Question

The refractive indices of water and glass with respect to air are ​$\dfrac{4}{3}$ and $1.5$ ​ respectively. What is the refractive index of glass with respect to water?
(A) $(\dfrac{4}{3} + 1.5)$
(B) $(1.5 - \dfrac{4}{3})$
(C) $(1.5 \times \dfrac{4}{3})$
(D) $(1.5 \div \dfrac{4}{3})$

Answer 1

To solve this question, we find the ratio of the refractive index of glass with respect to the air to the refractive index of water with respect to air. The Refractive index of a medium is the ratio of the velocity of light in vacuum or air to the velocity of light in that medium.

Step by step solution
Let us consider the velocity of light in a vacuum as $c$
Velocity of light in glass ${n_g}$
Velocity of light in water ${n_l}$
From the definition of the refractive index, the refractive index of glass with respect to air is $\dfrac{c}{{{n_g}}} = {\mu _g}$
The refractive index of water with respect to air is $\dfrac{c}{{{n_l}}} = {\mu _l}$
$\mu$ Represents the refractive index of the respective medium.
From this, we can say that the refractive index of glass with respect to water is the ratio of the velocity of light in water to the velocity of light in the glass.
$\dfrac{{{\mu _g}}}{{{\mu _l}}} = \dfrac{{(\dfrac{c}{{{n_g}}})}}{{(\dfrac{c}{{{n_l}}})}} = \dfrac{{{n_l}}}{{{n_g}}}$
From the question,
Refractive indices of water and glass with respect to air are ​$\dfrac{4}{3}$ and $1.5$
The refractive index of glass with respect to water, $\dfrac{{{\mu _g}}}{{{\mu _l}}} = 1.5 \div \dfrac{4}{3}$

Hence option (D) $1.5 \div \dfrac{4}{3}$ is the correct answer.

Note We can simply find the answer to this problem by dividing the refractive indices of glass and water in the air. This relation can be used for similar questions too but the refractive index of the two mediums should be with respect to a common medium. For example, the air in case of this question.
One might make a mistake by taking the refractive index of a medium as velocity of light in medium to velocity of light in air. Which is wrong, the refractive index is always the ratio of the velocity of light in the medium in which it is traveling into the velocity of light in the retracting medium.