Question

A sound wave traveling with a velocity $V$ in a medium $A$ reaches a point on the interface of medium $A$ and medium $B$. If the velocity in medium $B$ is $2V$, then the angle of incident for the total internal reflection of the wave will be greater than:

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

By Snell's law,

$\frac{\sin {\theta }_1}{\sin {\theta }_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1}$

$\frac{\sin {\theta }_1}{\sin {\theta }_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1}=\frac{1}{2}$

$\frac{\sin {\theta }_1}{\sin {\theta }_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1}$.

For total internal reflation, $\sin {\theta }_2=1$, and $\sin {\theta }_1=\frac{1}{2}$, ie, ${\theta }_1>30$.

Option 'B' is correct.