Abstract:
There is provided a first lens having a refractive power, an object-side surface thereof being convex toward an object; a second lens having positive refractive power; a third lens having negative refractive power; a fourth lens having positive refractive power; and a fifth lens having negative refractive power. The optical system satisfies the condition:
 
 T 34/ T 23&gt;8.0
       where T 23  is a distance between the second and third lenses, and T 34  is a distance between the third and fourth lenses.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of Korean Patent Application No. 10-2014-0008240 filed on Jan. 23, 2014, with the Korean Intellectual Property Office, the disclosure of which is incorporated in its entirety herein by reference. 
     BACKGROUND 
     The present disclosure relates to an optical system. 
     Recent mobile communications terminals have been provided with camera modules to enable images to be captured and video calls to be made. In addition, as the functionality camera modules provided in mobile communications terminals has gradually increased, cameras for mobile communications terminals have gradually been required to have high degrees of resolution and high levels of performance. 
     However, since there a trend for mobile communications terminals to be miniaturized and lightened exists, there are limitations on implementing camera modules having high degrees of resolution and high levels of performance. 
     In order to solve these problems, recently, lenses provided in camera modules have has been formed of plastic, a material lighter than glass, and lens modules have been configured using five or more lenses in order to implement high degrees of resolution. 
     However, in the case of lenses formed of plastic, the improvement of chromatic aberrations and the implementation of relatively bright optical systems have been problematic, when compared to than lenses formed of glass. 
     SUMMARY 
     An aspect of the present disclosure may provide an optical system allowing for improvements in an aberration improvement effect and allowing for the implementation of high degrees of resolution. 
     According to an aspect of the present disclosure, an optical system may include: a first lens having refractive power, an object-side surface thereof being convex toward an object; a second lens having positive refractive power; a third lens having negative refractive power; a fourth lens having positive refractive power; and a fifth lens having negative refractive power, wherein the optical system satisfies Conditional Expression 1:
 
 T 34/ T 23&gt;8.0  [Conditional Expression 1]
 
     where T 23  is a distance (air gap) [mm] between the second and third lenses, and T 34  is a distance (air gap) [mm] between the third and fourth lenses. 
     The optical system may satisfy Conditional Expression 2:
 
 f 1/ f&lt;− 1.0  [Conditional Expression 2]
 
     where f1 is a focal length [mm] of the first lens, and f is an overall focal length [mm] of the optical system. 
     The optical system may satisfy Conditional Expression 3:
 
 f 12/ f&lt; 1.0  [Conditional Expression 3]
 
     where f12 is a synthetic focal length [mm] of the first and second lenses, and f is an overall focal length [mm] of the optical system. 
     The optical system may satisfy Conditional Expression 4:
 
20&lt; v 2− v 3&lt;70  [Conditional Expression 4]
 
     where v2 is an Abbe number of the second lens, and v3 is an Abbe number of the third lens. 
     The optical system may satisfy Conditional Expression 5:
 
−3.0&lt; f 3/ f 2&lt;−0.3  [Conditional Expression 5]
 
     where f2 is a focal length [mm] of the second lens, and f 3  is a focal length [mm] of the third lens. 
     The optical system may satisfy Conditional Expression 6:
 
0.5&lt; OAL/f&lt; 2.0  [Conditional Expression 6]
 
     where OAL is a distance [mm] from an object-side surface of the first lens to an image surface, and f is an overall focal length [mm] of the optical system. 
     The optical system may satisfy Conditional Expression 7:
 
 v 3&lt;40  [Conditional Expression 7]
 
     where v3 is an Abbe number of the third lens. 
     The optical system may satisfy Conditional Expression 8:
 
−5.0&lt; f 4/ f 1&lt;0  [Conditional Expression 8]
 
     where f1 is a focal length [mm] of the first lens, and f2 is a focal length [mm] of the fourth lens. 
     The optical system may satisfy Conditional Expression 9:
 
1.60&lt; n 3&lt;2.10  [Conditional Expression 9]
 
     where n 3  is a refractive index of the third lens. 
     The first lens may have negative refractive power. 
     The object-side surface of the first lens may be convex toward the object. 
     The first lens may have a meniscus shape in which it is convex toward the object. 
     An object-side surface of the second lens may be convex toward the object. 
     Both surfaces of the second lens may be convex. 
     The second lens may have a meniscus shape in which it is convex toward the object. 
     An image-side surface of the third lens may be concave toward an image. 
     Both surfaces of the third lens may be concave. 
     The third lens may have a meniscus shape in which it is convex toward the object. 
     The fourth lens may have a meniscus shape in which it is convex toward an image. 
     Both surfaces of the fifth lens may be concave. 
     The fifth lens may have an inflection point formed on an object-side surface or an image-side surface thereof. 
     The fifth lens may have at least one inflection point formed on an image-side surface thereof. 
     The first to fifth lenses may be formed of plastic. 
     At least one of an object-side surface and an image-side surface of each of the first to fifth lenses may be aspherical. 
     According to another aspect of the present disclosure, an optical system may include: a first lens having negative refractive power, an object-side surface thereof being convex toward an object; a second lens having positive refractive power; a third lens having negative refractive power; a fourth lens having positive refractive power; and a fifth lens having negative refractive power, wherein the first and second lenses overall have positive refractive power, and the optical system satisfies Conditional Expression 1:
 
 T 34/ T 23&gt;8.0  [Conditional Expression 1]
 
     where T 23  is a distance (air gap) [mm] between the second and third lenses, and T 34  is a distance (air gap) [mm] between the third and fourth lenses. 
     The optical system may satisfy Conditional Expression 2:
 
 f 1/ f&lt;− 1.0  [Conditional Expression 2]
 
     where f1 is a focal length [mm] of the first lens, and f is an overall focal length [mm] of the optical system. 
     The optical system may satisfy Conditional Expression 3:
 
 f 12/ f&lt; 1.0  [Conditional Expression 3]
 
     where f12 is a synthetic focal length [mm] of the first and second lenses, and f is an overall focal length [mm] of the optical system. 
     The optical system may satisfy Conditional Expression 4:
 
