Question

Light falls from glass (μ = 1.5) to air. Find the angle of incidence for which the angle of deviation is 90°.

Answer 1

Given,
Light falls from glass to air.
Refractive index (μ) of glass = 1.5

Critical angle (θ_c) $={\sin }^{-1}\left(\frac{1}{\mathrm{\mu }}\right)$
$={\sin }^{-1}\left(\frac{1}{1.5}\right)=41.80$

We know that the maximum attainable angle of deviation in refraction is (90° − 41.8°)
= 47.2°
In this case, total internal reflection must have taken place.
In reflection,
Deviation = 180° − 2i = 90°
⇒ 2i = 90°
⇒ i = 45°
Hence, the required angle of incidence is 45°.