A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids `L_(1)` or `L_(2)` having refractive indices `n_(1)` and `n_(2)`, respectively `(n_(2) gt n_(1) gt 1)`. The lens will diverge parallel beam of light if it is filles with

Options

A. air and placed in air
B. air and immersed in `L_(1)`
C. `L_(1)` and immersed in `L_(2)`
D. `L_(2)` and immersed in `L_(1)`

Answer

D

Explanation

The lens Maker's formula is :
`(1)/(f) = ((n_(L))/(n_(m)) -1) ((1)/(R_(1)) - (1)/(R_(2)))`
where `n_(L)` = Refractive index of lens and
`n_(m)` = Refractive index of medium.
In case of double concave lens. `R_(1)` is negative and `R_(2)` is positive .
Therefore, `((1)/(R_(1)) - (1)/(R_(2)))` will be -ve.
For the lens to be diverging in nature, focal length f should be negative or `((n_(L))/(n_(m)) -1)` should be positive or `n_(L) gt n_(m)` but since `n_(2) gt n_(1)` (given) , therefore the lens should be filled with `L_(2)` and immersed in `L_(1)`.