Question

A biconcave lens made of a transparent material of refractive index $ 1.25 $ is immersed in water of refractive index $ 1.33 $ . Will the lens behave as a converging or a diverging lens? Give reason.

Answer 1

Hint : A biconcave lens placed in air will diverge rays of light (hence behaves as a diverging lens). The lenses behave in reverse when placed in a medium whose refractive index is greater than theirs.

Formula used: In this solution we will be using the following formula;
 $ \Rightarrow {n_1}\sin {\theta _1} = {n_2}\sin {\theta _2} $ where $ {n_1} $ is the refractive index of incident medium, $ {\theta _1} $ is the angle of incidence, $ {n_2} $ is the index of refraction in transparent medium, and $ {\theta _2} $ is the angle of refraction.

Complete step by step answer
Generally, a biconcave lens in air will diverge rays of light hence behaves as a diverging lens. This happens because when light is travelling from a less dense medium to a denser medium it bends towards the normal, as in from
 $ \Rightarrow {n_1}\sin {\theta _1} = {n_2}\sin {\theta _2} $ where $ {n_1} $ is the refractive index of incident medium, $ {\theta _1} $ is the angle of incidence, $ {n_2} $ is the index of refraction in transparent medium, and $ {\theta _2} $ is the angle of refraction.
By rearranging to reveal the nature of the refraction angle $ {\theta _2} $
 $ \Rightarrow \sin {\theta _2} = \dfrac{{{n_1}}}{{{n_2}}}\sin {\theta _1} $ , hence if the incident medium index is less than the refractive medium index, then the angle reduces.
But if the incident medium index is greater than the refractive medium index, then the angle increases.
Hence, for the biconcave lens that behaves as a diverging lens in air (lower index) will behave as a converging lens in water (higher index).

Note
Similarly for a convex lens in air, when placed in water behaves as a diverging lens. However, to avoid confusions, the concave lens will behave less converging in water than it is diverging in air. And also, the convex lens will be less diverging in water than it is converging in air. Also, if the material is greater than the refractive index of water it remains the same way as it is in air but less powerful.