Question

A concave lens of refractive index $1.5$ is immersed in a medium of refractive index $1.65$ . What is the nature of the lens?

Answer 1

Hint: When a lens is immersed in a medium, three cases arise. The refractive index of the lens may be less than, equal to, or greater than the refractive index of the medium. The nature of the lens changes accordingly. Choose the correct situation and then answer the question accordingly.

Complete step by step solution:
Let ${\mu _1}$ be the refractive index of lens and ${\mu _2}$ be the refractive index of surrounding medium
For a concave lens,
If ${\mu _1} > {\mu _2}$ , then the concave lens is a diverging lens
If ${\mu _1} = {\mu _2}$ , then the concave lens works as a plain glass slab
If ${\mu _1} < {\mu _2}$ , then the concave lens is a converging lens
Given,
${\mu _1} = 1.5$ and ${\mu _2} = 1.65$
Since ${\mu _1} < {\mu _2}$ , then the concave lens is a converging lens.

Additional Information:
An optical lens is generally made up of two spherical surfaces. A convex lens is a lens which is tapering towards the ends and bulging at the centre. In contrast to it, a concave lens is bulging at the ends and tapering in the centre. Let ${\mu _1}$ be the refractive index of lens and ${\mu _2}$ be the refractive index of surrounding medium
For a convex lens,
If ${\mu _1} > {\mu _2}$ , then the concave lens is a converging lens.
If ${\mu _1} = {\mu _2}$ , then the concave lens works as a plain glass slab.
If ${\mu _1} < {\mu _2}$ , then the concave lens is a diverging lens.

Note: Remember the conditions mentioned. A convex lens doesn’t always behave as a converging lens. It depends on the refractive index of the lens and the surrounding medium. Similarly a concave lens isn’t always a diverging lens. Hence always be careful in answering these types of questions.