JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Geometrical Optics

A ray of light passing through a prism

(μ = 3)

surface minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ______ (in degrees).

Answer: 60

Solution

At minimum deviation, the ray passes symmetrically through the prism, so

i = e

and

r_{1} = r_{2} = r

. Given

i = 2 r

. Using Snell's law at the first surface:

sin i = μ sin r

, so

sin (2 r) = 3 sin r

. Using

sin (2 r) = 2 sin r cos r

2 sin r cos r = 3 sin r

, giving

cos r = \frac{3}{2}

, so

r = 30°

. The prism angle

A = r_{1} + r_{2} = 2 r = 60°

JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Numerical answer

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