                 (ASP) 
                 0.555 
                 Plastic 
                 1.544 
                 56.0 
                 11.97 
               
               
                 16 
                   
                 2.572 
                 (ASP) 
                 1.020 
               
               
                 17 
                 Lens 8 
                 3.415 
                 (ASP) 
                 0.510 
                 Plastic 
                 1.545 
                 56.1 
                 −9.41 
               
               
                 18 
                   
                 1.942 
                 (ASP) 
                 0.600 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 19 
                 Filter 
                 Plano 
                 0.210 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 20 
                   
                 Plano 
                 0.581 
               
               
                 21 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 801 (Surface 8) is 1.690 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 16 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 k = 
                 −1.7305E+00 
                  0.0000E+00 
                 −1.2625E+00 
                  2.1940E−01 
                 1.4551E+00 
                 −3.1361E−01 
               
               
                 A4 = 
                  4.9471E−03 
                 −2.1364E−02 
                 −3.0922E−02 
                 −1.9983E−02 
                 −2.0200E−02  
                 −3.4239E−02 
               
               
                 A6 = 
                  1.9867E−03 
                  1.2095E−02 
                  3.5897E−03 
                 −1.3527E−02 
                 2.5809E−03 
                  1.2158E−02 
               
               
                 A8 = 
                 −2.0137E−03 
                 −6.0456E−03 
                 −2.7015E−03 
                  7.2857E−03 
                 −5.5344E−03  
                 −1.3972E−02 
               
               
                 A10 = 
                  1.0166E−03 
                  2.4414E−03 
                  3.0576E−03 
                 −2.7942E−03 
                 1.4978E−03 
                  7.9503E−03 
               
               
                 A12 = 
                 −2.8845E−04 
                 −6.8271E−04 
                 −1.3247E−03 
                  8.2538E−04 
                 8.4562E−05 
                 −2.1414E−03 
               
               
                 A14 = 
                  4.1534E−05 
                  1.0587E−04 
                  2.5267E−04 
                 −2.1391E−04 
                 −1.7155E−04  
                  2.4448E−04 
               
               
                 A16 = 
                 −2.6336E−06 
                 −6.6604E−06 
                 −1.6042E−05 
                  2.8250E−05 
                 3.1195E−05 
                 −9.3062E−06 
               
               
                   
               
               
                 Surface # 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
               
               
                   
               
               
                 k = 
                  0.0000E+00 
                 5.5358E+00 
                 0.0000E+00 
                 −4.9658E−02 
                 −1.0000E+00 
                 −1.0000E+00 
               
               
                 A4 = 
                 −3.7301E−02 
                 −3.5065E−02  
                 −2.4897E−02  
                 −4.0500E−02 
                  7.2719E−02 
                  3.6045E−02 
               
               
                 A6 = 
                  1.3115E−02 
                 3.4172E−02 
                 3.6747E−02 
                  1.3341E−02 
                 −6.9643E−02 
                 −3.6883E−02 
               
               
                 A8 = 
                 −1.8395E−02 
                 −4.0870E−02  
                 −3.6580E−02  
                 −1.4145E−03 
                  5.8201E−02 
                  3.1020E−02 
               
               
                 A10 = 
                  1.0897E−02 
                 2.7491E−02 
                 2.0030E−02 
                 −2.2885E−03 
                 −3.3615E−02 
                 −1.6529E−02 
               
               
                 A12 = 
                 −1.7033E−03 
                 −1.0580E−02  
                 −5.5609E−03  
                  1.4981E−03 
                  1.3105E−02 
                  5.8302E−03 
               
               
                 A14 = 
                 −6.8261E−04 
                 2.2669E−03 
                 1.4281E−04 
                 −4.1206E−04 
                 −3.2313E−03 
                 −1.3177E−03 
               
               
                 A16 = 
                  2.8286E−04 
                 −2.4481E−04  
                 3.3305E−04 
                  5.2440E−05 
                  4.7217E−04 
                  1.8481E−04 
               
               
                 A18 = 
                 −3.1526E−05 
                 9.7038E−06 
                 −7.8024E−05  
                 −2.3456E−06 
                 −3.6496E−05 
                 −1.4816E−05 
               
               
                 A20 = 
                 — 
                 — 
                 5.5633E−06 
                 −4.2338E−09 
                  1.0955E−06 
                  5.2183E−07 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface # 
                 15 
                 16 
                 17 
                 18 
               
               
                   
                   
               
               
                   
                 k = 
                 −1.0000E+00 
                 −1.0000E+00 
                 −1.0000E+00 
                  1.0000E+00 
               
               
                   
                 A4 = 
                 −4.9892E−02 
                 −3.6695E−03 
                 −9.9850E−02 
                 −1.0842E−01 
               
               
                   
                 A6 = 
                  1.5818E−02 
                 −3.5100E−03 
                  2.3121E−02 
                  3.1129E−02 
               
               
                   
                 A8 = 
                 −7.5900E−03 
                 −8.2471E−04 
                 −3.8552E−03 
                 −7.4738E−03 
               
               
                   
                 A10 = 
                  2.1914E−03 
                  5.5081E−04 
                  5.5559E−04 
                  1.3379E−03 
               
               
                   
                 A12 = 
                 −4.3550E−04 
                 −1.1744E−04 
                 −6.6598E−05 
                 −1.6973E−04 
               
               
                   
                 A14 = 
                  6.2691E−05 
                  1.3489E−05 
                  5.9463E−06 
                  1.4443E−05 
               
               
                   
