Question

Refractive index of glass with respect to water is 5/4 and the refractive index of water with respect to air is 4/3, what is the refractive index of glass with respect to air?
A. 5/3
B. 5/4
C. 16/15
D. 1.5

Answer 1

Hint: We can define the refractive index of one medium with respect to another by taking the ratios of speed of light of light in two mediums. They can be connected to other mediums also through related equations.

Complete step-by-step answer:
Snell’s law of refraction states that when light travels from one medium to another, it undergoes refraction in which it bends towards or away from the normal at the point of incidence. This occurs because the light has different speed in different mediums.
To understand how much refraction occurs in a medium, we have a refractive index which can be defined in a number of ways. It is defined as the ratio of sine of angle of incidence and sine of angle of refraction. It is also equal to the ratio of speed of light in the two mediums.
We are given that refractive index of glass with respect to water is 5/4 which we can write as
${\mu }_{\text{glass to water}}={\displaystyle \frac{{\mu }_{glass}}{{\mu }_{water}}}={\displaystyle \frac{5}{4}}...\text{(i)}$
Also it is given that the refractive index of water with respect to air is 4/3 which can be written as
${\mu }_{\text{water to air}}={\displaystyle \frac{{\mu }_{water}}{{\mu }_{air}}}={\displaystyle \frac{4}{3}}...\text{(ii)}$
We can get the refractive index of glass with respect to air as follows
${\mu }_{\text{glass to air}}={\displaystyle \frac{{\mu }_{glass}}{{\mu }_{air}}}$

Multiplying equation (i) and (ii), we get
$$\begin{gathered} {\displaystyle \frac{{\mu }_{glass}}{{\mu }_{air}}}={\displaystyle \frac{{\mu }_{glass}}{{\mu }_{water}}}\times {\displaystyle \frac{{\mu }_{water}}{{\mu }_{air}}}={\displaystyle \frac{5}{4}}\times {\displaystyle \frac{4}{3}}={\displaystyle \frac{5}{3}} \\ \Rightarrow {\mu }_{\text{glass to air}}={\displaystyle \frac{5}{3}} \end{gathered}$$

This is the required answer and option A is correct.

Note: The velocity of light is constant in vacuum and changes only when it travels from one medium to another with a change in direction. Also during refraction, there is no change in the frequency and wavelength of light which means colour remains the same.