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

Answer: (D)

$90^{\circ}$

Answer 2

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, $v_{2}=2 u, v_{1}=u, i=30^{\circ}, \sin 30^{\circ}=\frac{1}{2}$
$\therefore \sin r=2 \times \frac{1}{2}=1$
$\Rightarrow r=90^{\circ}$