A light ray enters through a right angled prism at point P with the angle of incidence 3 0 ∘ as shown in figure. It travels through the prism parallel to its base BC and emerges along the face A C . T

Question

A light ray enters through a right angled prism at point P with the angle of incidence 3 0 ∘ as shown in figure. It travels through the prism parallel to its base BC and emerges along the face A C . The refractive index of the prism is:

TestHub · Accepted Answer

In prism, r 1 ​ + c = A r 1 ​ = 9 0 ∘ − c … ( 1 ) sin c = μ 1 ​ ⇒ cos c = μ μ 2 − 1 ​ ​ ​ ⇒ Apply Snell's law, on incidence surface 1 ⋅ sin 3 0 ∘ = μ sin ( r 1 ​ ) ⇒ 1 × 2 1 ​ 2 1 ​ ​ = μ × sin ( 9 0 ∘ − c ) = μ × μ μ 2 − 1 ​ ​ ​ On squaring 4 1 ​ = μ 2 − 1 ⇒ μ 2 = 4 5 ​ ⇒ μ = 2 5 ​ ​

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