Question

A ray of light falls on transparent glass slab with refractive index 1.62 ( relative to air ) incidence for which the reflected and refracted rays are mutually perpendicular

Answer 1

Question: A ray of light falls on a transparent glass slab with refractive index (relative to air) of 1.62. The angle of incidence for which the reflected and refracted rays are mutually perpendicular is

Given: A ray of light falls on a transparent glass slab with refractive index (relative to air) of 1.62.

To Find: The angle of incidence for which the reflected and refracted rays are mutually perpendicular is:

Solution:  $tan^{-1} (1.62)$

Explanation:

From law of reflection: $r=i$

And from figure: $R+90^{o} +r=180^{o}$

⇒ $R=90^{o} -r$

⇒ $R=90^{o} -i$

Now from Snell's law:  $\frac{sin\: i}{sin R} =$ μ

⇒ $\frac{sin\: i}{sin(90^{o})-i } =$ μ

⇒ $\frac{sin\:i}{cos\:i} =$ μ

⇒ $tan\:i=$ μ ⇒ $i=tan^{-1}$μ

$i=tan^{-1} (1.62)$