                 A16 = 
                 −6.4685E−06 
                 −8.8149E−07 
                 −3.5648E−07 
                 −7.6824E−07 
               
               
                   
                 A18 = 
                  4.2414E−07 
                  3.0153E−08 
                  1.2545E−08 
                  2.2828E−08 
               
               
                   
                 A20 = 
                 −1.2584E−08 
                 −4.0331E−10 
                 −1.9301E−10 
                 −2.8775E−10 
               
               
                   
                   
               
            
           
         
       
     
     In the 8th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 8th embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 15 and Table 16 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 8th Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 5.67 
                 R3/R4 
                 1.26 
               
               
                 Fno 
                 1.51 
                 (R9 + R10)/(R9 − R10) 
                 0.82 
               
               
                 HFOV [deg.] 
                 39.6 
                 f/f1 
                 0.73 
               
               
                 (Vi/Ni)min 
                 11.65 
                 f/f2 
                 −0.23 
               
               
                 V2 
                 19.5 
                 |f/f2| + |f/f3| 
                 0.25 
               
               
                 V2 + V3 + V4 
                 58.4 
                 f/f2 + f/f3 + f/f4 
                 −0.27 
               
               
                 V2 + V4 
                 38.9 
                 f/f3 
                 −0.02 
               
               
                 V2/N2 
                 11.65 
                 f/f4 
                 −0.02 
               
               
                 V6 
                 19.5 
                 f/f5 
                 0.69 
               
               
                 ΣCT/CT5 
                 3.83 
                 f/f6 
                 −0.30 
               
               
                 (CT2 + CT3 + CT4)/ 
                 0.47 
                 f/f7 
                 0.47 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 1.03 
                 f/f8 
                 −0.60 
               
               
                 CT5/CT1 
                 1.32 
                 f/f12 
                 0.55 
               
               
                 CT5/CT3 
                 3.64 
                 f/f23 
                 −0.26 
               
               
                 CT7/CT5 
                 0.48 
                 f/|R11| + f/|R12| 
                 5.85 
               
               
                 TD/CT5 
                 5.55 
                 f5/CT5 
                 7.03 
               
               
                 TD/f2 
                 −0.26 
                 f5/f1 
                 1.05 
               
               
                 TL [mm] 
                 7.85 
                 f8/f7 
                 −0.79 
               
               
                 TL/f 
                 1.38 
                 Y82/Y11 
                 2.07 
               
               
                 TL/ImgH 
                 1.64 
                 Yc72/Yc71 
                 1.28 
               
               
                 R1/R2 
                 0.21 
                 Yc82/Y82 
                 0.44 
               
               
                 R3/f 
                 0.63 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     9th Embodiment 
       FIG. 17  is a schematic view of an image capturing unit according to the 9th embodiment of the present disclosure.  FIG. 18  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 9th embodiment. In  FIG. 17 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  999 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  900 , a first lens element  910 , a second lens element  920 , a stop  901 , a third lens element  930 , a fourth lens element  940 , a stop  902 , a fifth lens element  950 , a sixth lens element  960 , a seventh lens element  970 , an eighth lens element  980 , a filter  990  and an image surface  995 . The photographing optical system includes eight lens elements ( 910 ,  920 ,  930 ,  940 ,  950 ,  960 ,  970  and  980 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  910  with positive refractive power has an object-side surface  911  being convex in a paraxial region thereof and an image-side surface  912  being concave in a paraxial region thereof. The first lens element  910  is made of plastic material and has the object-side surface  911  and the image-side surface  912  being both aspheric. The image-side surface  912  of the first lens element  910  has three inflection points. 
     The second lens element  920  with positive refractive power has an object-side surface  921  being convex in a paraxial region thereof and an image-side surface  922  being concave in a paraxial region thereof. The second lens element  920  is made of plastic material and has the object-side surface  921  and the image-side surface  922  being both aspheric. The image-side surface  922  of the second lens element  920  has one inflection point. The image-side surface  922  of the second lens element  920  has one critical point in an off-axis region thereof. 
     The third lens element  930  with positive refractive power has an object-side surface  931  being concave in a paraxial region thereof and an image-side surface  932  being convex in a paraxial region thereof. The third lens element  930  is made of plastic material and has the object-side surface  931  and the image-side surface  932  being both aspheric. The object-side surface  931  of the third lens element  930  has two inflection points. The image-side surface  932  of the third lens element  930  has three inflection points. The image-side surface  932  of the third lens element  930  has three critical points in an off-axis region thereof. 
     The fourth lens element  940  with negative refractive power has an object-side surface  941  being concave in a paraxial region thereof and an image-side surface  942  being concave in a paraxial region thereof. The fourth lens element  940  is made of plastic material and has the object-side surface  941  and the image-side surface  942  being both aspheric. The object-side surface  941  of the fourth lens element  940  has three inflection points. The image-side surface  942  of the fourth lens element  940  has three inflection points. The image-side surface  942  of the fourth lens element  940  has one critical point in an off-axis region thereof. 
     The fifth lens element  950  with positive refractive power has an object-side surface  951  being convex in a paraxial region thereof and an image-side surface  952  being concave in a paraxial region thereof. The fifth lens element  950  is made of plastic material and has the object-side surface  951  and the image-side surface  952  being both aspheric. The image-side surface  952  of the fifth lens element  950  has two inflection points. The image-side surface  952  of the fifth lens element  950  has one critical point in an off-axis region thereof. 
     The sixth lens element  960  with negative refractive power has an object-side surface  961  being convex in a paraxial region thereof and an image-side surface  962  being concave in a paraxial region thereof. The sixth lens element  960  is made of plastic material and has the object-side surface  961  and the image-side surface  962  being both aspheric. The object-side surface  961  of the sixth lens element  960  has one inflection point. The image-side surface  962  of the sixth lens element  960  has two inflection points. The object-side surface  961  of the sixth lens element  960  has one critical point in an off-axis region thereof. The image-side surface  962  of the sixth lens element  960  has one critical point in an off-axis region thereof. 
     The seventh lens element  970  with positive refractive power has an object-side surface  971  being convex in a paraxial region thereof and an image-side surface  972  being convex in a paraxial region thereof. The seventh lens element  970  is made of plastic material and has the object-side surface  971  and the image-side surface  972  being both aspheric. The object-side surface  971  of the seventh lens element  970  has two inflection points. The image-side surface  972  of the seventh lens element  970  has four inflection points. The object-side surface  971  of the seventh lens element  970  has one critical point in an off-axis region thereof. The image-side surface  972  of the seventh lens element  970  has two critical points in an off-axis region thereof. 
     The eighth lens element  980  with negative refractive power has an object-side surface  981  being concave in a paraxial region thereof and an image-side surface  982  being concave in a paraxial region thereof. The eighth lens element  980  is made of plastic material and has the object-side surface  981  and the image-side surface  982  being both aspheric. The object-side surface  981  of the eighth lens element  980  has one inflection point. The image-side surface  982  of the eighth lens element  980  has one inflection point. The image-side surface  982  of the eighth lens element  980  has one critical point in an off-axis region thereof. 
     The filter  990  is made of glass material and located between the eighth lens element  980  and the image surface  995 , and will not affect the focal length of the photographing optical system. The image sensor  999  is disposed on or near the image surface  995  of the photographing optical system. 
     The detailed optical data of the 9th embodiment are shown in Table 17 and the aspheric surface data are shown in Table 18 below. 
     
