Patent Publication Number: US-2022236537-A1

Title: Optical system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a Continuation Application of U.S. patent application Ser. No. 16/596,833, filed on Oct. 9, 2019, which is a Continuation Application of U.S. patent application Ser. No. 15/069,520 filed on Mar. 14, 2016, which claims the priority and benefit under 35 USC 119(a) of Korean Patent Application No. 10-2015-0112493, filed on Aug. 10, 2015, with the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference. 
    
    
     BACKGROUND 
     1. Field 
     The following description relates to an optical system including lenses having refractive power. 
     2. Description of Related Art 
     Over the years, camera modules have gradually been miniaturized. In addition, camera module performance has gradually improved. As an example, pixels of an image sensor have become small enough to enable realization of high resolution. 
     Typically, an optical system of a small camera module includes four lenses. However, it is difficult for the optical system including the four lenses to implement a clear image. Therefore, development of an optical system including five or more lenses is needed in order to enable realization of a clear image. 
     SUMMARY 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. 
     In accordance with an embodiment, there is provided an optical system, including: a first lens including a positive refractive power; a second lens including a positive refractive power and a convex image-side surface; a third lens; a fourth lens; a fifth lens including a concave object-side surface and a concave image-side surface; and a sixth lens including an inflection point formed on an image-side surface thereof, wherein the first to sixth lenses are sequentially disposed from an object toward an imaging plane.
         f, an overall focal length of the optical system and, f1, a focal length of the first lens may satisfy 1.0&lt;f1/f&lt;1.8.   V1, an Abbe number of the first lens and, V2, an Abbe number of the second lens may satisfy V1−V2&lt;25.   f, an overall focal length of the optical system and, f2, a focal length of the second lens may satisfy 0.5&lt;f2/f&lt;2.0.   f, an overall focal length of the optical system and, f3, a focal length of the third lens may satisfy −3&lt;f3/f&lt;−1.   f, an overall focal length of the optical system and, f4, a focal length of the fourth lens may satisfy 3&lt;|f4/f|.   f1, a focal length of the first lens and, f2, a focal length of the second lens may satisfy 0.5&lt;f1/f2&lt;2.0.   f, an overall focal length of the optical system and, r6, a radius of curvature of an image-side surface of the third lens may satisfy 0.3&lt;r6/f&lt;1.4.   f, an overall focal length of the optical system and r10 a radius of curvature of an image-side surface of the fifth lens may satisfy 30&lt;r10/f.       

     EPD, a diameter of an entrance pupil of the optical system and, f12, a synthetic focal length of the first lens and the second lens may satisfy 0.18&lt;(EPD/2)/f12. 
     In accordance with another embodiment, there is provided an optical system, including: a first lens including a positive refractive power; a second lens including a convex image-side surface; a third lens including a convex object-side surface; a fourth lens including a convex image-side surface; a fifth lens including a concave object-side surface and a concave image-side surface; and a sixth lens including an inflection point formed on an image-side surface thereof, wherein the first to sixth lenses are sequentially disposed from an object toward an imaging plane. 
     The first lens may include a convex object-side surface and a concave image-side surface. 
     The second lens may include a convex object-side surface. 
     The third lens may include a concave image-side surface. 
     The fourth lens may include a concave object-side surface. 
     The sixth lens may include a convex object-side surface and a concave image-side surface. 
     In accordance with another embodiment, there is provided an optical system, including: a first lens; a second lens including a convex image-side surface; a third lens including a convex object-side surface; a fourth lens including a convex image-side surface; a fifth lens including a concave object-side surface and a concave image-side surface; and a sixth lens including an inflection point formed on an image-side surface thereof, wherein the second lens has a same refractive power as a refractive power of the first lens, the third lens, the fourth lens, and the fifth lens have a refractive power higher than the refractive powers of the first and second lenses, and the sixth lens has a refractive power lower than the refractive powers of the first and second lenses.
         V1, an Abbe number of the first lens, V2, an Abbe number of the second lens, V3, an Abbe number of the third lens, and, V5, an Abbe number of the fifth lens may satisfy V1−V2&lt;25, 15&lt;|V1−V3|, and 25&lt;V1−V5&lt;45.   f, an overall focal length of the optical system, and f5 a focal length of the fifth lens may satisfy f5/f&lt;−10.   f, an overall focal length of the optical system, and TTL a distance from the object-side surface of the first lens to an imaging plane may satisfy TTL/f&lt;1.5.   f2, a focal length of the second lens, and, f3, a focal length of the third lens may satisfy −1.2&lt;f2/f3&lt;0.   f, an overall focal length of the optical system, and, BFL, a distance from an object-side surface of the sixth lens to an imaging plane may satisfy BFL/f&lt;0.5.   f, an overall focal length of the optical system, and, D2, a distance from the image-side surface of the first lens to an object-side surface of the second lens may satisfy D2/f&lt;0.1.   FOV, a field of view of the optical system may satisfy 75&lt;FOV.       

     Other features and aspects will be apparent from the following detailed description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       These and/or other aspects will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings in which: 
         FIG. 1  is a view of an optical system, according to a first embodiment; 
         FIG. 2  is graphs having curves representing aberration of the optical system, according to the first embodiment; 
         FIG. 3  is a table representing characteristics of the optical system, according to the first embodiment; 
         FIG. 4  is a table representing aspherical characteristics of the optical system according to the first embodiment; 
         FIG. 5  is a view of an optical system, according to a second embodiment; 
         FIG. 6  is graphs having curves representing aberration of the optical system, according to the second embodiment; 
         FIG. 7  is a table representing characteristics of the optical system, according to the second embodiment; 
         FIG. 8  is a table representing aspherical characteristics of the optical system according to the second embodiment; 
         FIG. 9  is a view of an optical system, according to a third embodiment; 
         FIG. 10  is graphs having curves representing aberration of the optical system, according to the third embodiment; 
         FIG. 11  is a table representing characteristics of the optical system, according to the third embodiment; 
         FIG. 12  is a table representing aspherical characteristics of the optical system, according to the third embodiment; 
         FIG. 13  is a view of an optical system, according to a fourth embodiment; 
         FIG. 14  is graphs having curves representing aberration of the optical system, according to the fourth embodiment; 
         FIG. 15  is a table representing characteristics of the optical system, according to the fourth embodiment; 
         FIG. 16  is a table representing aspherical characteristics of the optical system, according to the fourth embodiment; 
         FIG. 17  is a view of an optical system, according to a fifth embodiment; 
         FIG. 18  is graphs having curves representing aberration of the optical system, according to the fifth embodiment; 
         FIG. 19  is a table representing characteristics of the optical system, according to the fifth embodiment; 
         FIG. 20  is a table representing aspherical characteristics of the optical system, according to the fifth embodiment; 
         FIG. 21  is a view of an optical system according to a sixth embodiment; 
         FIG. 22  is graphs having curves representing aberration of the optical system, according to the sixth embodiment; 
         FIG. 23  is a table representing characteristics of the optical system, according to the sixth embodiment; and 
         FIG. 24  is a table representing aspherical characteristics of the optical system, according to the sixth embodiment. 
     
