The formula for refraction of light from the spherical surface is
n2v−n1u=n2−n1R where OB=−u,OI=+v,BC=+R
n2 is refractive index of medium 2 i.e. spherical glass
and n1 is refractive index of medium 1.
Figure (a) shows the geometry of image formation by a double convex lens. the image formation can be seen in two steps, the first refracting surface forms an image I1 which acts as a virtual object for the second surface. applying the equation above written for surface 1
n1OB+n2BI1=n2−n1BC2
similarly, form the second interface
−n2DI1+n1DI=n2−n1DC2 (refractive index of right side medium is n1 and for left side medium is n2, and also DI1is negative.)
now for thin lens BI1=DI1. adding both the equations we get
n1OB+n1DI=(n2−n1)(1BC1+1DC2)
and assuming the object at infinity means OB will be very large
we get n1DI=(n2−n1)(1BC1+1DC2)
and dividing both sides with n1
1DI=(n21−1)(1BC1+1DC2)
replacing DI=f,BC1=+R1,DC2=−R2
Finally, we get 1f=(n21−1)(1R1+1R2).
This equation is known as lens makers formula.