A convex lens has a focal length `f`. It is cut into two parts along the dotted line as shown in figure. The focal length of each part will be

Options

A. `f/2`
B. `f`
C. `3/2 f`
D. `2f`

Answer

D

Explanation

According to the lens maker formula
`1/f = (mu - 1) [1/(R_1) - ((-1)/(R_2))]`
`1/f = (mu - 1) [2/R] [R_1 = R_2 = R]`
`f = R/(2(mu - 1)) " " ....(1) `
After cutting the lens as shown convex lens becomes plano-convex lens whose `R_1 = R, R_2 =oo`
`therefore 1/(f.) = (mu - 1)[1/R - 1/(oo)] implies 1/(f.) (mu - 1) [1/R]`
`f. = R/((mu - 1)) " " ....(2)`
From equation (1) and (2) we get
`(f.)/(f) = R/(mu - 1) xx ((mu - 1) xx 2)/(R) implies f. = 2f`

Short Note : (1) If lens cut as its focal length of new lens becomes twice the previous focal length.
(2) If lens cut as its focal length remain same because nature of lens remain constant as converging

`R_1 = R, R_2 = R`