    
    
     Throughout the drawings and the detailed description, unless otherwise described, the same drawing reference numerals will be understood to refer to the same elements, features, and structures. The relative size and depiction of these elements may be exaggerated for clarity, illustration, and convenience. 
     DETAILED DESCRIPTION 
     The following detailed description is provided to assist the reader in gaining a comprehensive understanding of the methods, apparatuses, and/or systems described herein. However, various changes, modifications, and equivalents of the methods, apparatuses, and/or systems described herein will be apparent to one of ordinary skill in the art. The sequences of operations described herein are merely examples, and are not limited to those set forth herein, but may be changed as will be apparent to one of ordinary skill in the art, with the exception of operations necessarily occurring in a certain order. Also, descriptions of functions and constructions that are well known to one of ordinary skill in the art may be omitted for increased clarity and conciseness. 
     The features described herein may be embodied in different forms, and are not to be construed as being limited to the examples described herein. Rather, the examples described herein have been provided so that this disclosure will be thorough and complete, and will convey the full scope of the disclosure to one of ordinary skill in the art. 
     The features described herein may be embodied in different forms, and are not to be construed as being limited to the examples described herein. Rather, the examples described herein have been provided so that this disclosure will be thorough and complete, and will convey the full scope of the disclosure to one of ordinary skill in the art. 
     It will be understood that, although the terms first, second, third, etc. may be used herein to describe various lenses, these lenses should not be limited by these terms. These terms are only used to distinguish one lens from another lens. These terms do not necessarily imply a specific order or arrangement of the lenses. Thus, a first lens discussed below could be termed a second lens without departing from the teachings description of the various embodiments. 
     In addition, a surface of each lens closest to an object is referred to as a first surface or an object-side surface, and a surface of each lens closest to an imaging surface is referred to as a second surface or an image-side surface. Further, all numerical values of radii of curvature, thicknesses/distances, TTLs, and other parameters of the lenses are represented in millimeters (mm). A person skilled in the relevant art will appreciate that other units of measurement may be used. Further, in the present specification, all radii of curvature, thicknesses, OALs (optical axis distances from the first surface of the first lens to the image sensor (OALs), a distance on the optical axis between the stop and the image sensor (SLs), image heights (IMGHs) (image heights), and black focus lengths (BFLs) (back focus lengths) of the lenses, an overall focal length of an optical system, and a focal length of each lens are indicated in millimeters (mm). Further, thicknesses of lenses, gaps between the lenses, OALs, and SLs are distances measured based on an optical axis of the lenses. 
     In addition, in an embodiment, shapes of lenses are described and illustrated in relation to optical axis portions of the lenses. 
     A surface of a lens being convex means that an optical axis portion of a corresponding surface is convex, and a surface of a lens being concave means that an optical axis portion of a corresponding surface is concave. Therefore, in a configuration in which one surface of a lens is described as being convex, an edge portion of the lens may be concave. Likewise, in a configuration in which one surface of a lens is described as being concave, an edge portion of the lens may be convex. In other words, a paraxial region of a lens may be convex, while the remaining portion of the lens outside the paraxial region is either convex, concave, or flat. Further, a paraxial region of a lens may be concave, while the remaining portion of the lens outside the paraxial region is either convex, concave, or flat. 
     In addition, in an embodiment, thicknesses and radii of curvatures of lenses are measured in relation to optical axes of the corresponding lenses. 
     An optical system, according to an embodiment, includes six lenses. As an example, the optical system may include a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and a sixth lens. The lens module may include from four lenses up to six lenses without departing from the scope of the embodiments herein described. In accordance with an illustrative example, the embodiments described of the optical system include six lenses with a refractive power. However, a person of ordinary skill in the relevant art will appreciate that the number of lenses in the optical system may vary, for example, between two to six lenses, while achieving the various results and benefits described hereinbelow. Also, although each lens is described with a particular refractive power, a different refractive power for at least one of the lenses may be used to achieve the intended result. In the optical system, according to embodiments, the first to sixth lenses are formed of materials including glass, plastic or other similar types of polycarbonate materials. In another embodiment, at least one of the first through sixth lenses is formed of a material different from the materials forming the other first through sixth lenses. 
     The first lens has a refractive power. As an example, the first lens has a positive refractive power. An image-side surface of the first lens is concave. The first lens may have an aspherical surface. As an example, both of the object-side surface and an image-side surface of the first lens are aspherical. The first lens is formed of plastic. However, a material of the first lens is not limited to plastic. 
     The second lens has a refractive power. As an example, the second lens has a positive refractive power. An object-side surface or an image-side surface of the second lens is convex. The second lens may have an aspherical surface. As an example, both of the object-side surface and the image-side surface of the second lens are aspherical. The second lens may be formed of plastic. However, a material of the second lens is not limited to plastic. 
     The third lens has a refractive power, such as a positive refractive power or a negative refractive power. An object-side surface of the third lens is convex. The third lens may have an aspherical surface. As an example, both of the object-side surface and an image-side surface of the third lens are aspherical. The third lens may be formed of plastic. However, a material of the third lens is not limited to plastic. 
     The fourth lens has a refractive power. As an example, the fourth lens may have a positive refractive power. As another example, the fourth lens may also have a negative refractive power. An image-side surface of the fourth lens is convex. The fourth lens may have an aspherical surface. As an example, both of an object-side surface and the image-side surface of the fourth lens are aspherical. The fourth lens may be formed of plastic. However, a material of the fourth lens is not limited to plastic. In one example, the object-side surface of the fourth lens is concave in a paraxial region and gradually flattens at edge portions thereof. 
     The fifth lens has a refractive power. As an example, the fifth lens has a negative refractive power. Both surfaces of the fifth lens are concave. The fifth lens may have an aspherical surface. As an example, both of an object-side surface and an image-side surface of the fifth lens are aspherical. The fifth lens has an inflection point. As an example, one or more inflection points are formed on the image-side surface of the fifth lens. The fifth lens may be formed of plastic. However, a material of the fifth lens is not limited to plastic. In one example, the object-side surface of the fourth lens is concave in a paraxial region and gradually flattens at edge portions thereof. 
     The sixth lens has a refractive power. An image-side surface of the sixth lens is concave. The sixth lens may have an aspherical surface. As an example, both of an object-side surface and the image-side surface of the sixth lens are aspherical. The sixth lens has an inflection point. As an example, one or more inflection points are formed on the image-side surface of the sixth lens. The sixth lens may be formed of plastic. However, a material of the sixth lens is not limited to plastic. 
     A person of ordinary skill in the relevant art will appreciate that each of the first through fifth lenses may be configured in an opposite refractive power from the configuration described above. For example, in an alternative configuration, the first lens has a negative refractive power, the second lens has a negative refractive power, the third lens has a negative refractive power, the fourth lens has a positive refractive power, the fifth lens has a positive refractive power, and the sixth lens has a negative refractive power. 
     The optical system includes a filter and an image sensor. The filter is disposed between the sixth lens and the image sensor. The filter may filter an infrared component from incident light refracted through the first to sixth lenses. The image sensor is disposed behind the filter, and converts the incident light refracted through the first to sixth lenses into electrical signals. 
     The optical system includes a stop. The stop may adjust an amount of light incident to the first to sixth lenses. As an example, the stop is disposed adjacently to the object-side surface of the first lens to adjust an amount of light incident to the first lens. 
     The optical system satisfies the following Conditional Expression 1: 
       1.0&lt;f1/f&lt;1.8.   [Conditional Expression 1]
 