20&lt; v 2− v 3&lt;70  [Conditional Expression 4]
 
     where v2 is an Abbe number of the second lens, and v3 is an Abbe number of the third lens. 
     The optical system may satisfy Conditional Expression 5:
 
−3.0&lt; f 3/ f 2&lt;−0.3  [Conditional Expression 5]
 
     where f2 is a focal length [mm] of the second lens, and f 3  is a focal length [mm] of the third lens. 
     The optical system may satisfy Conditional Expression 6:
 
0.5&lt; OAL/f&lt; 2.0  [Conditional Expression 6]
 
     where OAL is a distance [mm] from an object-side surface of the first lens to an image surface, and f is an overall focal length [mm] of the optical system. 
     The optical system may satisfy Conditional Expression 7:
 
 v 3&lt;40  [Conditional Expression 7]
 
     where v3 is an Abbe number of the third lens. 
     The optical system may satisfy Conditional Expression 8:
 
−5.0&lt; f 4/ f 1&lt;0  [Conditional Expression 8]
 
     where f1 is a focal length [mm] of the first lens, and f 4  is a focal length [mm] of the fourth lens. 
     The optical system may satisfy Conditional Expression 9:
 
1.60&lt; n 3&lt;2.10  [Conditional Expression 9]
 
     where n 3  is a refractive index of the third lens. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The above and other aspects, features and other advantages of the present disclosure will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a configuration diagram of an optical system according to a first exemplary embodiment of the present disclosure; 
         FIG. 2  is a curve showing aberration characteristics of the optical system shown in  FIG. 1 ; 
         FIG. 3  is a configuration diagram of an optical system according to a second exemplary embodiment of the present disclosure; 
         FIG. 4  is a curve showing aberration characteristics of the optical system shown in  FIG. 3 ; 
         FIG. 5  is a configuration diagram of an optical system according to a third exemplary embodiment of the present disclosure; 
         FIG. 6  is a curve showing aberration characteristics of the optical system shown in  FIG. 5 ; 
         FIG. 7  is a configuration diagram of an optical system according to a fourth exemplary embodiment of the present disclosure; and 
         FIG. 8  is a curve showing aberration characteristics of the optical system shown in  FIG. 7 . 
     
    
    
     DETAILED DESCRIPTION 
     Exemplary embodiments of the present disclosure will now be described in detail with reference to the accompanying drawings. 
     In the following lens configuration diagrams, thicknesses, sizes, and shapes of lenses have been slightly exaggerated for explanation. Particularly, a shape of a spherical surface or an aspherical surface shown in the lens configuration diagrams has been shown only by way of example. That is, the spherical surface or the aspherical surface is not limited to having the shown shape. 
     In addition, it is to be noted that a first lens refers to a lens that is the closest to an object, and a sixth lens refers to a lens that is the closest to an image. 
     Further, it is noted to be that the term ‘front’ refers to a direction from the optical system toward the object, while the term ‘rear’ refers to a direction from the optical system toward an image sensor or the image. Further, it is to be noted that in each lens, a first surface refers to a surface toward the object (or an object-side surface) and a second surface refers to a surface toward the image (or an image-side surface). In addition, it is to be noted that the present specification, units of all of numerical values of radii of curvature, thicknesses, OALs, BFLs, and D 1  of lenses are mm. 
     An optical system according to an exemplary embodiment of the present disclosure may include five lenses. 
     That is, the optical system according to an exemplary embodiment of the present disclosure may include a first lens  10 , a second lens  20 , a third lens  30 , a fourth lens  40 , and a fifth lens  50 . 
     However, the optical system according to an exemplary embodiment of the present disclosure is not limited to including only five lenses, but may further include other components if necessary. For example, the optical system may include a stop ST for controlling an amount of light. In addition, the optical system may further include an infrared cut-off filter  60  cutting off an infrared ray. Further, the optical system may further include an image sensor  70  for converting an image of a subject incident into an electrical signal. Further, the optical system may further include an interval maintaining member adjusting an interval between lenses. 
     The first to fifth lenses  10  to  50  configuring the optical system according to an exemplary embodiment of the present disclosure may be formed of plastic. 
     In addition, at least one of the first to fifth lenses  10  to  50  may have an aspherical surface. In addition, the first to fifth lenses  10  to  50  may have at least one aspherical surface. 
     That is, at least one of first and second surfaces of the first to fifth lenses  10  to  50  may be aspherical. 
     In addition, the optical system including the first to fifth lenses  10  to  50  may have negative refractive power/positive refractive power/negative refractive power/positive refractive power/negative refractive power sequentially from an object side. 
     The optical system configured as described above may improve optical performance through aberration improvement. In addition, the optical system configured as described above may improve sensitivity of the lenses by decreasing a refraction angle. Therefore, in the optical system according to an exemplary embodiment of the present disclosure, all of the five lenses may be formed of plastic. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 1.
 
 T 34/ T 23&gt;8.0  [Conditional Expression 1]
 
     Here, T 23  is a distance (air gap) [mm] between the second and third lenses, and T 34  is a distance (air gap) [mm] between the third and fourth lenses. 
     Here, when T 34 /T 23  is out of a lower limit value of Conditional Expression 1, the air gap between the second and third lenses may become large, such that it is difficult to secure resolution of a peripheral portion of each lens, or an overall optical system may become long, such that it is difficult to miniaturize the optical system. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 2.
 
 f 1/ f&lt;− 1.0  [Conditional Expression 2]
 
     Here, f1 is a focal length [mm] of the first lens, and f is an overall focal length [mm] of the optical system. 
     Here, when f1/f is out of an upper limit value of Conditional Expression 2, the negative refractive power of the first lens may become strong, such that it is difficult to secure the resolution of the peripheral portion of each lens, or the overall optical system may become long, such that it is difficult to miniaturize the optical system. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 3.
 
 f 12/ f&lt; 1.0  [Conditional Expression 3]
 
     Here, f12 is a synthetic focal length [mm] of the first and second lenses, and f is the overall focal length [mm] of the optical system. 
     Here, when f12/f is out of an upper limit value of Conditional Expression 3, the positive refractive power of the second lens may become weak, such that it is difficult to secure the resolution of the peripheral portion of each lens, or the overall optical system may become long, such that it is difficult to miniaturize the optical system. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 4.
 
