Question

A light is travelling from air into a medium. Velocity of light in a medium is reduced to $0.75$ times the velocity in air. Assume that angle of incident 'i' is very small, the deviation of the ray is

• A. $i$
• B. $\frac{i}{3}$
• C. $\frac{i}{4}$
• D. $\frac{3i}{4}$

Answer 1

The correct option is C $\frac{i}{4}$

$\begin{array}{c}\text{Velocity of light in a medium}\left(c_m\right)=0.75\text{(velocity)}\\ \text{of light in air (c)}\sqrt{C_m}=0.75C\\ \text{Refractive index}=\mu \\ \mu =\frac{c}{C_m}=\frac{1}{0.75}=\frac{4}{3}\\ \text{So Refractive index of medium}=4/3\end{array}$

$\begin{array}{c}\text{air}\\ \text{medium}\\ \mu =1\\ \begin{array}{c}\mu =\frac{4}{3}\\ \text{medium}\\ \text{deviation}=1-r\end{array}\end{array}$

Sine rule is

${\mu }_1\sin i_1={\mu }_2\sin {\gamma }_2$

given that Incidence angle is small

So

$\begin{array}{c}\sin i_1\approx 1_1\\ \sin x_2\simeq x_2\end{array}$

According to sine rule

$\text{(1)}\sin i_1=\frac{4}{3}\sin {\gamma }_2$

$\begin{array}{cc}{i}_1& =\frac{4}{3}\gamma \\ \gamma & =\frac{3i}{4}\\ \text{Deviation}=i-\gamma & =i\frac{3i}{4}=\frac{i}{4}\end{array}$

Hence option (c) $i/4$ in correct option.