     In one example, f is an overall focal length of the optical system, and f1 is a focal length of the first lens. The above Conditional Expression 1 indicates a condition that limits a magnitude of refractive power of the first lens to overall refractive power of the optical system. As an example, in a case in which f1/f is outside of a lower limit value of the above Conditional Expression 1, the first lens has a significantly great refractive power, in such a manner that it is difficult to correct spherical aberration. As another example, in a case in which f1/f is outside of an upper limit value of the above Conditional Expression 1, the first lens has significantly low refractive power, which is advantageous in correcting spherical aberration, but makes miniaturization of the optical system difficult. 
     The optical system satisfies one or more of the following Conditional Expressions 2 through 4: 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       ⁢ 
                       1 
                     
                     - 
                     
                       V 
                       ⁢ 
                       2 
                     
                   
                   &lt; 
                   25 
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     2 
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   15 
                   &lt; 
                   
                     
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                       &#34;\[LeftBracketingBar]&#34; 
                     
                     
                       
                         V 
                         ⁢ 
                         1 
                       
                       - 
                       
                         V 
                         ⁢ 
                         3 
                       
                     
                     
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                       &#34;\[RightBracketingBar]&#34; 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     3 
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   25 
                   &lt; 
                   
                     
                       V 
                       ⁢ 
                       1 
                     
                     - 
                     
                       V 
                       ⁢ 
                       5 
                     
                   
                   &lt; 
                   
                     4 
                     ⁢ 
                     
                       5 
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     In an example, V1 is an Abbe number of the first lens, V2 is an Abbe number of the second lens, V3 is an Abbe number of the third lens, and V5 is an Abbe number of the fifth lens. The Conditional Expressions 2 through 4 represent or define limit conditions to correct chromatic aberration of the optical system. As an example, in a case in which V1−V2, |V1−V3|, and V1−V5 are out of numerical ranges of the Conditional Expressions 2 through 4, respectively, the optical system has significantly high chromatic aberration, in such a manner that it is difficult to use the optical system in a camera module that needs to provide a high resolution. 
     The optical system satisfies the following Conditional Expression 5: 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     5 
                   
                   &lt; 
                   
                     f 
                     ⁢ 
                     2 
                     / 
                     f 
                   
                   &lt; 
                   
                     2 
                     . 
                     0 
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     In an example, f is the overall focal length of the optical system, and f2 is a focal length of the second lens. The Conditional Expression 5 represents or defines a condition to limit a magnitude of refractive power of the second lens to the overall refractive power of the optical system. As an example, in a case in which f2/f is outside of a lower limit value of the Conditional Expression 5, the second lens has significantly great refractive power, in such a manner that it is difficult to correct spherical aberration. As another example, in a case in which f2/f is outside of an upper limit value of the Conditional Expression 5, the second lens has significantly low refractive power, which is advantageous to correct spherical aberration, but makes miniaturization of the optical system difficult. 
     The optical system satisfies the following Conditional Expression 6: 
     
       
         
           
             
               
                 
                   
                     - 
                     3. 
                   
                   &lt; 
                   
                     f 
                     ⁢ 
                     3 
                     / 
                     f 
                   
                   &lt; 
                   
                     - 
                     
                       1. 
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
     In an example, f is the overall focal length of the optical system, and f3 is a focal length of the third lens. The Conditional Expression 6 represents or defines a condition for limiting a magnitude of refractive power of the third lens to the overall refractive power of the optical system. As an example, in a case in which f3/f is outside of a lower limit value of the Conditional Expression 6, the third lens has significantly great refractive power making it difficult to correct spherical aberration. As another example, in a case in which f3/f is outside of an upper limit value of the Conditional Expression 6, the third lens has significantly low refractive power, which is advantageous in correcting spherical aberration, but makes miniaturization of the optical system difficult. 
     The optical system satisfies the following Conditional Expression 7: 
     
       
         
           
             
               
                 
                   3 
                   &lt; 
                   
                     
                       
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                         f 
                         ⁢ 
                         4 
                         / 
                         f 
                       
                       
                         ❘ 
                         &#34;\[RightBracketingBar]&#34; 
                       
                     
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     In an example, f is the overall focal length of the optical system, and f4 is a focal length of the fourth lens. The Conditional Expression 7 represents or defines a condition for limiting a magnitude of refractive power of the fourth lens to the overall refractive power of the optical system. As an example, in a case in which f4/f is outside of a lower limit value of the Conditional Expression 7, the fourth lens has significantly great refractive power, in such a manner that it is difficult to correct spherical aberration. 
     The optical system satisfies the following Conditional Expression 8: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁢ 
                     5 
                       
                     / 
                     f 
                   
                   &lt; 
                   
                     
                       - 
                       1 
                     
                     ⁢ 
                     
                       0 
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
     In an embodiment, f is the overall focal length of the optical system, and f5 is a focal length of the fifth lens. The Conditional Expression 8 represents or defines a condition to limit a magnitude of refractive power of the fifth lens to the overall refractive power of the optical system. As an example, in a case in which f5/f is outside of an upper limit value of the Conditional Expression 8, the fifth lens has significantly great refractive power making it difficult to correct spherical aberration. 
     The optical system satisfies the following Conditional Expression 9: 
     
       
         
           
             
               
                 
                   
                     TTL 
                     / 
                     f 
                   
                   &lt; 
                   
                     1.5 
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
     In an example, f is the overall focal length of the optical system, and TTL is a distance from the object-side surface of the first lens to an imaging plane. The Conditional Expression 9 represents or defines a condition for miniaturizing the optical system. As an example, in a case in which TTL/f is outside of an upper limit value of the Conditional Expression 9, it is difficult to mount the optical system in a small portable terminal. 
     The optical system satisfies the following Conditional Expression 10: 
     
       
         
           
             
               
                 
                   
                     0 
                     . 
                     5 
                   
                   &lt; 
                   
                     f 
                     ⁢ 
                     1 
                     / 
                     f 
                     ⁢ 
                     2 
                   
                   &lt; 
                   
                     2 
                     . 
                     0 
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
     In one example, f1 is the focal length of the first lens, and f2 is the focal length of the second lens. The Conditional Expression 10 represents or defines a condition for limiting a ratio of refractive power between the first lens and the second lens. As an example, in a case in which f1/f2 is outside of a numerical range of the Conditional Expression 10, refractive power of the first lens or the second lens is significantly great making it difficult to correct aberration. 
     The optical system satisfies the following Conditional Expression 11: 
     
