Question

A biconvex lens of focal length $f$ and radii of curvature of both the surfaces R is made of a material of refractive index ${n_1}$ . This lens is placed in a liquid of refractive index ${n_2}$. Now this lens will behave like:
A. either as convex or a concave lens depending solely on R
B. a convex lens depending on ${n_1}$ and ${n_2}$
C. a concave lens depending on ${n_1}$ and ${n_2}$
D. a convex lens of same focal length irrespective of R, ${n_1}$ and ${n_2}$

Answer 1

A biconvex lens will behave like a convex or concave lens depending upon the values of ${n_1}$ and ${n_2}$. For a convex lens ${n_1} > {n_2}$. For a concave lens ${n_1} < {n_2}$. Look at the possibilities for the values of ${n_1}$ and ${n_2}$.

Complete step by step answer:
When a ray of light enters from one medium to another, there is a change in the path of the light. Refractive index of medium 1 with respect to medium 2 is the ratio of the speed of light in medium 2 to the speed of light in medium 1. A biconvex lens is made of two convex lenses having the same radius of curvature. A biconvex lens has the ability to converge the incident light. If a biconvex lens of refractive index ${n_1}$is placed in a liquid of refractive index ${n_2}$, then obviously the path of light will depend the values of ${n_1}$ and ${n_2}$In the given problem, it is not clear that whether ${n_1}$ is greater or ${n_2}$ is greater.
If ${n_1} > {n_2}$, the given biconvex lens will behave like a converging lens, that is, a convex lens.
If ${n_1} < {n_2}$, the given biconvex lens will behave like a diverging lens, that is, a concave lens.
Hence, the given biconvex lens will behave like a converging or diverging depending upon the values of the refractive indexes.

Hence, the correct options are (B) and (C).

Note:
The value of the refractive index will depend upon whether the light enters from a rarer to a denser medium or from denser to a rarer medium. In a convex refracting surface, light enters from a rarer to a denser medium. On the other hand, in a concave refracting surface light enters from a denser to a rarer medium.