Question

The refractive indices of water and glass relative to air are $\dfrac{4}{3}$and$\dfrac{3}{2}$respectively. The refractive index of glass relative to water will be:
$\text{A}\text{. }\left( \dfrac{4}{3}+\dfrac{3}{2} \right)$
$\text{B}\text{. }\left( \dfrac{3}{2}-\dfrac{4}{3} \right)$
$\text{C}\text{. }\left( \dfrac{3}{2}\times \dfrac{4}{3} \right)$
$\text{D}\text{. }\left( \dfrac{3}{2}\div \dfrac{4}{3} \right)$

Answer 1

Hint: For calculating relative refractive index of a medium, refractive index of one medium with respect to another, ratio of absolute refractive indices of the two media is taken, considering the appropriate ratio.

Formula used:
${{n}_{21}}=\dfrac{{{n}_{2air}}}{{{n}_{1air}}}$

Complete step by step answer:
Refractive index of a material is defined as the measure of bending of light rays while the light ray enters from one medium to another.
$n=\dfrac{c}{v}$
Where,
$c$ is the speed of light in air
$v$ is the speed of light in given medium
Factors on which value of refractive index depend:
Nature of medium
Physical conditions
Colour of the wavelength of light
Absolute refractive index is expressed when light travels from vacuum to another medium.
When we measure the value of speed of light in two different media, having different values of refractive index, relative refractive index of medium 2with respect to medium 1is defined as the ratio of speed of light in medium 1 to speed of light in medium 2.
${{n}_{21}}=\dfrac{\text{speed of light in medium 1}}{\text{speed of light in medium }2}$
Expression for relative refractive index:
${{n}_{21}}=\dfrac{{{n}_{2air}}}{{{n}_{1air}}}$
Where,
${{n}_{21}}$ is the refractive index of medium 2 with respect to medium 1
${{n}_{2air}}$ is the refractive index of medium 2 with respect to air
${{n}_{1air}}$ is the refractive index of medium 1 with respect to air
We are given that the refractive indices of water and glass relative to air are $\dfrac{4}{3}$ and $\dfrac{3}{2}$ respectively. We have to find the refractive index of glass relative to water.
Refractive index of glass with respect to water is the ratio of refractive index of glass with respect to air to the refractive index of water with respect to air.
${{n}_{gw}}=\dfrac{{{n}_{gair}}}{{{n}_{wair}}}$
${{n}_{gw}}=\dfrac{\dfrac{3}{2}}{\dfrac{4}{3}}=\dfrac{3}{2}\div \dfrac{4}{3}$
${{n}_{gw}}=\dfrac{3}{2}\div \dfrac{4}{3}$
Hence, the correct option is D.

Note: While calculating the relative refractive index, ratio should be taken carefully considering whose refractive index is to be calculated and with respect to which medium. Also, while defining the formula of relative refractive index of medium 1 with respect to medium 2, speed of light in the two media are taken inversely in the formula.