       
         
           
             
               
                 
                   
                     - 
                     1.2 
                   
                   &lt; 
                   
                     f 
                     ⁢ 
                     2 
                     / 
                     f 
                     ⁢ 
                     3 
                   
                   &lt; 
                   
                     0 
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
     In an embodiment, f2 is the focal length of the second lens, and f3 is the focal length of the third lens. The Conditional Expression 11 represents or defines a condition to limit a ratio of refractive power between the second lens and the third lens. As an example, in a case in which f2/f3 is outside of a numerical range of the Conditional Expression 11, refractive power of the second lens or the third lens is significantly great, in such a manner that it is difficult to correct aberration. 
     The optical system satisfies the following Conditional Expression 12: 
     
       
         
           
             
               
                 
                   
                     BFL 
                     / 
                     f 
                   
                   &lt; 
                   
                     0 
                     . 
                     5 
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
     In one example, f is the overall focal length of the optical system, and BFL is a distance from the object-side surface of the sixth lens to the imaging plane. The Conditional Expression 12 represents or defines a condition for miniaturizing the optical system. As an example, in a case in which BFL/f is outside of an upper limit value of the Conditional Expression 12, it is difficult to miniaturize the optical system. 
     The optical system satisfies the following Conditional Expression 13: 
     
       
         
           
             
               
                 
                   
                     D 
                     ⁢ 
                     2 
                     / 
                     f 
                   
                   &lt; 
                   
                     0 
                     . 
                     1 
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     13 
                   
                   ] 
                 
               
             
           
         
       
     
     In an example, f is the overall focal length of the optical system, and D2 is a distance from the image-side surface of the first lens to the object-side surface of the second lens. The Conditional Expression 13 represents or defines a condition for improving longitudinal chromatic aberration characteristics. As an example, in a case in which D2/f is outside of an upper limit value of the Conditional Expression 13, longitudinal chromatic aberration characteristics of the first lens and the second lens deteriorate. 
     The optical system satisfies the following Conditional Expression 14: 
     
       
         
           
             
               
                 
                   0.3 
                   &lt; 
                   
                     r 
                     ⁢ 
                     6 
                     / 
                     f 
                   
                   &lt; 
                   
                     1.4 
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     14 
                   
                   ] 
                 
               
             
           
         
       
     
     In an embodiment, f is the overall focal length of the optical system, and r6 is a radius of curvature of the image-side surface of the third lens. The above Conditional Expression 14 represents or defines a condition to limit refractive power of the third lens. As an example, in a case in which r6/f is outside of a numerical range of the Conditional Expression 14, it is not easy to manufacture the third lens, and it is difficult to secure the required refractive power. 
     The optical system satisfies the following Conditional Expression 15: 
     
       
         
           
             
               
                 
                   
                     3 
                     ⁢ 
                     0 
                   
                   &lt; 
                   
                     r 
                     ⁢ 
                     10 
                     / 
                     
                       f 
                       . 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     15 
                   
                   ] 
                 
               
             
           
         
       
     
     In an example, f is the overall focal length of the optical system, and r10 is a radius of curvature of the image-side surface of the fifth lens. The above Conditional Expression represents or defines a condition for limiting refractive power of the fifth lens. As an example, in a case in which r10/f is outside of a numerical range of the Conditional Expression 15, it is not easy to manufacture the fifth lens, and it is difficult to secure the required refractive power. 
     The optical system satisfies the following Conditional Expression 16: 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       1 
                     
                     ⁢ 
                     8 
                   
                   &lt; 
                   
                     
                       ( 
                       
                         EPD 
                         / 
                         2 
                       
                       ) 
                     
                     / 
                     f 
                       
                     12. 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     16 
                   
                   ] 
                 
               
             
           
         
       
     
     In one embodiment, EPD is a diameter of an entrance pupil of the optical system, and f12 is a synthetic focal length of the first lens and the second lens. The above Conditional Expression represents or defines a condition for realizing an optical system capable of realizing bright images. As an example, in a case in which EPD/2 is outside of a lower limit value of the Conditional Expression 16, it is difficult to secure an amount of light incident to the image sensor, in such a manner that the optical system may not be adequately used in a camera module and produce high resolution. 
     The optical system satisfies one or more of the following Conditional 
     Expressions 17 and 18: 
     
       
         
           
             
               
                 
                   
                     7 
                     ⁢ 
                     5 
                   
                   &lt; 
                   FOV 
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     17 
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     ⁢ 
                         
                     number 
                   
                   &lt; 
                   
                     2.3 
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Conditional 
                     ⁢ 
                         
                     Expression 
                     ⁢ 
                         
                     18 
                   
                   ] 
                 
               
             
           
         
       
     