20&lt; v 2− v 3&lt;70  [Conditional Expression 4]
 
     Here, v2 is an Abbe number of the second lens, and v3 is an Abbe number of the third lens. 
     Here, in the case in which v2−v3 is out of a lower limit value of Conditional Expression 4, it may be difficult to correct chromatic aberration, such that it is difficult to implement high resolution, and in the case in which v2−v3 is out of an upper limit value of Conditional Expression 4, it may be difficult to decrease a manufacturing cost of the optical system. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 5.
 
−3.0&lt; f 3/ f 2&lt;−0.3  [Conditional Expression 5]
 
     Here, f2 is a focal length [mm] of the second lens, and f 3  is a focal length [mm] of the third lens. 
     Here, in the case in which f3/f2 is out of a lower limit value or an upper limit value of Conditional Expression 5, refractive power of the second or third lens may become strong and a curvature thereof may become small, such that it is difficult to manufacture a shape of the lens. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 6.
 
0.5&lt; OAL/f&lt; 2.0  [Conditional Expression 6]
 
     Here, OAL is a distance [mm] from an object-side surface of the first lens to an image surface, and f is the overall focal length [mm] of the optical system. 
     Here, in the case in which OAL/f is out of a lower limit value of Conditional Expression 6, a viewing angle of the optical system may become small, and in the case in which OAL/f is out of an upper limit value of Conditional Expression 6, the overall optical system may become long, such that it is difficult to miniaturize the optical system. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 7.
 
 v 3&lt;40  [Conditional Expression 7]
 
     Here, v3 is the Abbe number of the third lens. 
     Here, in the case in which v3 is out of an upper limit value of Conditional Expression 7, it may be difficult to correct the chromatic aberration, such that it is difficult to implement high resolution. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 8.
 
−5.0&lt; f 4/ f 1&lt;0  [Conditional Expression 8]
 
     Here, f1 is the focal length [mm] of the first lens, and f4 is a focal length [mm] of the fourth lens. 
     Here, in the case in which f4/f1 is out of a lower limit value of Conditional Expression 8, the negative refractive power of the first lens may become strong, such that it is difficult to secure the resolution of the peripheral portion of each lens, and in the case in which f4/f1 is out of an upper limit value of Conditional Expression 8, the fourth lens may have negative refractive power or the first lens may have positive refractive power, such that overall refractive power is changed. 
     The optical system according to an exemplary embodiment of the present disclosure may satisfy Conditional Expression 9.
 
1.60&lt; n 3&lt;2.10  [Conditional Expression 9]
 
     Here, n 3  is a refractive index of the third lens. 
     Here, in the case in which n 3  is out of a lower limit value of Conditional Expression 9, it may be difficult to correct chromatic aberration, such that it is difficult to implement high resolution, and in the case in which n 3  is out of an upper limit value of Conditional Expression 9, it may be difficult to decrease a manufacturing cost of the optical system. 
     Next, the first to fifth lenses  10  to  50  configuring the optical system according to an exemplary embodiment of the present disclosure will be described. 
     The first lens  10  may have negative refractive power. In addition, the first lens  10  may have a meniscus shape in which it is convex toward an object. In detail, first and second surfaces of the first lens  10  may be convex toward the object. 
     At least one of the first and second surfaces of the first lens  10  may be aspherical. For example, both surfaces of the first lens may be aspherical. 
     The second lens  20  may have positive refractive power. In addition, a first surface of the second lens  20  may be convex toward the object, and a second surface thereof may be concave toward the object or be convex toward the object. In detail, the second lens  20  may have a meniscus shape in which both surfaces thereof are convex or are convex toward the object. 
     At least one of the first and second surfaces of the second lens  20  may be aspherical. For example, both surfaces of the second lens  20  may be aspherical. 
     Meanwhile, the first and second lenses  10  and  20  may overall have positive refractive power. 
     The third lens  30  may have negative refractive power. In addition, both surfaces of the third lens  30  may be concave. In detail, a first surface of the third lens  30  may be concave toward the object, and a second surface thereof may be concave toward the image. 
     Unlike this, the third lens  30  may have a meniscus shape in which it is convex toward an object. In detail, the first and second surfaces of the third lens  30  may be convex toward the object. 
     At least one of the first and second surfaces of the third lens  30  may be aspherical. For example, both surfaces of the third lens  30  may be aspherical. 
     The fourth lens  40  may have positive refractive power. In addition, the fourth lens  40  may have a meniscus shape in which it is convex toward the image. In detail, a first surface of the fourth lens  40  may be concave toward the object, and a second surface thereof may be convex toward the image. 
     At least one of the first and second surfaces of the fourth lens  40  may be aspherical. For example, both surfaces of the fourth lens  40  may be aspherical. 
     The fifth lens  50  may have negative refractive power. In addition, both surfaces of the firth lens  50  may be concave. In detail, a first surface of the fifth lens  50  may be concave toward the object, and a second surface thereof may be concave toward the image. 
     In addition, the fifth lens  50  may have an inflection point formed on at least any one of the first and second surfaces thereof. For example, the second surface of the fifth lens  50  may be concave at the center of an optical axis and become convex toward an edge thereof. 
     In addition, at least one of the first and second surfaces of the fifth lens  50  may be aspherical. For example, both surfaces of the fifth lens  50  may be aspherical. 
     In the optical system configured as described above, a plurality of lenses perform an aberration correction function, whereby aberration improvement performance may be improved. In addition, in the optical system, a refraction angle of the lens is decreased, whereby sensitivity of the lenses may be improved. Therefore, in the optical system, all of the lenses may be formed of plastic having optical performance lower than that of glass, whereby a manufacturing cost of a lens module may be decreased and manufacturing efficiency thereof may be increased. 
     An optical system according to a first exemplary embodiment of the present disclosure will be described with reference to  FIGS. 1 and 2 . 
     An optical system according to a first exemplary embodiment of the present disclosure may include a first lens  10 , a second lens  20 , a third lens  30 , a fourth lens  40 , and a fifth lens  50 , and may further include an infrared cut-off filter  60 , an image sensor  70 , and a stop ST. 
     Here, as shown in Table 1, a distance (OAL) from an object-side surface of the first lens  10  to a first surface (image surface) of the image sensor  70  may be 5.15 mm, and a distance (BFL) from an image-side surface of the fifth lens  50  to the image surface may be 1.313 mm. In addition, a focal length f 1  of the first lens  10  may be −16.534 mm, a focal length f2 of the second lens  20  may be 2.486 mm, a focal length f3 of the third lens  30  may be −6.209 mm, a focal length f4 of the fourth lens  40  may be 2.661 mm, a focal length f5 of the fifth lens  50  may be −2.344 mm, a synthetic focal length f12 of the first and second lenses  10  and  20  may be 3.111 mm, and an overall focal length f of the optical system may be 4.238 mm. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 f1 
                 −16.534 
               