       
         
           
               
             
               
                 TABLE 17 
               
             
            
               
                   
               
               
                 9th Embodiment 
               
               
                 f = 5.69 mm, Fno = 1.47, HFOV = 39.7 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.641 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 3.533 
                 (ASP) 
                 0.771 
                 Plastic 
                 1.545 
                 56.1 
                 10.13 
               
               
                 3 
                   
                 9.063 
                 (ASP) 
                 0.020 
               
               
                 4 
                 Lens 2 
                 2.590 
                 (ASP) 
                 0.235 
                 Plastic 
                 1.679 
                 18.4 
                 101.16 
               
               
                 5 
                   
                 2.593 
                 (ASP) 
                 0.426 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 6 
                 Stop 
                 Plano 
                 0.349 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 Lens 3 
                 −195.313 
                 (ASP) 
                 0.336 
                 Plastic 
                 1.679 
                 18.4 
                 93.51 
               
               
                 8 
                   
                 −47.962 
                 (ASP) 
                 0.020 
               
               
                 9 
                 Lens 4 
                 −229.606 
                 (ASP) 
                 0.263 
                 Plastic 
                 1.639 
                 23.5 
                 −9.37 
               
               
                 10 
                   
                 6.146 
                 (ASP) 
                 0.113 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 11 
                 Stop 
                 Plano 
                 −0.066 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 12 
                 Lens 5 
                 7.570 
                 (ASP) 
                 1.173 
                 Plastic 
                 1.544 
                 56.0 
                 14.29 
               
               
                 13 
                   
                 269.542 
                 (ASP) 
                 0.282 
               
               
                 14 
                 Lens 6 
                 4.631 
                 (ASP) 
                 0.680 
                 Plastic 
                 1.562 
                 44.6 
                 −30.94 
               
               
                 15 
                   
                 3.464 
                 (ASP) 
                 0.158 
               
               
                 16 
                 Lens 7 
                 2.035 
                 (ASP) 
                 0.659 
                 Plastic 
                 1.544 
                 56.0 
                 3.70 
               
               
                 17 
                   
                 −188.679 
                 (ASP) 
                 0.897 
               
               
                 18 
                 Lens 8 
                 −13.062 
                 (ASP) 
                 0.350 
                 Plastic 
                 1.534 
                 55.9 
                 −4.04 
               
               
                 19 
                   
                 2.611 
                 (ASP) 
                 0.560 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 20 
                 Filter 
                 Plano 
                 0.110 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 21 
                   
                 Plano 
                 0.556 
               
               
                 22 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 901 (Surface 6) is 1.738 mm. 
               
               
                 active radius of the stop 902 (Surface 11) is 2.074 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 18 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                  5.3870E−02 
                 −9.9000E+01 
                 −6.6463E+00 
                 −4.5732E+00 
                 −9.9000E+01 
                 −9.9000E+01 
               
               
                 A4 = 
                  4.5974E−03 
                 −4.1530E−02 
                 −1.4312E−02 
                  1.8460E−02 
                  1.2173E−02 
                  6.8900E−02 
               
               
                 A6 = 
                 −8.8344E−04 
                  3.9438E−02 
                 −1.9189E−02 
                 −5.1369E−02 
                 −3.0855E−02 
                 −7.4555E−02 
               
               
                 A8 = 
                 −8.5696E−04 
                 −1.8042E−02 
                  3.0911E−02 
                  4.2622E−02 
                  5.2873E−03 
                  2.9837E−02 
               
