Lens maker formula 

 

 

1) Suppose a convex lens is taken.



2) The lens has centre of curvature C1 & C2, P1 & P2 their poles. And C is the optical centre of the lens as shown in the diagram.  




3) Suppose is the refractive index of the rarer medium &is the refractive index of the lens.



4) Suppose O is an object.



5) Rays coming from object O passes through the optical centre of the lens, without any deviation, along OC direction



6) An another rays coming from object O strikes at X point of the lens and passes through the lens, creating an image at I1 position.



Now we see  





[this equation was already proved in refraction though spherical surface]



7) After successfully passing through the first spherical surface light further gets refraction on the second spherical surface.



8) For the second refraction I1 is acting as an object.


9) And after second refraction light meets principal axis rays at I position. So here I is the image.



10) For I1 object and I image we get the equation   









& radius of curvature P2C2  = R1









Now adding 9.29 &  9.92
















 11) Where





andis the refractive index of the lens material with respect to the surrounding



Now when







12) Here f is the focal length of the lens. Then the above equation becomes