Question

A ray of light is incident on a medium with angle of incidence i and refracted into a second medium with angle of refraction $r$. The graph of $\sin \left(i\right)$ Vs $\sin \left(r\right)$ is as shown in the figure. Then the velocity of light in the first medium is ................. times the velocity of light in the second medium.

• A. $\sqrt{3}$
• B. $1/\sqrt{3}$
• C. $\sqrt{3}/2$
• D. $2/\sqrt{3}$

Answer 1

The correct option is A $\sqrt{3}$

Given

Ray of light is refracted when it is passed from one medium to another

Solution

Let refractive index of medium 1 is ${\mu }_1$

similarly refractive index of medium 2 is ${\mu }_2$

Using Snell law

${\mu }_1\sin i={\mu }_2\sin r$

$\frac{{\mu }_1}{{\mu }_2}=\frac{\sin r}{\sin i}$

Slope of graph$=\tan 30=\frac{\sin r}{\sin i}$

$\frac{{\mu }_1}{{\mu }_2}=3^{-1/2}$

We know that velocity of light in a medium is inversely proportional to refractive index, ie $\mu =\frac{c}{v}$

$\frac{{\mu }_1}{{\mu }_2}=\frac{v_2}{v_1}=3^{-1/2}$

$v_1=3^{1/2}\times v_2$

The correct option is A