     In an example, FOV is a field of view of the optical system. 
     In the optical system configured as described above, strong positive refractive power is dispersed to the first lens and the second lens. In addition, in the optical system according to an embodiment, tolerance sensitivity of the first lens is reduced, and a phenomenon that a radius of curvature of the object-side surface of the first lens becomes excessively low is alleviated. 
     Also, in one embodiment, each of the first to sixth lenses may be separate lenses configured as described above. A distance between lenses may vary. In another embodiment, at least one of the first to sixth lenses may be operatively connected or in contact with another one of the first to sixth lenses. 
     In a further alternative embodiment, two or more of the lenses of the first to sixth lenses may be configured as a group and in operative connection or contact with another lens. For instance, the first, second, and third lenses may be in contact with each other as a first group lens, while the fourth, fifth, and sixth lenses are configured separate from each other and from the first group lens. In the alternative, the first, second, and third lenses may be in contact with each other as a first group lens, the fourth and the fifth lenses may be in contact with each other as a second group lens, and the sixth lens is configured separate from the first and second group lenses. 
     Next, several embodiments will be described. 
     An optical system, according to a first embodiment will be described with reference to  FIG. 1 . 
     The optical system  100 , according to an embodiment, includes first to sixth lenses  110  to  160 . The first to sixth lenses  110  to  160  are sequentially disposed from an object toward an imaging plane. 
     The first lens  110  has a positive refractive power. An object-side surface of the first lens  110  is convex, and an image-side surface thereof is concave. For example, a first surface of the first lens  110  is convex in a paraxial region, and a second surface of the first lens  110  is concave in the paraxial region. The first lens  110  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the first lens  110  are aspherical. In one example, the first lens  110  is formed of a material having a refractive index of 1.547. A focal length of the first lens  110  may be 6.430 mm. 
     The second lens  120  has a positive refractive power. An object-side surface of the second lens  120  is convex, and an image-side surface thereof is convex. In one example, the first and second surfaces of the second lens are convex in the paraxial region. The second lens  120  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the second lens  120  are aspherical. The second lens  120  is formed of a material that is substantially the same as or similar to that of the first lens. As an example, the second lens  120  has a refractive power of 1.547, which is the same as that of the first lens. A focal length of the second lens  120  may be 4.024 mm. 
     The third lens  130  has a negative refractive power. An object-side surface of the third lens  130  is convex, and an image-side surface thereof is concave. For example, a first surface of the third lens  130  is convex in the paraxial region, and a second surface of the third lens  130  is concave in the paraxial region. The third lens  130  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the third lens  130  are aspherical. The third lens  130  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the third lens  130  is 1.657, which is higher than those of the first and second lenses. A focal length of the third lens  130  may be −6.017 mm. 
     The fourth lens  140  has a positive refractive power. An object-side surface of the fourth lens  140  is concave, and an image-side surface thereof may be convex. For example, a first surface of the fourth lens  140  is concave in the paraxial region, and a second surface of the fourth lens  140  is convex in the paraxial region. The fourth lens  140  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fourth lens  140  are aspherical. The fourth lens  140  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fourth lens  140  is 1.657, which is higher than those of the first and second lenses. A focal length of the fourth lens  140  may be 347.95 mm. 
     The fifth lens  150  has a negative refractive power. An object-side surface of the fifth lens  150  is concave, and an image-side surface thereof is concave. For example, a first surface of the fifth lens  150  is concave in the paraxial region, and a second surface of the fifth lens  150  is concave in the paraxial region. The fifth lens  150  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fifth lens  150  are aspherical. An inflection point is formed on the fifth lens  150 . As an example, one or more inflection points are formed on the image-side surface of the fifth lens  150 . The fifth lens  150  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fifth lens  150  is 1.657, which is higher than those of the first and second lenses. A focal length of the fifth lens  150  may be −120.555 mm. 
     The sixth lens  160  has a negative refractive power. An object-side surface of the sixth lens  160  is convex, and an image-side surface thereof is concave. For example, a first surface of the sixth lens  160  is convex in the paraxial region, and a second surface of the sixth lens  160  is concave in the paraxial region. The sixth lens  160  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the sixth lens  160  are aspherical. An inflection point is formed on the sixth lens  160 . As an example, one or more inflection points is formed on the object-side surface and the image-side surface of the sixth lens  160 . The sixth lens  160  has a low refractive power. As an example, the refractive power of the sixth lens  160  is 1.537, which is lower than those of the first and second lenses. A focal length of the sixth lens  160  may be −9.940 mm. 
     The optical system  100  includes a filter  170  and an image sensor  180 . 
     The filter  170  is adjacently disposed to the image-side surface of the sixth lens  160 . The filter  170  has a substantially flat plate. The filter  170  filters infrared rays from light refracted from the sixth lens  160 . 
     The image sensor  180  is disposed behind the filter  170 . The image sensor  180  has a predetermined size. As an example, a distance (Img HT) (see  FIG. 2 ) from an intersection point between an imaging plane of the image sensor  180  and an optical axis to a diagonal corner of the image sensor  180  may be 3.26 mm. 
     The optical system  100  includes a stop ST. The stop ST may be disposed adjacently to the object-side surface of the first lens  110 . However, a person skill in the art will appreciate that the stop ST may be positioned in between two of the lenses  110  to  160 . 
     The optical system  100  configured as described above represent aberration characteristics and optical characteristics as illustrated in  FIGS. 2 and 3 . As an example, an F number of the optical system  100  according to an embodiment may be 2.13, an overall length (TTL), which is a distance from the object-side surface of the first lens to the imaging plane of the optical system  100 , is 4.632 mm, an overall focal length of the optical system  100  is 4.083 mm, EPD/2 of the optical system  100  is 0.96 mm, and f12 is 2.68082 mm. For reference,  FIG. 4  is a table representing aspherical coefficients of the optical system  100 . 
     An optical system, according to a second embodiment, will be described with reference to  FIG. 5 . 
     The optical system  200 , according to an embodiment, includes first to sixth lenses  210  to  260 . The first to sixth lenses  210  to  260  are sequentially disposed from an object toward an imaging plane. 
     The first lens  210  has a positive refractive power. An object-side surface of the first lens  210  is convex, and an image-side surface thereof is concave. The first lens  210  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the first lens  210  are aspherical. The first lens  210  may be formed of a material having a refractive index of 1.547. A focal length of the first lens  210  may be 6.479 mm. 
     The second lens  220  has a positive refractive power. An object-side surface of the second lens  220  is convex, and an image-side surface thereof is convex. The second lens  220  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the second lens  220  are aspherical. The second lens  220  is formed of a material that is substantially the same as or similar to that of the first lens. As an example, the second lens  220  has a refractive power of 1.547, which is the same as that of the first lens. A focal length of the second lens  220  may be 4.032 mm. 
     The third lens  230  has a negative refractive power. An object-side surface of the third lens  230  is convex, and an image-side surface thereof is concave. The third lens  230  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the third lens  230  are aspherical. The third lens  230  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the third lens  230  may be 1.657, which is higher than those of the first and second lenses. A focal length of the third lens  230  may be −6.104 mm. 
     The fourth lens  240  has a negative refractive power. An object-side surface of the fourth lens  240  is concave, and an image-side surface thereof is convex. The fourth lens  240  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fourth lens  240  are aspherical. The fourth lens  240  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fourth lens  240  is 1.657, which is higher than those of the first and second lenses. A focal length of the fourth lens  240  may be −833.75 mm. 
     The fifth lens  250  has a negative refractive power. An object-side surface of the fifth lens  250  is concave, and an image-side surface thereof is concave. The fifth lens  250  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fifth lens  250  are aspherical. An inflection point is formed on the fifth lens  250 . As an example, one or more inflection points is formed on the image-side surface of the fifth lens  250 . The fifth lens  250  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fifth lens  250  is 1.657, which is higher than those of the first and second lenses. A focal length of the fifth lens  250  may be −279.664 mm. 
     The sixth lens  260  has a negative refractive power. An object-side surface of the sixth lens  260  is convex, and an image-side surface thereof is concave. The sixth lens  260  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the sixth lens  260  re aspherical. An inflection point is formed on the sixth lens  260 . As an example, one or more inflection points is formed on the object-side surface and the image-side surface of the sixth lens  260 . The sixth lens  260  has a low refractive power. As an example, the refractive power of the sixth lens  260  may be 1.537, which is lower than those of the first and second lenses. A focal length of the sixth lens  260  may be −9.708 mm. 