               
                   
                 f2 
                 2.486 
               
               
                   
                 f3 
                 −6.209 
               
               
                   
                 f4 
                 2.661 
               
               
                   
                 f5 
                 −2.344 
               
               
                   
                 f12 
                 3.111 
               
               
                   
                 f 
                 4.238 
               
               
                   
                 BFL 
                 1.313 
               
               
                   
                 FNO 
                 2.3 
               
               
                   
                 OAL 
                 5.150 
               
               
                   
                 FOV 
                 68.5 
               
               
                   
                   
               
             
          
         
       
     
     Other characteristics of lenses (radii of curvature of lenses, thicknesses of lenses, distances between lenses, refractive indices of lenses, Abbe numbers of lenses) are shown in Table 2. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                 Thickness 
                 Refractive 
                 Abbe 
               
               
                 Surface No. 
                 Radius of Curvature 
                 or Distance 
                 Index 
                 Number 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 2.001 
                 0.30 
                 1.544 
                 56.1 
               
               
                 2 
                 1.550 
                 0.05 
               
               
                 3 
                 1.385 
                 0.54 
                 1.544 
                 56.1 
               
               
                 4 
                 −62.800 
                 0.00 
               
               
                 Stop 
                 Infinity 
                 0.06 
               
               
                 6 
                 −12.683 
                 0.27 
                 1.635 
                 24 
               
               
                 7 
                 5.850 
                 1.05 
               
               
                 8 
                 −3.555 
                 0.77 
                 1.544 
                 56.1 
               
               
                 9 
                 −1.111 
                 0.39 
               
               
                 10  
                 −11.363 
                 0.40 
                 1.544 
                 56.1 
               
               
                 11  
                 1.46167 
                 0.31 
               
               
                 12  
                 Infinity 
                 0.30 
                 1.517 
                 64.2 
               
               
                 13  
                 Infinity 
                 0.70 
               
               
                 Image 
                 Infinity 
               
               
                   
               
             
          
         
       
     
     In a first exemplary embodiment of the present disclosure, the first lens  10  may have negative refractive power and may have a meniscus shape in which it is convex toward an object. The second lens  20  may have positive refractive power, and both surfaces thereof may be convex. The third lens  30  may have negative refractive power, and both surfaces thereof may be concave. The fourth lens  40  may have positive refractive power and may have a meniscus shape in which it is convex toward an image. The fifth lens  50  may have negative refractive power, and both surfaces thereof may be concave. In addition, the fifth lens  50  may have an inflection point formed on at least any one of first and second surfaces thereof. Further, the stop ST may be disposed between the second lens  20  and the third lens  30 . 
     The stop ST may be disposed between the second lens  20  and the third lens  30 , thereby decreasing sensitivity of each lens to a decentered tolerance. 
     Meanwhile, the respective surfaces of the first to fifth lenses  10  to  50  may have aspherical coefficients as shown in Table 3. That is, all of the first surface of the first lens  10  to the second surface of the fifth lens  50  may be aspherical. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 surface# 
                 1 
                 2 
                 3 
                 4 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Conic 
                 −0.870402 
                 −6.750919 
                 −4.443183 
                 0 
                 0 
                 −4.706606 
                 4.197184 
                 −0.51196 
                 0 
                 −7.40486 
               
               
                 Constant 
               
               
                 (K) 
               
               
                 4th Order 
                 −0.035407 
                 −0.078259 
                 −0.042446 
                 0.0210553 
                 0.0934843 
                 0.1047722 
                 −0.05778 
                 0.143353 
                 −0.05894 
                 −0.0526 
               
               
                 Coefficient 
               
               
                 (A) 
               
               
                 6th Order 
                 0.0653051 
                 0.0888674 
                 0.0497927 
                 −0.177217 
                 −0.200423 
                 −0.0734 
                 0.023796 
                 −0.10908 
                 0.021844 
                 0.016863 
               
               
                 Coefficient 
               
               
                 (B) 
               
               
                 8th Order 
                 −0.095628 
                 0.0334932 
                 0.0345238 
                 −0.037944 
                 0.0781283 
                 0.1031949 
                 −0.06056 
                 0.083622 
                 −0.00268 
                 −0.00382 
               
               
                 Coefficient 
               
               
                 (C) 
               
               
                 10th Order 
                 0.1153479 
                 0.0398428 
                 0.0043924 
                 0.3308742 
                 0.2080983 
                 −0.072032 
                 0.031074 
                 −0.04163 
                 7.68E−05 
                 0.000469 
               
               
                 Coefficient 
               
               
                 (D) 
               
               
                 12th Order 
                 −0.045425 
                 0 
                 0 
                 −0.208267 
                 −0.157165 
                 0.0385763 
                 −0.00819 
                 0.01005 
                 0 
                 −2.47E−05 
               
               
                 Coefficient 
               
               
                 (E) 
               
               
                   
               
             
          
         
       
     