               
                 A10 = 
                  1.3077E−03 
                  4.8140E−03 
                 −1.9234E−02 
                 −1.8801E−02 
                 −7.0960E−04 
                 −6.1939E−03 
               
               
                 A12 = 
                 −6.0344E−04 
                 −6.8608E−04 
                  6.4091E−03 
                  4.2737E−03 
                  5.3096E−04 
                  5.7945E−04 
               
               
                 A14 = 
                  1.3052E−04 
                  3.8796E−05 
                 −1.1297E−03 
                 −4.0056E−04 
                 −1.0803E−04 
                 — 
               
               
                 A16 = 
                 −1.0982E−05 
                 − 
                  8.3137E−05 
                 — 
                 — 
                 — 
               
               
                   
               
               
                 Surface # 
                 9 
                 10 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 k = 
                 9.0000E+01 
                  4.1332E+00 
                  5.1893E+00 
                  9.0000E+01 
                 −5.9873E+01  
                 −6.1866E+00 
               
               
                 A4 = 
                 2.4018E−03 
                 −5.2518E−02 
                  5.3577E−03 
                 −3.0806E−02 
                 1.7289E−03 
                 −1.3528E−01 
               
               
                 A6 = 
                 −2.5230E−02  
                  1.6565E−02 
                 −1.3508E−02 
                  1.5587E−02 
                 2.8606E−03 
                  7.3277E−02 
               
               
                 A8 = 
                 2.5354E−02 
                 −1.3403E−03 
                  6.7561E−03 
                 −1.0595E−02 
                 −4.4874E−03  
                 −2.7914E−02 
               
               
                 A10 = 
                 −1.0110E−02  
                  3.9710E−04 
                 −1.5311E−03 
                  3.8383E−03 
                 1.4402E−03 
                  6.6565E−03 
               
               
                 A12 = 
                 1.7396E−03 
                 −5.3271E−04 
                  1.5083E−04 
                 −7.4337E−04 
                 −3.7219E−04  
                 −1.0401E−03 
               
               
                 A14 = 
                 −1.0558E−04  
                  1.4793E−04 
                 −1.0665E−06 
                  7.3950E−05 
                 8.4162E−05 
                  1.1068E−04 
               
               
                 A16 = 
                 — 
                 −1.2842E−05 
                 −5.7391E−07 
                 −2.9214E−06 
                 −1.0693E−05  
                 −7.2841E−06 
               
               
                 A18 = 
                 — 
                 — 
                 — 
                 — 
                 5.0813E−07 
                  2.1496E−07 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface # 
                 16 
                 17 
                 18 
                 19 
               
               
                   
                   
               
               
                   
                 k = 
                 −7.0247E−01 
                 −9.9000E+01 
                  9.3821E+00 
                 −1.6981E+00 
               
               
                   
                 A4 = 
                 −6.3664E−02 
                  9.1981E−02 
                 −6.1133E−02 
                 −8.3365E−02 
               
               
                   
                 A6 = 
                  6.4182E−03 
                 −5.8061E−02 
                 −3.5240E−03 
                  2.0710E−02 
               
               
                   
                 A8 = 
                  7.3294E−04 
                  1.8445E−02 
                  8.0553E−03 
                 −3.0238E−03 
               
               
                   
                 A10 = 
                 −1.8560E−03 
                 −3.7362E−03 
                 −2.2045E−03 
                  2.4783E−04 
               
               
                   
                 A12 = 
                  7.2607E−04 
                  4.9469E−04 
                  3.0998E−04 
                 −7.8099E−06 
               
               
                   
                 A14 = 
                 −1.3597E−04 
                 −4.2291E−05 
                 −2.5933E−05 
                 −4.2273E−07 
               
               
                   
                 A16 = 
                  1.2692E−05 
                  2.2505E−06 
                  1.3057E−06 
                  5.0517E−08 
               
               
                   
                 A18 = 
                 −4.6653E−07 
                 −6.8088E−08 
                 −3.6682E−08 
                 −1.8635E−09 
               
               
                   
                 A20 = 
                 — 
                  9.0052E−10 
                  4.4343E−10 
                  2.5048E−11 
               
               
                   
                   
               
            
           
         
       
     
     In the 9th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 9th embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 17 and Table 18 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 9th Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 5.69 
                 R3/R4 
                 1.00 
               
               
                 Fno 
                 1.47 
                 (R9 + R10)/(R9 − R10) 
                 −1.06 
               
               
                 HFOV [deg.] 
                 39.7 
                 f/f1 
                 0.56 
               
               
                 (Vi/Ni)min 
                 10.98 
                 f/f2 
                 0.06 
               
               
                 V2 
                 18.4 
                 |f/f2| + |f/f3| 
                 0.12 
               
               
                 V2 + V3 + V4 
                 60.4 
                 f/f2 + f/f3 + f/f4 
                 −0.49 
               
               
                 V2 + V4 
                 41.9 
                 f/f3 
                 0.06 
               
               
                 V2/N2 
                 10.98 
                 f/f4 
                 −0.61 
               
               
                 V6 
                 44.6 
                 f/f5 
                 0.40 
               
               
                 ΣCT/CT5 
                 3.81 
                 f/f6 
                 −0.18 
               
               
                 (CT2 + CT3 + CT4)/ 
                 0.43 
                 f/f7 
                 1.54 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 1.43 
                 f/f8 
                 −1.41 
               
               
                 CT5/CT1 
                 1.52 
                 f/f12 
                 0.63 
               
               
                 CT5/CT3 
                 3.49 
                 f/f23 
                 0.11 
               
               
                 CT7/CT5 
                 0.56 
                 f/|R11| + f/|R12| 
                 2.87 
               