     The optical system  200  may include a filter  270  and an image sensor  280 . 
     The filter  270  may be disposed adjacently to the image-side surface of the sixth lens  260 . The filter  270  may have a substantially flat plate. The filter  270  filters infrared rays from light refracted from the sixth lens  260 . 
     The image sensor  280  may be disposed behind the filter  270 . The image sensor  280  has a predetermined size. As an example, a distance (Img HT) (see  FIG. 6 ) from an intersection point between an imaging plane of the image sensor  280  and an optical axis to a diagonal corner of the image sensor  280  is 3.26 mm. 
     The optical system  200  may include a stop ST. The stop ST may be disposed adjacently to the object-side surface of the first lens  210 . 
     The optical system  200  configured as described above, represents aberration characteristics and optical characteristics as illustrated in  FIGS. 6 and 7 . As an example, an F number of the optical system  200 , according to an embodiment, may be 2.13, an overall length (TTL), which is a distance from the object-side surface of the first lens to the imaging plane, of the optical system  200  is 4.632 mm, an overall focal length of the optical system  200  is 4.091 mm, EPD/2 of the optical system  200  is 0.96 mm, and f12 is 2.69113 mm. For reference,  FIG. 8  is a table representing aspherical coefficients of the optical system  200 . 
     An optical system, according to a third embodiment, will be described with reference to  FIG. 9 . 
     The optical system  300 , according to an embodiment, includes first to sixth lenses  310  to  360 . The first to sixth lenses  310  to  360  are sequentially disposed from an object toward an imaging plane. 
     The first lens  310  has a positive refractive power. An object-side surface of the first lens  310  is convex, and an image-side surface thereof is concave. The first lens  310  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the first lens  310  are aspherical. The first lens  310  is formed of a material having a refractive index of 1.547. A focal length of the first lens  310  may be 6.362 mm. 
     The second lens  320  has a positive refractive power. An object-side surface of the second lens  320  is convex, and an image-side surface thereof is convex. The second lens  320  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the second lens  320  are aspherical. The second lens  320  is formed of a material that is substantially the same as or similar to that of the first lens. As an example, the second lens  320  has a refractive power of 1.547, which is the same as that of the first lens. A focal length of the second lens  320  may be 4.008 mm. 
     The third lens  330  has a negative refractive power. An object-side surface of the third lens  330  is convex, and an image-side surface thereof is concave. The third lens  330  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the third lens  330  are aspherical. The third lens  330  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the third lens  330  is 1.657, which is higher than those of the first and second lenses. A focal length of the third lens  330  may be −6.002 mm. 
     The fourth lens  340  has a positive refractive power. An object-side surface of the fourth lens  340  is concave, and an image-side surface thereof is convex. The fourth lens  340  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fourth lens  340  are aspherical. The fourth lens  340  has a refractive power higher than those of the first and second lenses. As an example, refractive power of the fourth lens  340  is 1.657, which is higher than those of the first and second lenses. A focal length of the fourth lens  340  may be 186.48 mm. 
     The fifth lens  350  has a negative refractive power. An object-side surface of the fifth lens  350  is concave, and an image-side surface thereof is concave. The fifth lens  350  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fifth lens  350  are aspherical. An inflection point is formed on the fifth lens  350 . As an example, one or more inflection points is formed on the image-side surface of the fifth lens  350 . The fifth lens  350  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fifth lens  350  is 1.657, which is higher than those of the first and second lenses. A focal length of the fifth lens  350  may be −63.924 mm. 
     The sixth lens  360  has a negative refractive power. An object-side surface of the sixth lens  360  is convex, and an image-side surface thereof is concave. The sixth lens  360  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the sixth lens  360  are aspherical. An inflection point is formed on the sixth lens  360 . As an example, one or more inflection points is formed on the object-side surface and the image-side surface of the sixth lens  360 . The sixth lens  360  has a low refractive power. As an example, the refractive power of the sixth lens  360  is 1.537, which is lower than those of the first and second lenses. A focal length of the sixth lens  360  may be −9.739 mm. 
     The optical system  300  may include a filter  370  and an image sensor  380 . 
     The filter  370  may be disposed adjacently to the image-side surface of the sixth lens  360 . The filter  370  may have a substantially flat plate. The filter  370  may filter infrared rays from light refracted from the sixth lens  360 . 
     The image sensor  380  may be disposed behind the filter  370 . The image sensor  380  has a predetermined size. As an example, a distance (Img HT) (see  FIG. 10 ) from an intersection point between an imaging plane of the image sensor  380  and an optical axis to a diagonal corner of the image sensor  380  may be 3.26 mm. 
     The optical system  300  may include a stop ST. The stop ST may be disposed adjacently to the object-side surface of the first lens  310 . 
     The optical system  300  configured as described above represents aberration characteristics and optical characteristics as illustrated in  FIGS. 10 and 11 . As an example, an F number of the optical system  300 , according to an embodiment, is 2.13, an overall length (TTL), which is a distance from the object-side surface of the first lens to the imaging plane, of the optical system  300  is 4.632 mm, an overall focal length of the optical system  300  is 4.096 mm, EPD/2 of the optical system  300  is 0.96 mm, and f12 is 2.66683 mm. For reference,  FIG. 12  is a table representing aspherical coefficients of the optical system  300 . 
     An optical system, according to a fourth embodiment, will be described with reference to  FIG. 13 . 
     The optical system  400 , according to an embodiment, includes first to sixth lenses  410  to  460 . The first to sixth lenses  410  to  460  are sequentially disposed from an object toward an imaging plane. 
     The first lens  410  has a positive refractive power. An object-side surface of the first lens  410  is convex, and an image-side surface thereof is concave. The first lens  410  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the first lens  410  are aspherical. The first lens  410  is formed of a material having a refractive index of 1.547. A focal length of the first lens  410  may be 5.410 mm. 
     The second lens  420  has a positive refractive power. An object-side surface of the second lens  420  is convex, and an image-side surface thereof is convex. The second lens  420  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the second lens  420  are aspherical. The second lens  420  is formed of a material that is substantially the same as or similar to that of the first lens. As an example, the second lens  420  has a refractive power of 1.547, which is the same as that of the first lens. A focal length of the second lens  420  may be 5.455 mm. 
     The third lens  430  has a negative refractive power. An object-side surface of the third lens  430  is convex, and an image-side surface thereof is concave. The third lens  430  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the third lens  430  are aspherical. The third lens  430  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the third lens  430  is 1.657, which is higher than those of the first and second lenses. A focal length of the third lens  430  may be −6.393 mm. 
     The fourth lens  440  has a positive refractive power. An object-side surface of the fourth lens  440  is concave, and an image-side surface thereof is convex. The fourth lens  440  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fourth lens  440  are aspherical. The fourth lens  440  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fourth lens  440  may be 1.657, which is higher than those of the first and second lenses. A focal length of the fourth lens  440  may be 15.92 mm. 
     The fifth lens  450  has a negative refractive power. An object-side surface of the fifth lens  450  is concave, and an image-side surface thereof is concave. The fifth lens  450  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fifth lens  450  are aspherical. An inflection point is formed on the fifth lens  450 . As an example, one or more inflection points is formed on the image-side surface of the fifth lens  450 . The fifth lens  450  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fifth lens  450  is 1.657, which is higher than those of the first and second lenses. A focal length of the fifth lens  450  may be −762.392 mm. 
     The sixth lens  460  has a negative refractive power. An object-side surface of the sixth lens  460  is convex, and an image-side surface thereof is concave. The sixth lens  460  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the sixth lens  460  are aspherical. An inflection point is formed on the sixth lens  460 . As an example, one or more inflection points is formed on the object-side surface and the image-side surface of the sixth lens  460 . The sixth lens  460  has a low refractive power. As an example, the refractive power of the sixth lens  460  is 1.537, which is lower than those of the first and second lenses. A focal length of the sixth lens  460  may be −5.537 mm. 
     The optical system  400  may include a filter  470  and an image sensor  480 . 
     The filter  470  may be disposed adjacently to the image-side surface of the sixth lens  460 . The filter  470  may have a substantially flat plate. The filter  470  may filter infrared rays from light refracted from the sixth lens  460 . 
     The image sensor  480  may be disposed behind the filter  470 . The image sensor  480  has a predetermined size. As an example, a distance (Img HT) (see  FIG. 14 ) from an intersection point between an imaging plane of the image sensor  480  and an optical axis to a diagonal corner of the image sensor  480  is 3.43 mm. 
     The optical system  400  may include a stop ST. The stop ST may be disposed adjacently to the object-side surface of the first lens  410 . 
