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'=2f,f' '=f`
B. `f'= f,f' '=f`
C. `f'=2f,f' '=2f`
D. `f' = f,f''=2f`

Answer

A

Explanation

`(1)/(f)=(mu-1)((1)/(R)-(1)/(-R))=(2(mu-1))/(R)`
`f=(R)/(2(mu-1))`
`(1)/(f')=(mu-1)((1)/(infty)-(1)/(-R))=(mu-1)/(R)`
`f'=(R)/((mu-1))`
`(1)/(f'')=(mu-1)((1)/(R)-(1)/(-R))=(2(mu-1))/(R)`
`f=(R)/(2(mu-1))`
`f'=2f,f''=f`