A light ray enters through a right angled prism at point P with the angle of incidence 30° as shown in figure. It travels through the prism parallel to its base BC and emerges along the face AC. The refractive index of the prism is:

Calculation:

The formula for the refractive index is given as:

r₁ + c = A

⇒ r₁ = 90 - c

Snell's law at the emergent boundary

Sin(c) = 1 / μ

⇒ Cos(c) = (μ² - 1)^1/2 / μ

According to Snell's law at incident boundary

Sin(30) = μ × Sin(r₁)

1/2 = μ × Sin(90 - c) =μ Cos(c)

⇒ 1/2 = μ × (μ² - 1)^1/2 / μ

Squaring both sides:

1/4 = μ² - 1

μ² = 5 / 4

μ = √(5 / 4) = √5 / 2

Thus, the correct option is option 2: μ = √5 / 2