Question

The refractive index of glass with respect to air is $\dfrac{3}{2}$. The refractive index of air with respect to glass will be:
(A) $1$
(B) $\dfrac{3}{2}$
(C) $2$
(D) $\dfrac{2}{3}$

Answer 1

Hint
In physics there is a statement or equation that shows the relation between the refractive index of glass with respect to air and the refractive index of air with respect to glass, by using this statement, the refractive index of air with respect to glass will be determined.

Complete step by step answer
Given that, The refractive index of glass with respect to air is, ${}^a{\mu _g} = \dfrac{3}{2}$.
To determine the ${}^g{\mu _a}$:
The refractive index of glass with respect to air is, ${}^a{\mu _g} = \dfrac{{{\mu _g}}}{{{\mu _a}}} = \dfrac{3}{2}$.
Similarly, by the above equation, the refractive index of air with respect to glass will be $\Rightarrow {}^g{\mu _a} = \dfrac{{{\mu _a}}}{{{\mu _g}}}$.
In physics there is statement or equation that shows the relation between the refractive index of glass with respect to air and the refractive index of air with respect to glass is the product of the relation between the refractive index of glass with respect to air and the refractive index of air with respect to glass is equal to one.
By the above statement,
$\Rightarrow {}^a{\mu _g} \times {}^g{\mu _a} = 1\,................\left( 1 \right)$
By substituting the given refractive index of glass with respect to air in the equation (1), then the equation (1) is written as,
$\Rightarrow \dfrac{3}{2} \times {}^g{\mu _a} = 1$
By keeping the refractive index of air with respect to glass in one side and the other terms in other side, then the above equation is written as,
$\Rightarrow {}^g{\mu _a} = \dfrac{1}{{\left( {\dfrac{3}{2}} \right)}}$
By rearranging the terms, then the above equation is written as,
$\Rightarrow {}^g{\mu _a} = \dfrac{2}{3}$
Thus, the above equation shows the refractive index of air with respect to glass.
Hence, the option (D) is the correct answer.

Note
The solution of this question is also determined by another method. By comparing the formula of the refractive index of glass with respect to air and the refractive index of air with respect to glass which is given above in the solution, it is very clear that the refractive index of air with respect to glass is equal to the reciprocal of the refractive index of glass with respect to air.