Question

A converging lens of refractive index 1.5 is kept in a liquid medium having the same refractive index. What would be the focal length of the lens in this medium?
A. f = 1
B. f =0
C. $f=\infty $
D. cannot be determined

Answer 1

Hint: As a very first step, we could read the question carefully and hence note down all the given quantities. From the given condition that the refractive index of the lens and the medium is the same, we could conclude that the lens would act as a plane glass. Hence, we could get the answer easily.

Complete step-by-step solution:
In the question, we are given a converging lens of refractive index 1.5. This lens is then kept in a liquid medium with the same refractive index, that is, 1.5. We are supposed to find the focal length of the lens in this new medium.
So, we are clearly given this condition that,
Refractive index of the lens = Refractive index of the medium = 1.5
This condition directly implies that the lens in the liquid will act as a plane sheet of glass. And we know that the focal length of a plane sheet of glass is infinity. So, the focal length of the given lens in this new medium would be infinite. Option C is correct.

Note: We have found the answer by simply using some theoretical facts. We could use an alternate method to find the focal length and hence prove our conclusion.
The lens maker’s formula is given by,
$\dfrac{1}{f}=\left( \dfrac{{{\mu }_{2}}}{{{\mu }_{1}}}-1 \right)\left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)$
But we have this condition,
${{\mu }_{1}}={{\mu }_{2}}$
$\Rightarrow \dfrac{1}{f}=0$
$\therefore f=\infty $
Hence, verified.