     The optical system  400  configured as described above represents aberration characteristics and optical characteristics as illustrated in  FIGS. 14 and 15 . As an example, an F number of the optical system  400 , according to an embodiment, is 2.31, an overall length (TTL), which is a distance from the object-side surface of the first lens to the imaging plane of the optical system  400  is 4.650 mm, an overall focal length of the optical system  400  is 4.150 mm, EPD/2 of the optical system  400  is 0.90 mm, and f12 is 2.90358 mm. For reference,  FIG. 16  is a table representing aspherical coefficients of the optical system  400 . 
     An optical system, according to a fifth embodiment, will be described with reference to  FIG. 17 . 
     The optical system  500 , according to an embodiment, includes first to sixth lenses  510  to  560 . The first to sixth lenses  510  to  560  are sequentially disposed from an object toward an imaging plane. 
     The first lens  510  has a positive refractive power. An object-side surface of the first lens  510  is convex, and an image-side surface thereof is concave. The first lens  510  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the first lens  510  are aspherical. The first lens  510  may be formed of a material having a refractive index of 1.547. A focal length of the first lens  510  may be 5.249 mm. 
     The second lens  520  has a positive refractive power. An object-side surface of the second lens  520  is convex, and an image-side surface thereof is concave. In an alternative configuration, the second lens  520  includes an object-side surface that is convex, and an image-side surface thereof is flat or substantially flat. 
     The second lens  520  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the second lens  520  are aspherical. The second lens  520  is formed of a material that is substantially the same as or similar to that of the first lens. As an example, the second lens  520  has a refractive power of 1.547, which is the same as that of the first lens. A focal length of the second lens  520  may be 6.964 mm. 
     The third lens  530  has a negative refractive power. An object-side surface of the third lens  530  is convex, and an image-side surface thereof is concave. The third lens  530  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the third lens  530  are aspherical. The third lens  530  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the third lens  530  is 1.657, which is higher than those of the first and second lenses. A focal length of the third lens  530  may be −8.818 mm. 
     The fourth lens  540  has a positive refractive power. An object-side surface of the fourth lens  540  is concave, and an image-side surface thereof is convex. The fourth lens  540  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fourth lens  540  are aspherical. The fourth lens  540  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fourth lens  540  is 1.657, which is higher than those of the first and second lenses. A focal length of the fourth lens  540  may be 17.91 mm. 
     The fifth lens  550  has a negative refractive power. An object-side surface of the fifth lens  550  is concave, and an image-side surface thereof is concave. The fifth lens  550  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fifth lens  550  are aspherical. An inflection point is formed on the fifth lens  550 . As an example, one or more inflection points is formed on the image-side surface of the fifth lens  550 . The fifth lens  550  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fifth lens  550  is 1.657, which is higher than those of the first and second lenses. A focal length of the fifth lens  550  may be −686.904 mm. 
     The sixth lens  560  has a negative refractive power. An object-side surface of the sixth lens  560  is convex, and an image-side surface thereof is concave. The sixth lens  560  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the sixth lens  560  are aspherical. An inflection point is formed on the sixth lens  560 . As an example, one or more inflection points is formed on the object-side surface and the image-side surface of the sixth lens  560 . The sixth lens  560  has a low refractive power. As an example, the refractive power of the sixth lens  560  is 1.537, which is lower than those of the first and second lenses. A focal length of the sixth lens  560  may be −6.296 mm. 
     The optical system  500  may include a filter  570  and an image sensor  580 . 
     The filter  570  may be disposed adjacently to the image-side surface of the sixth lens  560 . The filter  570  may have a substantially flat plate. The filter  570  may filter infrared rays from light refracted from the sixth lens  560 . 
     The image sensor  580  may be disposed behind the filter  570 . The image sensor  580  may have a predetermined size. As an example, a distance (Img HT) (see  FIG. 18 ) from an intersection point between an imaging plane of the image sensor  580  and an optical axis to a diagonal corner of the image sensor  580  is 3.43 mm. 
     The optical system  500  may include a stop ST. The stop ST may be disposed adjacently to the object-side surface of the first lens  510 . 
     The optical system  500  configured as described above represents aberration characteristics and optical characteristics as illustrated in  FIGS. 18 and 19 . As an example, an F number of the optical system  500 , according to an embodiment, is 2.25, an overall length (TTL), which is a distance from the object-side surface of the first lens to the imaging plane of the optical system  500 , is 4.500 mm, an overall focal length of the optical system  500  is 4.059 mm, EPD/2 of the optical system  500  is 0.90 mm, and f12 is 3.13502 mm. For reference,  FIG. 20  is a table representing aspherical coefficients of the optical system  500 . 
     An optical system, according to a sixth embodiment, will be described with reference to  FIG. 21 . 
     The optical system  600 , according to an embodiment, includes first to sixth lenses  610  to  660 . The first to sixth lenses  610  to  660  are sequentially disposed from an object toward an imaging plane. 
     The first lens  610  has a positive refractive power. An object-side surface of the first lens  610  is convex, and an image-side surface thereof is concave. The first lens  610  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the first lens  610  are aspherical. The first lens  610  is formed of a material having a refractive index of 1.547. A focal length of the first lens  610  may be 5.236 mm. 
     The second lens  620  has a positive refractive power. An object-side surface of the second lens  620  is convex, and an image-side surface thereof is convex. The second lens  620  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the second lens  620  are aspherical. The second lens  620  is formed of a material that is substantially the same as or similar to that of the first lens. As an example, the second lens  620  has a refractive power of 1.547, which is the same as that of the first lens. A focal length of the second lens  620  may be 6.072 mm. 
     The third lens  630  has a negative refractive power. An object-side surface of the third lens  630  is convex, and an image-side surface thereof is concave. The third lens  630  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the third lens  630  are aspherical. The third lens  630  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the third lens  630  is 1.657, which is higher than those of the first and second lenses. A focal length of the third lens  630  may be −7.313 mm. 
     The fourth lens  640  has a positive refractive power. An object-side surface of the fourth lens  640  is concave, and an image-side surface thereof is convex. The fourth lens  640  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fourth lens  640  are aspherical. The fourth lens  640  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fourth lens  640  is 1.657, which is higher than those of the first and second lenses. A focal length of the fourth lens  640  may be 20.74 mm. 
     The fifth lens  650  has a negative refractive power. An object-side surface of the fifth lens  650  is concave, and an image-side surface thereof is concave. The fifth lens  650  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the fifth lens  650  are aspherical. An inflection point is formed on the fifth lens  650 . As an example, one or more inflection points is formed on the image-side surface of the fifth lens  650 . The fifth lens  650  has a refractive power higher than those of the first and second lenses. As an example, the refractive power of the fifth lens  650  is 1.657, which is higher than those of the first and second lenses. A focal length of the fifth lens  650  may be −762.404 mm. 
     The sixth lens  660  has a negative refractive power. An object-side surface of the sixth lens  660  is convex, and an image-side surface thereof is concave. The sixth lens  660  has an aspherical shape. As an example, both of the object-side surface and the image-side surface of the sixth lens  660  are aspherical. An inflection point is formed on the sixth lens  660 . As an example, one or more inflection points is formed on the object-side surface and the image-side surface of the sixth lens  660 . The sixth lens  660  has a low refractive power. As an example, the refractive power of the sixth lens  660  is 1.537, which is lower than those of the first and second lenses. A focal length of the sixth lens  660  may be −6.090 mm. 
     The optical system  600  may include a filter  670  and an image sensor  680 . 
     The filter  670  may be disposed adjacently to the image-side surface of the sixth lens  660 . The filter  670  may have a substantially flat plate. The filter  670  may filter infrared rays from light refracted from the sixth lens  660 . 
     The image sensor  680  may be disposed behind the filter  670 . The image sensor  680  has a predetermined size. As an example, a distance (Img HT) (see  FIG. 22 ) from an intersection point between an imaging plane of the image sensor  680  and an optical axis to a diagonal corner of the image sensor  680  is 3.43 mm. 
     The optical system  600  may include a stop ST. The stop ST may be disposed adjacently to the object-side surface of the first lens  610 . 
     The optical system  600  configured as described above represents aberration characteristics and optical characteristics as illustrated in  FIGS. 22 and 23 . As an example, an F number of the optical system  600 , according to an embodiment, is 2.29, an overall length (TTL), which is a distance from the object-side surface of the first lens to the imaging plane of the optical system  600 , is 4.600 mm, an overall focal length of the optical system  600  is 4.129 mm, EPD/2 of the optical system  600  is 0.90 mm, and f12 is 2.98069 mm. For reference,  FIG. 24  is a table representing aspherical coefficients of the optical system  600 . 
     The optical systems, according to the first to sixth embodiments configured as described above, satisfy all of the Conditional Expressions 1 through 18, as represented in Table 1. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Conditional 
                 First 
                 Second 
                 Third 
                 Fourth 
                 Fifth 
                 Sixth 
               
