Question

A monochromatic beam of light is travelling from medium $A$ of refractive index $n_1$ to a medium $B$ of refractive index $n_2$. In the medium $A$, there are $x$ number of waves in certain distance. In the medium $B$, there are $y$ number of waves in the same distance. Then, refractive index of medium $A$ with respect to medium $B$ is _______.

• A. $\frac{y}{x}$
• B. $\sqrt{\frac{x}{y}}$
• C. $\frac{x}{y-x}$
• D. $\frac{x}{y}$

Answer 1

The correct option is D $\frac{x}{y}$

Let the distance in which $x$ waves in medium $A$ are present be $d$.

Then,

Wavelength in medium $A$ is ${\lambda }_A=\frac{d}{x}$

Wavelength in medium $B$ is ${\lambda }_B=\frac{d}{y}$

Refractive index is inversely proportional to wavelength.

Hence,

$n_{AB}=\frac{n_A}{n_B}=\frac{{\lambda }_B}{{\lambda }_A}=\frac{x}{y}$