               
                 TD/CT5 
                 5.68 
                 f5/CT5 
                 12.18 
               
               
                 TD/f2 
                 0.07 
                 f5/f1 
                 1.41 
               
               
                 TL [mm] 
                 7.89 
                 f8/f7 
                 −1.09 
               
               
                 TL/f 
                 1.39 
                 Y82/Y11 
                 2.07 
               
               
                 TL/ImgH 
                 1.65 
                 Yc72/Yc71 
                 0.08; 1.09 
               
               
                 R1/R2 
                 0.39 
                 Yc82/Y82 
                 0.38 
               
               
                 R3/f 
                 0.46 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     10th Embodiment 
       FIG. 19  is a schematic view of an image capturing unit according to the 10th embodiment of the present disclosure.  FIG. 20  shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 10th embodiment. In  FIG. 19 , the image capturing unit includes the photographing optical system (its reference numeral is omitted) of the present disclosure and an image sensor  1099 . The photographing optical system includes, in order from an object side to an image side, an aperture stop  1000 , a first lens element  1010 , a second lens element  1020 , a third lens element  1030 , a stop  1001 , a fourth lens element  1040 , a fifth lens element  1050 , a sixth lens element  1060 , a seventh lens element  1070 , an eighth lens element  1080 , a filter  1090  and an image surface  1095 . The photographing optical system includes eight lens elements ( 1010 ,  1020 ,  1030 ,  1040 ,  1050 ,  1060 ,  1070  and  1080 ) with no additional lens element disposed between each of the adjacent eight lens elements. 
     The first lens element  1010  with positive refractive power has an object-side surface  1011  being convex in a paraxial region thereof and an image-side surface  1012  being concave in a paraxial region thereof. The first lens element  1010  is made of plastic material and has the object-side surface  1011  and the image-side surface  1012  being both aspheric. The object-side surface  1011  of the first lens element  1010  has one inflection point. The image-side surface  1012  of the first lens element  1010  has one inflection point. 
     The second lens element  1020  with positive refractive power has an object-side surface  1021  being convex in a paraxial region thereof and an image-side surface  1022  being concave in a paraxial region thereof. The second lens element  1020  is made of plastic material and has the object-side surface  1021  and the image-side surface  1022  being both aspheric. 
     The third lens element  1030  with negative refractive power has an object-side surface  1031  being convex in a paraxial region thereof and an image-side surface  1032  being concave in a paraxial region thereof. The third lens element  1030  is made of plastic material and has the object-side surface  1031  and the image-side surface  1032  being both aspheric. 
     The fourth lens element  1040  with negative refractive power has an object-side surface  1041  being convex in a paraxial region thereof and an image-side surface  1042  being concave in a paraxial region thereof. The fourth lens element  1040  is made of plastic material and has the object-side surface  1041  and the image-side surface  1042  being both aspheric. The object-side surface  1041  of the fourth lens element  1040  has one inflection point. The image-side surface  1042  of the fourth lens element  1040  has two inflection points. The object-side surface  1041  of the fourth lens element  1040  has one critical point in an off-axis region thereof. The image-side surface  1042  of the fourth lens element  1040  has two critical points in an off-axis region thereof. 
     The fifth lens element  1050  with positive refractive power has an object-side surface  1051  being convex in a paraxial region thereof and an image-side surface  1052  being convex in a paraxial region thereof. The fifth lens element  1050  is made of plastic material and has the object-side surface  1051  and the image-side surface  1052  being both aspheric. The object-side surface  1051  of the fifth lens element  1050  has two inflection points. The image-side surface  1052  of the fifth lens element  1050  has one inflection point. The object-side surface  1051  of the fifth lens element  1050  has two critical points in an off-axis region thereof. 
     The sixth lens element  1060  with positive refractive power has an object-side surface  1061  being convex in a paraxial region thereof and an image-side surface  1062  being convex in a paraxial region thereof. The sixth lens element  1060  is made of plastic material and has the object-side surface  1061  and the image-side surface  1062  being both aspheric. The object-side surface  1061  of the sixth lens element  1060  has two inflection points. The image-side surface  1062  of the sixth lens element  1060  has two inflection points. The object-side surface  1061  of the sixth lens element  1060  has one critical point in an off-axis region thereof. 
     The seventh lens element  1070  with positive refractive power has an object-side surface  1071  being convex in a paraxial region thereof and an image-side surface  1072  being convex in a paraxial region thereof. The seventh lens element  1070  is made of plastic material and has the object-side surface  1071  and the image-side surface  1072  being both aspheric. The object-side surface  1071  of the seventh lens element  1070  has two inflection points. The image-side surface  1072  of the seventh lens element  1070  has three inflection points. The object-side surface  1071  of the seventh lens element  1070  has one critical point in an off-axis region thereof. The image-side surface  1072  of the seventh lens element  1070  has two critical points in an off-axis region thereof. 
     The eighth lens element  1080  with negative refractive power has an object-side surface  1081  being concave in a paraxial region thereof and an image-side surface  1082  being concave in a paraxial region thereof. The eighth lens element  1080  is made of plastic material and has the object-side surface  1081  and the image-side surface  1082  being both aspheric. The object-side surface  1081  of the eighth lens element  1080  has one inflection point. The image-side surface  1082  of the eighth lens element  1080  has two inflection points. The object-side surface  1081  of the eighth lens element  1080  has one critical point in an off-axis region thereof. The image-side surface  1082  of the eighth lens element  1080  has one critical point in an off-axis region thereof. 
     The filter  1090  is made of glass material and located between the eighth lens element  1080  and the image surface  1095 , and will not affect the focal length of the photographing optical system. The image sensor  1099  is disposed on or near the image surface  1095  of the photographing optical system. 
     The detailed optical data of the 10th embodiment are shown in Table 19 and the aspheric surface data are shown in Table 20 below. 
     