     Meanwhile, it may be appreciated from Table 4 that the optical system according to a first exemplary embodiment of the present disclosure satisfies Conditional Expressions 1 to 9 described above. Therefore, optical performance of the lens may be improved. 
     In addition, the optical system configured as described above may have aberration characteristics shown in  FIG. 2 . 
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
             
             
               
                   
                 CONDITIONAL EXPRESSION 1 
                 16.094612 
                 T34/T23 
               
               
                   
                 CONDITIONAL EXPRESSION 2 
                 −3.901481 
                 f1/f 
               
               
                   
                 CONDITIONAL EXPRESSION 3 
                 0.7340727 
                 f12/f 
               
               
                   
                 CONDITIONAL EXPRESSION 4 
                 32.1 
                 v2-v3 
               
               
                   
                 CONDITIONAL EXPRESSION 5 
                 −2.497168 
                 f3/f2 
               
               
                   
                 CONDITIONAL EXPRESSION 6 
                 1.2151708 
                 OAL/f 
               
               
                   
                 CONDITIONAL EXPRESSION 7 
                 24 
                 v3 
               
               
                   
                 CONDITIONAL EXPRESSION 8 
                 −0.160909 
                 f4/f1 
               
               
                   
                 CONDITIONAL EXPRESSION 9 
                 1.635 
                 n3 
               
               
                   
                   
               
             
          
         
       
     
     An optical system according to a second exemplary embodiment of the present disclosure will be described with reference to  FIGS. 3 and 4 . 
     An optical system according to a second exemplary embodiment of the present disclosure may include a first lens  10 , a second lens  20 , a third lens  30 , a fourth lens  40 , and a fifth lens  50 , and may further include an infrared cut-off filter  60 , an image sensor  70 , and a stop ST. 
     Here, as shown in Table 5, a distance (OAL) from an object-side surface of the first lens  10  to an image surface of the image sensor  70  may be 4.749 mm, and a distance (BFL) from an image-side surface of the fifth lens  50  to the image surface may be 1.159 mm. In addition, a focal length f1 of the first lens  10  may be −12.265 mm, a focal length f2 of the second lens  20  may be 2.175 mm, a focal length f3 of the third lens  30  may be −5.952 mm, a focal length f4 of the fourth lens  40  may be 2.624 mm, a focal length f5 of the fifth lens  50  may be −2.178 mm, a synthetic focal length f12 of the first and second lenses  10  and  20  may be 2.873 mm, and an overall focal length f of the optical system may be 4.1 mm. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
             
             
               
                   
                 f1 
                 −12.265 
               
               
                   
                 f2 
                 2.175 
               
               
                   
                 f3 
                 −5.952 
               
               
                   
                 f4 
                 2.624 
               
               
                   
                 f5 
                 −2.178 
               
               
                   
                 f12 
                 2.873 
               
               
                   
                 f 
                 4.1 
               
               
                   
                 BFL 
                 1.159 
               
               
                   
                 FNO 
                 2.4 
               
               
                   
                 OAL 
                 4.749 
               
               
                   
                 FOV 
                 70.2 
               
               
                   
                   
               
             
          
         
       
     
     Other characteristics of lenses (radii of curvature of lenses, thicknesses of lenses, distances between lenses, refractive indices of lenses, Abbe numbers of lenses) are shown in Table 6. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                   
                   
                 Thickness 
                 Refractive 
                 Abbe 
               
               
                 Surface No. 
                 Radius of Curvature 
                 or Distance 
                 Index 
                 Number 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 1.855 
                 0.35 
                 1.544 
                 56.1 
               
               
                 2 
                 1.356 
                 0.05 
               
               
                 3 
                 1.090 
                 0.52 
                 1.544 
                 56.1 
               
               
                 4 
                 10.831 
                 0.00 
               
               
                 Stop 
                 Infinity 
                 0.05 
               
               
                 6 
                 −98.515 
                 0.27 
                 1.635 
                 24 
               
               
                 7 
                 3.974 
                 0.83 
               
               
                 8 
                 −3.006 
                 0.73 
                 1.544 
                 56.1 
               
               
                 9 
                 −1.054 
                 0.38 
               
               
                 10  
                 −2.583 
                 0.40 
                 1.544 
                 56.1 
               
               
                 11  
                 2.32924 
                 0.16 
               
               
                 12  
                 Infinity 
                 0.30 
                 1.517 
                 64.2 
               
               
                 13  
                 Infinity 
                 0.70 
               
               
                 Image 
                 Infinity 
               
               
                   
               
             
          
         
       
     
     In a second exemplary embodiment of the present disclosure, the first lens  10  may have negative refractive power and may have a meniscus shape in which it is convex toward an object. The second lens  20  may have positive refractive power and may have a meniscus shape in which it is convex toward the object. The third lens  30  may have negative refractive power, and both surfaces thereof may be concave. The fourth lens  40  may have positive refractive power and may have a meniscus shape in which it is convex toward an image. The fifth lens  50  may have negative refractive power, and both surfaces thereof may be concave. In addition, the fifth lens  50  may have an inflection point formed on at least any one of first and second surfaces thereof. Further, the stop ST may be disposed between the second lens  20  and the third lens  30 . 
     The stop ST may be disposed between the second lens  20  and the third lens  30 , thereby decreasing sensitivity of each lens to a decentered tolerance. 
     Meanwhile, the respective surfaces of the first to fifth lenses  10  to  50  may have aspherical coefficients as shown in Table 7. That is, all of the first surface of the first lens  10  to the second surface of the fifth lens  50  may be aspherical. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                 surface# 
                 1 
                 2 
                 3 
                 4 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Conic 
                 −1.398072 
                 −11.76191 
                 −6.64088 
                 0 
                 0 
                 −0.662077 
                 6.624837 
                 −0.45719 
                 0 
                 −19.1949 
               
               
                 Constant 
               
               
                 (K) 
               
               
                 4th Order 
                 −0.042304 
                 −0.098691 
                 0.0492035 
                 0.0133654 
                 0.0813346 
                 0.121106 
                 −0.07415 
                 0.131568 
                 −0.01382 
                 −0.06109 
               
