Question

A ray of monochromatic light incident on the plane surface of separation between two media $x$ and $y$ with angle of incidence $i$ in the medium $x$ and angle of refraction $r$ in the medium $y$. The graph shows the relation between $\sin i$ and $\sin r$. The speed of light in the medium $y$ is $n$ times that of in medium $x.$ The value of $n$ is

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

Answer 1

The correct option is B $\frac{1}{\sqrt{3}}$

Let the situation present in the question be as shown in the below figure.

From Snell's law,

$\frac{\sin i}{\sin r}=\frac{v_1}{v_2}$
From the given graph we have,
$\frac{\sin i}{\sin r}=\cot {30}^{\circ }=\frac{v_1}{v_2}$
$\Rightarrow v_2=\frac{v_1}{\sqrt{3}}$

The speed of light in the medium $y$ is $n=\frac{1}{\sqrt{3}}$ times that of in medium $x$.

So, option $\left(b\right)$ is correct.