A ray travels with speed 2 × 10⁸ m/s in an equilateral prism. Find the minimum angle of deviation.

Answer: 2 sin^-1(3/4) − 60°

Detailed Solution

The speed of light inside the prism is given as:

v = 2 × 10⁸ m/s

We know that refractive index:

μ = c/v

where c = 3 × 10⁸ m/s.

Substituting values:

μ = (3 × 10⁸) / (2 × 10⁸)

μ = 3/2

Since the prism is equilateral:

A = 60°

At minimum deviation:

r = A/2 = 30°

Applying Snell’s law:

μ = sin i / sin r

3/2 = sin i / sin 30°

3/2 = sin i /(1/2)

sin i = 3/4

Therefore:

i = sin^-1(3/4)

The minimum deviation formula is:

δ_min = 2i − A

Substituting values:

δ_min = 2 sin^-1(3/4) − 60°

Hence the minimum angle of deviation is:

δ_min = 2 sin^-1(3/4) − 60°