               
                 Coefficient 
               
               
                 (A) 
               
               
                 6th Order 
                 0.0982426 
                 0.1863962 
                 0.0216316 
                 −0.319996 
                 −0.270681 
                 −0.01851 
                 −0.00897 
                 −0.10955 
                 0.026942 
                 0.023822 
               
               
                 Coefficient 
               
               
                 (B) 
               
               
                 8th Order 
                 −0.136018 
                 −0.082599 
                 0.0557973 
                 0.1273475 
                 0.1446676 
                 0.0238441 
                 −0.02983 
                 0.106375 
                 −0.00512 
                 −0.00694 
               
               
                 Coefficient 
               
               
                 (C) 
               
               
                 10th Order 
                 0.1334919 
                 0.1008262 
                 0.0261717 
                 0.5288883 
                 0.3942123 
                 0.0264427 
                 0.002265 
                 −0.06808 
                 3.22E−04 
                 0.001079 
               
               
                 Coefficient 
               
               
                 (D) 
               
               
                 12th Order 
                 −0.042489 
                 0 
                 0 
                 −0.493 
                 −0.431801 
                 0.0081013 
                 −0.00358 
                 0.022302 
                 0 
                 −6.69E−05 
               
               
                 Coefficient 
               
               
                 (E) 
               
               
                   
               
             
          
         
       
     
     Meanwhile, it may be appreciated from Table 8 that the optical system according to a second exemplary embodiment of the present disclosure satisfies Conditional Expressions 1 to 9 described above. Therefore, optical performance of the lens may be improved. 
     In addition, the optical system configured as described above may have aberration characteristics shown in  FIG. 4 . 
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE 8 
               
               
                   
                   
               
             
             
               
                   
                 CONDITIONAL EXPRESSION 1 
                 16.698029 
                 T34/T23 
               
               
                   
                 CONDITIONAL EXPRESSION 2 
                 −2.991356 
                 f1/f 
               
               
                   
                 CONDITIONAL EXPRESSION 3 
                 0.7007317 
                 f12/f 
               
               
                   
                 CONDITIONAL EXPRESSION 4 
                 32.1 
                 v2-v3 
               
               
                   
                 CONDITIONAL EXPRESSION 5 
                 −2.736108 
                 f3/f2 
               
               
                   
                 CONDITIONAL EXPRESSION 6 
                 1.1583502 
                 OAL/f 
               
               
                   
                 CONDITIONAL EXPRESSION 7 
                 24 
                 v3 
               
               
                   
                 CONDITIONAL EXPRESSION 8 
                 −0.213954 
                 f4/f1 
               
               
                   
                 CONDITIONAL EXPRESSION 9 
                 1.635 
                 n3 
               
               
                   
                   
               
             
          
         
       
     
     An optical system according to a third exemplary embodiment of the present disclosure will be described with reference to  FIGS. 5 and 6 . 
     An optical system according to a third exemplary embodiment of the present disclosure may include a first lens  10 , a second lens  20 , a third lens  30 , a fourth lens  40 , and a fifth lens  50 , and may further include an infrared cut-off filter  60 , an image sensor  70 , and a stop ST. 
     Here, as shown in Table 9, a distance (OAL) from an object-side surface of the first lens  10  to an image surface of the image sensor  70  may be 5.150 mm, and a distance (BFL) from an image-side surface of the fifth lens  50  to the image surface may be 1.307 mm. In addition, a focal length f1 of the first lens  10  may be −7.627 mm, a focal length f2 of the second lens  20  may be 2.401 mm, a focal length f3 of the third lens  30  may be −11.645 mm, a focal length f4 of the fourth lens  40  may be 2.755 mm, a focal length f5 of the fifth lens  50  may be −2.292 mm, a synthetic focal length f12 of the first and second lenses  10  and  20  may be 3.758 mm, and an overall focal length f of the optical system may be 4.23 mm. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 9 
               
               
                   
                   
               
             
             
               
                   
                 f1 
                 −7.627 
               
               
                   
                 f2 
                 2.401 
               
               
                   
                 f3 
                 −11.645 
               
               
                   
                 f4 
                 2.755 
               
               
                   
                 f5 
                 −2.292 
               
               
                   
                 f12 
                 3.758 
               
               
                   
                 f 
                 4.23 
               
               
                   
                 BFL 
                 1.307 
               
               
                   
                 FNO 
                 2.25 
               
               
                   
                 OAL 
                 5.150 
               
               
                   
                 FOV 
                 68 
               
               
                   
                   
               
             
          
         
       
     
     Other characteristics of lenses (radii of curvature of lenses, thicknesses of lenses, distances between lenses, refractive indices of lenses, Abbe numbers of lenses) are shown in Table 10. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                   
                   
                 Thickness 
                 Refractive 
                 Abbe 
               
               
                 Surface No. 
                 Radius of Curvature 
                 or Distance 
                 Index 
                 Number 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 2.021 
                 0.30 
                 1.635 
                 24 
               
               
                 2 
                 1.347 
                 0.07 
               
               
                 3 
                 1.371 
                 0.58 
                 1.544 
                 56.1 
               
               
                 4 
                 −26.020 
                 0.00 
               
               
                 Stop 
                 Infinity 
                 0.05 
               
               
                 6 
                 10.713 
                 0.33 
                 1.635 
                 24 
               
               
                 7 
                 4.346 
                 1.13 
               
               
                 8 
                 −4.585 
                 0.63 
                 1.544 
                 56.1 
               
               
                 9 
                 −1.189 
                 0.34 
               
               
                 10  
                 −10.313 
                 0.40 
                 1.544 
                 56.1 
               
               
                 11  
                 1.44523 
                 0.31 
               
               
                 12  
                 Infinity 
                 0.30 
                 1.517 
                 64.2 
               
               
                 13  
                 Infinity 
                 0.70 
               
               
                 Image 
                 Infinity 
               
               
                   
               
             
          
         
       
     
