Question

On a glass slab, a beam of light is incident at an angle of ${60}^{\circ }$. Few light rays get reflected and others get refracted. If the reflected and the refracted light rays are mutually perpendicular, calculate the refractive index of the glass slab.

Answer 1

From the laws of reflection, let the:
Angle of incidence be $\angle i^{}$
Angle of reflection be $\angle r_1$
Angle of refraction be $\angle r_2$
Angle of incidence = Angle of reflection
$\angle i^{}$ $=$$\angle r_1$$=$${60}^o$
Since, the reflected rays are perpendicular to the refracted rays
So,
$\angle r_1+\angle r_2+{90}^o={180}^o$
$\angle r_2={30}^o$
From Snell's law,
Refractive index of a glass slab, $n=\frac{\sin i}{\sin r}$
In the figure given below,

$\angle i={60}^{\circ },\angle r={30}^{\circ }$
So, $n=\frac{\sin 60}{\sin 30}=\sqrt{3}$

Therefore, the refractive index of the glass slab is $\sqrt{3}$ or $1.732$.