Question

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

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

Answer 1

The correct option is D ${90}^o$

Let the absolute refractive index of medium P and medium Q are $n_p$ and $n_q$ respectively.

Given:

The velocity of the wave in medium P is $v$

The velocity of the wave in medium Q is $2v$

Angle of incidence $i={30}^o$ in medium P

The angle of refraction $r=?$ in medium Q

From the definition of the refractive index, we can write,

$n_p=\frac{c}{v}$ and $n_q=\frac{c}{2v}$

Thus, $\frac{n_p}{n_q}=\frac{2v}{v}=2$

Now, from Snell's law we know, $n_{p}sini=n_{q}sinr$

$\Rightarrow \frac{n_p}{n_q}=\frac{sinr}{sini}$

$\Rightarrow 2=\frac{sinr}{sin{30}^o}$

$\Rightarrow sinr=2\times \frac{1}{2}=1$

$\Rightarrow sinr=sin{90}^o$

$\therefore r={90}^o$