     In a third exemplary embodiment of the present disclosure, the first lens  10  may have negative refractive power and may have a meniscus shape in which it is convex toward an object. The second lens  20  may have positive refractive power, and both surfaces thereof may be convex. The third lens  30  may have negative refractive power and may have a meniscus shape in which it is convex toward the object. The fourth lens  40  may have positive refractive power and may have a meniscus shape in which it is convex toward an image. The fifth lens  50  may have negative refractive power, and both surfaces thereof may be concave. In addition, the fifth lens  50  may have an inflection point formed on at least any one of first and second surfaces thereof. Further, the stop ST may be disposed between the second lens  20  and the third lens  30 . 
     The stop ST may be disposed between the second lens  20  and the third lens  30 , thereby decreasing sensitivity of each lens to a decentered tolerance. 
     Meanwhile, the respective surfaces of the first to fifth lenses  10  to  50  may have aspherical coefficients as shown in Table 11. That is, all of the first surface of the first lens  10  to the second surface of the fifth lens  50  may be aspherical. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
               
                 surface# 
                 1 
                 2 
                 3 
                 4 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Conic 
                 −2.095872 
                 −4.210807 
                 −3.22884 
                 0 
                 0 
                 −42.74787 
                 10.92954 
                 −0.43242 
                 0 
                 −7.52446 
               
               
                 Constant 
               
               
                 (K) 
               
               
                 4th Order 
                 −0.049503 
                 −0.026556 
                 0.0016637 
                 0.0496435 
                 0.0190679 
                 0.0500226 
                 −0.05786 
                 0.168162 
                 −0.04267 
                 −0.05428 
               
               
                 Coefficient 
               
               
                 (A) 
               
               
                 6th Order 
                 0.0787004 
                 0.0640623 
                 0.0362791 
                 −0.208475 
                 −0.190358 
                 −0.103116 
                 0.038119 
                 −0.11434 
                 0.018253 
                 0.018465 
               
               
                 Coefficient 
               
               
                 (B) 
               
               
                 8th Order 
                 −0.080804 
                 −0.044393 
                 −0.058204 
                 −0.022953 
                 0.0400128 
                 0.1251464 
                 −0.08966 
                 0.085232 
                 −0.00221 
                 −0.00463 
               
               
                 Coefficient 
               
               
                 (C) 
               
               
                 10th Order 
                 0.0704193 
                 0.07497 
                 0.0422969 
                 0.253262 
                 0.2471989 
                 −0.073452 
                 0.055705 
                 −0.04401 
                 3.67E−05 
                 0.000638 
               
               
                 Coefficient 
               
               
                 (D) 
               
               
                 12th Order 
                 −0.023473 
                 0 
                 0 
                 −0.139966 
                 −0.136586 
                 0.0417762 
                 −0.0213 
                 0.011163 
                 0 
                 −3.70E−05 
               
               
                 Coefficient 
               
               
                 (E) 
               
               
                   
               
             
          
         
       
     
     Meanwhile, it may be appreciated from Table 12 that the optical system according to a third exemplary embodiment of the present disclosure satisfies Conditional Expressions 1 to 9 described above. Therefore, optical performance of the lens may be improved. 
     In addition, the optical system configured as described above may have aberration characteristics shown in  FIG. 6 . 
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE 12 
               
               
                   
                   
               
             
             
               
                   
                 CONDITIONAL EXPRESSION 1 
                 22.676897 
                 T34/T23 
               
               
                   
                 CONDITIONAL EXPRESSION 2 
                 −1.803052 
                 f1/f 
               
               
                   
                 CONDITIONAL EXPRESSION 3 
                 0.8884161 
                 f12/f 
               
               
                   
                 CONDITIONAL EXPRESSION 4 
                 32.1 
                 v2-v3 
               
               
                   
                 CONDITIONAL EXPRESSION 5 
                 −4.849917 
                 f3/f2 
               
               
                   
                 CONDITIONAL EXPRESSION 6 
                 1.217469 
                 OAL/f 
               
               
                   
                 CONDITIONAL EXPRESSION 7 
                 24 
                 v3 
               
               
                   
                 CONDITIONAL EXPRESSION 8 
                 −0.36125 
                 f4/f1 
               
               
                   
                 CONDITIONAL EXPRESSION 9 
                 1.635 
                 n3 
               
               
                   
                   
               
             
          
         
       
     
     An optical system according to a fourth exemplary embodiment of the present disclosure will be described with reference to  FIGS. 7 and 8 . 
     An optical system according to a fourth exemplary embodiment of the present disclosure may include a first lens  10 , a second lens  20 , a third lens  30 , a fourth lens  40 , and a fifth lens  50 , and may further include an infrared cut-off filter  60 , an image sensor  70 , and a stop ST. 
     Here, as shown in Table 13, a distance (OAL) from an object-side surface of the first lens  10  to an image surface of the image sensor  70  may be 4.770 mm, and a distance (BFL) from an image-side surface of the fifth lens  50  to the image surface may be 1.249 mm. In addition, a focal length f1 of the first lens  10  may be −5.795 mm, a focal length f2 of the second lens  20  may be 2.123 mm, a focal length f3 of the third lens  30  may be −12.724 mm, a focal length f4 of the fourth lens  40  may be 2.694 mm, a focal length f5 of the fifth lens  50  may be −2.148 mm, a synthetic focal length f12 of the first and second lenses  10  and  20  may be 3.608 mm, and an overall focal length f of the optical system may be 4.1 mm. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 13 
               
               
                   
                   
               
             
             
               
                   
                 f1 
                 −5.795 
               
               
                   
                 f2 
                 2.123 
               
               
                   
                 f3 
                 −12.724 
               
               
                   
                 f4 
                 2.694 
               
               
                   
                 f5 
                 −2.148 
               
               
                   
                 f12 
                 3.608 
               
               
                   
                 f 
                 4.1 
               
               
                   
                 BFL 
                 1.249 
               
               
                   
                 FNO 
                 2.2 
               
               
                   
                 OAL 
                 4.770 
               
               
                   
                 FOV 
                 69.6 
               
               
                   
                   
               
             
          
         
       
     
     Other characteristics of lenses (radii of curvature of lenses, thicknesses of lenses, distances between lenses, refractive indices of lenses, Abbe numbers of lenses) are shown in Table 14. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 14 
               
