Question

A wave has velocity $u$ in medium $P$ and velocity $ 2u $ in medium $Q$. If the wave is incident in medium $P$ at an angle $ 30^{\circ}, $ then the angle of refraction will be

• A. $ 30^{\circ} $
• B. $ 45^{\circ} $
• C. $ 60^{\circ} $
• D. $ 90^{\circ} $

Answer 1

The Correct Option is D

From Snell's law, refractive index $(\mu)$ is given by
$\mu=\frac{\sin i}{\sin r} .. .$ (i)
where $i$ is angle of incidence and $r$ of refraction.
Also, $\mu=\frac{v_{1}}{v_{2}}$..(ii)
Equating Eqs. (i) and (ii), we get
$\mu=\frac{\sin i}{\sin r}=\frac{v_{1}}{v_{2}}$
$\Rightarrow \sin r=\frac{v_{2}}{v_{1}} . \sin i$
Given, $v_{2}=2 u, v_{1}=u, i=30^{\circ}, \sin 30^{\circ}=\frac{1}{2}$
$\therefore \sin r=2 \times \frac{1}{2}=1$
$\Rightarrow r=90^{\circ}$