       
         
           
               
             
               
                 TABLE 19 
               
             
            
               
                   
               
               
                 10th Embodiment 
               
               
                 f = 5.72 mm, Fno = 1.50, HFOV = 39.6 deg. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface # 
                   
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 Focal Length 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 Infinity 
                   
               
               
                 1 
                 Ape. Stop 
                 Plano 
                 −0.844  
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 2 
                 Lens 1 
                 2.445 
                 (ASP) 
                 0.386 
                 Plastic 
                 1.545 
                 56.1 
                 28.34 
               
               
                 3 
                   
                 2.744 
                 (ASP) 
                 0.084 
               
               
                 4 
                 Lens 2 
                 2.706 
                 (ASP) 
                 0.865 
                 Plastic 
                 1.544 
                 56.0 
                 6.04 
               
               
                 5 
                   
                 13.577 
                 (ASP) 
                 0.039 
               
               
                 6 
                 Lens 3 
                 14.169 
                 (ASP) 
                 0.201 
                 Plastic 
                 1.660 
                 20.4 
                 −13.61 
               
               
                 7 
                   
                 5.466 
                 (ASP) 
                 0.346 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 8 
                 Stop 
                 Plano 
                 0.181 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 9 
                 Lens 4 
                 9.970 
                 (ASP) 
                 0.346 
                 Plastic 
                 1.679 
                 18.4 
                 −22.13 
               
               
                 10 
                   
                 5.910 
                 (ASP) 
                 0.083 
               
               
                 11 
                 Lens 5 
                 15.883 
                 (ASP) 
                 0.616 
                 Plastic 
                 1.544 
                 56.0 
                 17.99 
               
               
                 12 
                   
                 −25.166 
                 (ASP) 
                 0.424 
               
               
                 13 
                 Lens 6 
                 60.496 
                 (ASP) 
                 0.542 
                 Plastic 
                 1.562 
                 44.6 
                 17.88 
               
               
                 14 
                   
                 −12.003 
                 (ASP) 
                 0.196 
               
               
                 15 
                 Lens 7 
                 4.529 
                 (ASP) 
                 0.572 
                 Plastic 
                 1.562 
                 44.6 
                 7.48 
               
               
                 16 
                   
                 −56.116 
                 (ASP) 
                 0.440 
               
               
                 17 
                 Lens 8 
                 −10.012 
                 (ASP) 
                 0.501 
                 Plastic 
                 1.544 
                 56.0 
                 −3.83 
               
               
                 18 
                   
                 2.678 
                 (ASP) 
                 0.500 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 19 
                 Filter 
                 Plano 
                 0.210 
                 Glass 
                 1.517 
                 64.2 
                 — 
               
               
                 20 
                   
                 Piano 
                 0.555 
               
               
                 21 
                 Image 
                 Plano 
                 — 
               
               
                   
               
               
                 reference wavelength is 587.6 nm (d-line). 
               
               
                 active radius of the stop 1001 (Surface 8) is 1.500 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 20 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface # 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 k = 
                 −5.2842E−01 
                 −1.8831E−01 
                 2.4101E−02 
                 −2.6045E+01 
                  4.9631E+01 
                  7.0418E+00 
               
               
                 A4 = 
                  1.2124E−02 
                  2.7068E−02 
                 2.6756E−02 
                 −2.6191E−02 
                 −4.5547E−02 
                 −2.6192E−02 
               
               
                 A6 = 
                 −1.8345E−02 
                 −5.8215E−02 
                 −5.2980E−02  
                  3.7484E−02 
                  7.4578E−02 
                  5.3498E−02 
               
               
                 A8 = 
                  1.9477E−02 
                  5.8120E−02 
                 5.4303E−02 
                 −3.7351E−02 
                 −7.7054E−02 
                 −6.2683E−02 
               
               
                 A10 = 
                 −1.1387E−02 
                 −3.5615E−02 
                 −3.4819E−02  
                  2.3436E−02 
                  5.3776E−02 
                  4.9386E−02 
               
               
                 A12 = 
                  3.7248E−03 
                  1.2858E−02 
                 1.3195E−02 
                 −8.5410E−03 
                 −2.2423E−02 
                 −2.2964E−02 
               
               
                 A14 = 
                 −6.0339E−04 
                 −2.3953E−03 
                 −2.6400E−03  
                  1.6491E−03 
                  5.0395E−03 
                  5.5782E−03 
               
               
                 A16 = 
                  3.5261E−05 
                  1.7323E−04 
                 2.1609E−04 
                 −1.2761E−04 
                 −4.6565E−04 
                 −5.2375E−04 
               
               
                   
               
               
                 Surface # 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
               
               
                   
               
               
                 k = 
                 −5.7273E+01 
                 −4.0888E+01 
                 −9.9000E+01 
                  1.5723E+01 
                  7.3041E+01 
                 −8.2931E+01 
               
               
                 A4 = 
                 −5.1074E−02 
                 −6.0479E−02 
                 −7.6504E−02 
                 −3.5651E−02 
                 −2.1057E−02 
                 −6.0127E−02 
               
