Question

A ray of light falls on a transparent glass slab of
refractive index √2. If the reflected and refracted
rays are mutually perpendicular, then the angle of
incidence is
(1) tan
(2) sin (
(3) tan- (3)
(4) sin(3)​

Answer 1

Given info : A ray of light falls on a transparent glass slab of refractive index √2. If the reflected and refracted rays are mutually perpendicular.

To find : The angle of incidence is ...

solution : see figure, it is clearly shown that reflected and refracted rays are mutually perpendicular.

so, angle of incidence + angle between refracted and reflected rays + angle of refraction = 180°

⇒i + 90° + r = 180°

⇒i + r = 90°

⇒r = 90° - i

using Snell's law, μ₁sini = μ₂sinr

⇒1 × sini = √2 sin(90° - i)

⇒sini = √2 cosi

⇒tani = √2

or, sini = √2/√3 ⇒i = sin¯¹(√2/√3)

Therefore the angle of incidence is sin¯¹(√2/√3).