Rays parallel to principal axis, incident on the spherical mirror at different heights from principal axis are focused at different points. And due to this reason we cannot define unique focus. This is known as spherical aberration. Angle of incidence `theta` shown in figure depends on the height of ray above principal axis. Focal length of spherical mirror can be easily written in terms of angle `theta` shown in figure as follows :
`f = R- (R)/(2)sec theta`
Here R is radius of curvature of mirror. The light rays which are very close to principal axis are known as paraxial rays and rays far away from principal axis are called marginal rays.
Let `f_(P)` and fm represent the focal length corresponding to paraxial rays and marginal rays respectively then

Options

A. Let `f_(p)` and fm represent the focal length corresponding to paraxial rays and marginal rays respectively then
B. `f_(p)=f_(m)`
C. `f_(p)gtf_(m)`
D. `f_(p)ltf_(m)`

Explanation

We know that `sec theta gt = 1` Hence maximum possible value of f is `R//2` and that is for paraxial rays and for the rest focal length will be less than `R//2`. Hence focal length for paraxial rays is maximum. Hence, option (b) is correct.