An equiconvex lens is cut into two halves along `(i) XOX^(')` and `(ii) YOY^(')` as shown in the figure. Let `f,f^(')f^('')` be the focal lengths of the complete lens, of each half in case `(i)`, and of each half in case `(ii)`, respectively
Choose the correct statement from the following

Options

A. `f^(')=f,f^('')=2f`
B. `f^(')=2f,f^('')=f`
C. `f^(')=f,f^('')=f`
D. `f^(')=2f,f^('')=2f`

Answer

a.

Explanation

In the first case, neither the radii of curvature nor the material of the lens is affected. In the second case.
`(1)/(f^(''))=(mu-1)((1)/(R))` or
`(1)/(f^(''))=(1)/(2)(mu-1)((2)/(R))=(1)/(2f)`
``or `f^('')=2f`