               
                 A6 = 
                  5.0927E−02 
                  8.2757E−02 
                  9.1098E−02 
                 −2.5262E−03 
                  2.4249E−02 
                  1.2408E−02 
               
               
                 A8 = 
                 −8.4256E−02 
                 −1.0545E−01 
                 −8.6447E−02 
                  1.0972E−02 
                 −3.7517E−02 
                  8.5960E−03 
               
               
                 A10 = 
                  6.9584E−02 
                  7.3822E−02 
                  5.1025E−02 
                 −1.0443E−02 
                  3.1611E−02 
                 −9.2482E−03 
               
               
                 A12 = 
                 −3.4194E−02 
                 −3.0221E−02 
                 −1.5929E−02 
                  5.7042E−03 
                 −1.7240E−02 
                  3.7602E−03 
               
               
                 A14 = 
                  9.0841E−03 
                  6.1145E−03 
                  1.0332E−03 
                 −1.5605E−03 
                  5.9918E−03 
                 −8.1769E−04 
               
               
                 A16 = 
                 −9.6747E−04 
                 −1.2414E−05 
                  8.8375E−04 
                  1.2444E−04 
                 −1.2592E−03 
                  1.0037E−04 
               
               
                 A18 = 
                 — 
                 −1.9490E−04 
                 −2.5501E−04 
                  2.1436E−05 
                  1.4317E−04 
                 −6.5787E−06 
               
               
                 A20 = 
                 — 
                  2.1230E−05 
                  2.1343E−05 
                 −3.1508E−06 
                 −6.6699E−06 
                  1.7941E−07 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface # 
                 15 
                 16 
                 17 
                 18 
               
               
                   
                   
               
               
                   
                 k = 
                  7.5590E−02 
                 −9.9000E+01 
                  1.6318E+00 
                 −7.3600E−01 
               
               
                   
                 A4 = 
                 −3.2409E−02 
                  6.5170E−02 
                 −5.0388E−02 
                 −9.7127E−02 
               
               
                   
                 A6 = 
                 −3.0029E−02 
                 −7.8366E−02 
                 −1.0355E−02 
                  2.7965E−02 
               
               
                   
                 A8 = 
                  1.8953E−02 
                  3.4447E−02 
                  9.2490E−03 
                 −6.0303E−03 
               
               
                   
                 A10 = 
                 −5.4856E−03 
                 −8.8871E−03 
                 −2.1967E−03 
                  9.4704E−04 
               
               
                   
                 A12 = 
                  7.4636E−04 
                  1.3955E−03 
                  2.8330E−04 
                 −1.0708E−04 
               
               
                   
                 A14 = 
                 −4.0355E−05 
                 −1.2785E−04 
                 −2.2323E−05 
                  8.3262E−06 
               
               
                   
                 A16 = 
                  1.0710E−06 
                  5.8516E−06 
                  1.0814E−06 
                 −4.1660E−07 
               
               
                   
                 A18 = 
                 −1.9346E−07 
                 −5.3679E−08 
                 −2.9797E−08 
                  1.1994E−08 
               
               
                   
                 A20 = 
                  1.3564E−08 
                 −3.3607E−09 
                  3.5886E−10 
                 −1.5040E−10 
               
               
                   
                   
               
            
           
         
       
     
     In the 10th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 10th embodiment, so an explanation in this regard will not be provided again. 
     Moreover, these parameters can be calculated from Table 19 and Table 20 as the following values and satisfy the following conditions: 
     
       
         
           
               
             
               
                   
               
               
                 10th Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 5.72 
                 R3/R4 
                 0.20 
               
               
                 Fno 
                 1.50 
                 (R9 + R10)/(R9 − R10) 
                 −0.23 
               
               
                 HFOV [deg.] 
                 39.6 
                 f/f1 
                 0.20 
               
               
                 (Vi/Ni)min 
                 10.98 
                 f/f2 
                 0.95 
               
               
                 V2 
                 56.0 
                 |f/f2| + |f/f3| 
                 1.37 
               
               
                 V2 + V3 + V4 
                 94.8 
                 f/f2 + f/f3 + f/f4 
                 0.27 
               
               
                 V2 + V4 
                 74.4 
                 f/f3 
                 −0.42 
               
               
                 V2/N2 
                 36.26 
                 f/f4 
                 −0.26 
               
               
                 V6 
                 44.6 
                 f/f5 
                 0.32 
               
               
                 ΣCT/CT5 
                 6.54 
                 f/f6 
                 0.32 
               
               
                 (CT2 + CT3 + CT4)/ 
                 1.41 
                 f/f7 
                 0.76 
               
               
                 (CT1 + CT5) 
               
               
                 CT3/CT2 
                 0.23 
                 f/f8 
                 −1.49 
               
               
                 CT5/CT1 
                 1.60 
                 f/f12 
                 1.10 
               
               
                 CT5/CT3 
                 3.06 
                 f/f23 
                 0.59 
               
               
                 CT7/CT5 
                 0.93 
                 f/|R11| + f/|R12| 
                 0.57 
               
               
                 TD/CT5 
                 9.45 
                 f5/CT5 
                 29.21 
               
               
                 TD/f2 
                 0.96 
                 f5/f1 
                 0.63 
               
               
                 TL [mm] 
                 7.09 
                 f8/f7 
                 −0.51 
               
               
                 TL/f 
                 1.24 
                 Y82/Y11 
                 2.03 
               
               
                 TL/ImgH 
                 1.48 
                 Yc72/Yc71 
                 0.27; 0.85 
               
