Question

A ray of light strikes a transparent rectangular slab of refractive index $\sqrt{2}$ at an angle of incidence of ${45}^{\circ }$. The angle between the reflected and refracted rays is :

• A. ${75}^0$
• B. ${90}^0$
• C. ${105}^0$
• D. ${120}^0$

Answer 1

The correct option is C ${105}^0$

Given:

Angle of incident, $i={45}^{\circ }$

refractive index, $\mu =\sqrt{2}$

From snell's Law:

The angle of insident=Angle of reflection
$i=r={45}^{\circ }$

For refraction,

$\frac{\sin i}{\sin r_2}=\sqrt{2}$

$\frac{\sin 45}{\sin r_2}=\sqrt{2}$

$\Rightarrow r_2={30}^{\circ }$

Now, from figure angle between refracted and reflected ray is $45+60={105}^{\circ }$