Question

A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and refracted rays are mutually perpendicular. What is the angle of incidence? Give calculations.

Answer 1

Let a ray AO incident on the glass slab at O and is reflected along OB and refracted along OC having angle of incidence i and angle of refraction r as shown in the given figure.

From the figure

i + 90° + r = 180°

or  i + r = 90°

or r = 90° - i

From Snell's law

µ = \(\frac{sin\ i}{\sin r} = \frac{sin\ i}{sin (90-i)} = \frac{sin\ i}{cos\ i}\)

= tan i

or i = tan^-1 µ = tan ^-1 (1.62) = 59°19'