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 fills 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

`(1)/(f)=((n_(2))/(n_(1))-1)((1)/(R_(1))-(1)/(R_(2)))`
where `n_(2)` and `n_(1)` are the refractive indices of the material of the lens and of the surroundings respectively. For a double concave lens,
`((1)/(R_(1))-(1)/(R_(2)))` is always negative.
Hence `f` is negative only when `n_(2)gtn_(1)`