Let,
- refractive index of medium from which rays incident.
- refractive index of another medium.
u - distance of object from pole of spherical surface
v - distance of image from pole of spherical surface
Now, for NOC, i is the exterior angle.
.........(1)
Similarly,
.........(2)
Now by using snells law we get
Or for small angles
Substituting i and r from eq. (1) and (2), we get
As,
OM = -u, MI = +v, MC = + R
Hence equation becomes