               
                   
               
               
                   
                   
                 Thickness 
                 Refractive 
                 Abbe 
               
               
                 Surface No. 
                 Radius of Curvature 
                 or Distance 
                 Index 
                 Number 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 1.789 
                 0.27 
                 1.635 
                 24 
               
               
                 2 
                 1.136 
                 0.06 
               
               
                 3 
                 1.211 
                 0.63 
                 1.544 
                 56.1 
               
               
                 4 
                 −22.704 
                 0.00 
               
               
                 Stop 
                 Infinity 
                 0.05 
               
               
                 6 
                 2.689 
                 0.27 
                 1.635 
                 24 
               
               
                 7 
                 1.943 
                 0.95 
               
               
                 8 
                 −4.789 
                 0.61 
                 1.544 
                 56.1 
               
               
                 9 
                 −1.177 
                 0.28 
               
               
                 10  
                 −3.256 
                 0.40 
                 1.544 
                 56.1 
               
               
                 11  
                 1.91487 
                 0.23 
               
               
                 12  
                 Infinity 
                 0.30 
                 1.517 
                 64.2 
               
               
                 13  
                 Infinity 
                 0.72 
               
               
                 Image 
                 Infinity 
               
               
                   
               
             
          
         
       
     
     In a fourth exemplary embodiment of the present disclosure, the first lens  10  may have negative refractive power and may have a meniscus shape in which it is convex toward an object. The second lens  20  may have positive refractive power, and both surfaces thereof may be convex. The third lens  30  may have negative refractive power and may have a meniscus shape in which it is convex toward the object. The fourth lens  40  may have positive refractive power and may have a meniscus shape in which it is convex toward an image. The fifth lens  50  may have negative refractive power, and both surfaces thereof may be concave. In addition, the fifth lens  50  may have an inflection point formed on at least any one of first and second surfaces thereof. Further, the stop ST may be disposed between the second lens  20  and the third lens  30 . 
     The stop ST may be disposed between the second lens  20  and the third lens  30 , thereby decreasing sensitivity of each lens to a decentered tolerance. 
     Meanwhile, the respective surfaces of the first to fifth lenses  10  to  50  may have aspherical coefficients as shown in Table 15. That is, all of the first surface of the first lens  10  to the second surface of the fifth lens  50  may be aspherical. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 15 
               
               
                   
               
               
                 surface# 
                 1 
                 2 
                 3 
                 4 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Conic 
                 −3.66521 
                 −3.467763 
                 −2.55948 
                 0 
                 0 
                 −8.51905 
                 16.6167 
                 −0.54706 
                 0 
                 −15.2671 
               
               
                 Constant 
               
               
                 (K) 
               
               
                 4th Order 
                 −0.051284 
                 −0.03407 
                 0.0153702 
                 0.0461923 
                 −0.01622 
                 0.0976116 
                 −0.05763 
                 0.166092 
                 −0.05256 
                 −0.07943 
               
               
                 Coefficient 
               
               
                 (A) 
               
               
                 6th Order 
                 0.0687451 
                 0.0351119 
                 0.0378575 
                 −0.162695 
                 −0.115379 
                 −0.113339 
                 0.030638 
                 −0.13398 
                 0.044848 
                 0.033454 
               
               
                 Coefficient 
               
               
                 (B) 
               
               
                 8th Order 
                 −0.06829 
                 −0.037097 
                 −0.07812 
                 0.049779 
                 0.0015885 
                 0.1202049 
                 −0.14917 
                 0.098135 
                 −0.00929 
                 −0.01084 
               
               
                 Coefficient 
               
               
                 (C) 
               
               
                 10th Order 
                 0.0535837 
                 0.0672905 
                 0.0493466 
                 0.0519543 
                 0.2336525 
                 −0.062109 
                 0.155924 
                 −0.04502 
                 5.87E−04 
                 0.00188 
               
               
                 Coefficient 
               
               
                 (D) 
               
               
                 12th Order 
                 −0.016149 
                 0 
                 0 
                 −0.034547 
                 −0.119732 
                 0.0968946 
                 −0.08249 
                 0.009864 
                 0 
                 −1.32E−04 
               
               
                 Coefficient 
               
               
                 (E) 
               
               
                   
               
             
          
         
       
     
     Meanwhile, it may be appreciated from Table 16 that the optical system according to a fourth exemplary embodiment of the present disclosure satisfies Conditional Expressions 1 to 9 described above. Therefore, optical performance of the lens may be improved. 
     In addition, the optical system configured as described above may have aberration characteristics shown in  FIG. 8 . 
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE 16 
               
               
                   
                   
               
             
             
               
                   
                 CONDITIONAL EXPRESSION 1 
                 19.022264 
                 T34/T23 
               
               
                   
                 CONDITIONAL EXPRESSION 2 
                 −1.4135 
                 f1/f 
               
               
                   
                 CONDITIONAL EXPRESSION 3 
                 0.88 
                 f12/f 
               
               
                   
                 CONDITIONAL EXPRESSION 4 
                 32.1 
                 v2-v3 
               
               
                   
                 CONDITIONAL EXPRESSION 5 
                 −5.992158 
                 f3/f2 
               
               
                   
                 CONDITIONAL EXPRESSION 6 
                 1.1634526 
                 OAL/f 
               
               
                   
                 CONDITIONAL EXPRESSION 7 
                 24 
                 v3 
               
               
                   
                 CONDITIONAL EXPRESSION 8 
                 −0.464863 
                 f4/f1 
               
               
                   
                 CONDITIONAL EXPRESSION 9 
                 1.635 
                 n3 
               
               
                   
                   
               
             
          
         
       
     
     As set forth above, according to exemplary embodiments of the present disclosure, an aberration improvement effect may be improved, high resolution may be implemented, and sensitivity of lenses may be improved. 
     While exemplary embodiments have been shown and described above, it will be apparent to those skilled in the art that modifications and variations could be made without departing from the spirit and scope of the present disclosure as defined by the appended claims.