Question

A plane sound wave travelling with velocity $v$ in a medium $A$ reaches a point on the interface of medium $A$ and medium $B$. If velocity of sound in medium $B$ is $2v$, the angle of incidence for total internal reflection of the wave will be greater than ($\sin 30=0.5$ and $\sin 90=1$)

• A. $15$
• B. $30$
• C. $45$
• D. $90$

Answer 1

Answer: (B)

$30$

Light travel from medium $A$ with velocity $v$ to medium $B$ with velocity $2v$
Velocity is more in medium $B$, hence it is rarer.
Refractive index of medium $A$ with respect to medium $B$
$\mu {=}_B{\mu }_A=\frac{VelocityinmediumB}{VelocityinmediumA}$
${}_B{\mu }_A=2/1$
Now as $\sin C=\frac{1}{\mu }$

$\therefore \sin C=\frac{1}{2}=0.5$
$\Rightarrow C=30$