               
                 Remark 
                 Expression 
                 Embodiment 
                 Embodiment 
                 Embodiment 
                 Embodiment 
                 Embodiment 
                 Embodiment 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 1 
                 1 &lt; f1/f &lt; 1.8 
                 1.575 
                 1.584 
                 1.553 
                 1.304 
                 1.293 
                 1.268 
               
               
                 2 
                 V1 − V2 &lt; 25 
                 0.0 
                 0.0 
                 0.0 
                 0.0 
                 0.0 
                 0.0 
               
               
                 3 
                 15 &lt; |V1 − V3| 
                 34.60 
                 34.60 
                 34.60 
                 34.60 
                 34.60 
                 34.60 
               
               
                 4 
                 25 &lt; V1 − V5 &lt; 45 
                 34.60 
                 34.60 
                 34.60 
                 34.60 
                 34.60 
                 34.60 
               
               
                 5 
                 0.5 &lt; f2/f &lt; 2.0 
                 0.986 
                 0.986 
                 0.978 
                 1.315 
                 1.716 
                 1.470 
               
               
                 6 
                 −3 &lt; f3/f &lt; −1 
                 −1.474 
                 −1.492 
                 −1.465 
                 −1.541 
                 −2.172 
                 −1.771 
               
               
                 7 
                 3 &lt; |f4/f| 
                 85.214 
                 203.786 
                 45.523 
                 3.837 
                 4.412 
                 5.023 
               
               
                 8 
                 f5/f &lt; −10 
                 −29.525 
                 −68.356 
                 −15.605 
                 −183.709 
                 −169.238 
                 −184.633 
               
               
                 9 
                 TTL/f &lt; 1.5 
                 1.134 
                 1.132 
                 1.131 
                 1.120 
                 1.109 
                 1.114 
               
               
                 10 
                 0.5 &lt; f1/f2 &lt; 2.0 
                 1.598 
                 1.607 
                 1.588 
                 0.992 
                 0.754 
                 0.862 
               
               
                 11 
                 −1.2 &lt; f2/f3 &lt; 0 
                 −0.669 
                 −0.661 
                 −0.668 
                 −0.853 
                 −0.790 
                 −0.830 
               
               
                 12 
                 BFL/f &lt; 0.5 
                 0.273 
                 0.274 
                 0.269 
                 0.237 
                 0.255 
                 0.243 
               
               
                 13 
                 D2/f &lt; 0.5 
                 0.025 
                 0.025 
                 0.027 
                 0.039 
                 0.027 
                 0.034 
               
               
                 14 
                 0.3 &lt; r6/f &lt; 1.4 
                 0.839 
                 0.837 
                 0.845 
                 0.725 
                 0.927 
                 0.797 
               
               
                 15 
                 30 &lt; r10/f 
                 244.906 
                 55.073 
                 218.873 
                 240.964 
                 201.976 
                 242.172 
               
               
                 16 
                 0.18 &lt; (EPD/2)/f12 
                 0.358 
                 0.357 
                 0.360 
                 0.310 
                 0.287 
                 0.302 
               
               
                 17 
                 75 &lt; FOV 
                 75.30 
                 75.10 
                 75.10 
                 77.40 
                 78.70 
                 77.70 
               
               
                 18 
                 F number &lt; 2.3 
                 2.130 
                 2.130 
                 2.130 
                 2.310 
                 2.250 
                 2.290 
               
               
                   
               
            
           
         
       
     
     As set forth above, the optical system, according to an embodiment, photographs a clear image. 
     While this disclosure includes specific examples, it will be apparent to one of ordinary skill in the art that various changes in form and details may be made in these examples without departing from the spirit and scope of the claims and their equivalents. The examples described herein are to be considered in a descriptive sense only, and not for purposes of limitation. Descriptions of features or aspects in each example are to be considered as being applicable to similar features or aspects in other examples. Suitable results may be achieved if the described techniques are performed in a different order, and/or if components in a described system, architecture, device, or circuit are combined in a different manner and/or replaced or supplemented by other components or their equivalents. Therefore, the scope of the disclosure is defined not by the detailed description, but by the claims and their equivalents, and all variations within the scope of the claims and their equivalents are to be construed as being included in the disclosure.