               
                 R1/R2 
                 0.89 
                 Yc82/Y82 
                 0.38 
               
               
                 R3/f 
                 0.47 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     11th Embodiment 
       FIG. 21  is a perspective view of an image capturing unit according to the 11th embodiment of the present disclosure. In this embodiment, an image capturing unit  10  is a camera module including a lens unit  11 , a driving device  12 , an image sensor  13  and an image stabilizer  14 . The lens unit  11  includes the photographing optical system disclosed in the 1st embodiment, a barrel and a holder member (their reference numerals are omitted) for holding the photographing optical system; the lens unit  11  may include the photographing optical system disclosed in other embodiments, and the present disclosure is not limited thereto. The imaging light converges in the lens unit  11  of the image capturing unit  10  to generate an image with the driving device  12  utilized for image focusing on the image sensor  13 , and the generated image is then digitally transmitted to other electronic component for further processing. 
     The driving device  12  can have auto focusing functionality, and different driving configurations can be obtained through the usages of voice coil motors (VCM), micro electro-mechanical systems (MEMS), piezoelectric systems, or shape memory alloy materials. The driving device  12  is favorable for obtaining a better imaging position of the lens unit  11 , so that a clear image of the imaged object can be captured by the lens unit  11  with different object distances. The image sensor  13  (for example, CCD or CMOS), which can feature high photosensitivity and low noise, is disposed on the image surface of the photographing optical system to provide higher image quality. 
     The image stabilizer  14 , such as an accelerometer, a gyro sensor and a Hall Effect sensor, is configured to work with the driving device  12  to provide optical image stabilization (OIS). The driving device  12  working with the image stabilizer  14  is favorable for compensating for pan and tilt of the lens unit  11  to reduce blurring associated with motion during exposure. In some cases, the compensation can be provided by electronic image stabilization (EIS) with image processing software, thereby improving image quality while in motion or low-light conditions. 
     12th Embodiment 
       FIG. 22  is one perspective view of an electronic device according to the 12th embodiment of the present disclosure.  FIG. 23  is another perspective view of the electronic device in  FIG. 22 .  FIG. 24  is a block diagram of the electronic device in  FIG. 22 . 
     In this embodiment, an electronic device  20  is a smartphone including the image capturing unit  10  disclosed in the 11th embodiment, an image capturing unit  10   a,  an image capturing unit  10   b,  a flash module  21 , a focus assist module  22 , an image signal processor  23 , a user interface  24  and an image software processor  25 . The image capturing unit  10 , the image capturing unit  10   a  and the image capturing unit  10   b  are located on the same side of the electronic device  20  and all face the same direction. Furthermore, each of the image capturing unit  10   a  and the image capturing unit  10   b  has a configuration similar to that of the image capturing unit  10 . In detail, each of the image capturing unit  10   a  and the image capturing unit  10   b  includes a lens unit, a driving device, an image sensor and an image stabilizer, and the lens unit includes a lens system assembly, a barrel and a holder member for holding the lens system assembly. 
     In this embodiment, the image capturing units  10 ,  10   a  and  10   b  have different fields of view (e.g., the image capturing unit  10  is a wide-angle image capturing unit, the image capturing unit  10   a  is a telephoto image capturing unit, the image capturing unit  10   b  is an ultra-wide-angle image capturing unit, and the image capturing unit  10  has a maximum field of view ranging between that of the image capturing unit  10   a  and that of the image capturing unit  10   b ), such that the electronic device  20  has various magnification ratios so as to meet the requirement of optical zoom functionality. In this embodiment, the electronic device  20  includes multiple image capturing units  10 ,  10   a  and  10   b,  but the present disclosure is not limited to the number and arrangement of image capturing units. 
     When a user captures images of an object  26 , the light rays converge in the image capturing unit  10 , the image capturing unit  10   a  or the image capturing unit  10   b  to generate an image(s), and the flash module  21  is activated for light supplement. The focus assist module  22  detects the object distance of the imaged object  26  to achieve fast auto focusing. The image signal processor  23  is configured to optimize the captured image to improve image quality. The light beam emitted from the focus assist module  22  can be either conventional infrared or laser. The user interface  24  can be a touch screen or a physical button. The user is able to interact with the user interface  24  and the image software processor  25  having multiple functions to capture images and complete image processing. The image processed by the image software processor  25  can be displayed on the user interface  24 . 
     The smartphone in this embodiment is only exemplary for showing the image capturing unit  10  of the present disclosure installed in an electronic device, and the present disclosure is not limited thereto. The image capturing unit  10  can be optionally applied to optical systems with a movable focus. Furthermore, the photographing optical system of the image capturing unit  10  features good capability in aberration corrections and high image quality, and can be applied to 3D (three-dimensional) image capturing applications, in products such as digital cameras, mobile devices, digital tablets, smart televisions, network surveillance devices, dashboard cameras, vehicle backup cameras, multi-camera devices, image recognition systems, motion sensing input devices, wearable devices and other electronic imaging devices. 
     The foregoing description, for the purpose of explanation, has been described with reference to specific embodiments. It is to be noted that TABLES 1-20 show different data of the different embodiments; however, the data of the different embodiments are obtained from experiments. The embodiments were chosen and described in order to best explain the principles of the disclosure and its practical applications, to thereby enable others skilled in the art to best utilize the disclosure and various embodiments with various modifications as are suited to the particular use contemplated. The embodiments depicted above and the appended drawings are exemplary and are not intended to be exhaustive or to limit the scope of the present disclosure to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings.