JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Geometrical Optics

The refractive index of prism is

μ = 3

and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is ______

^{\circ}

Answer: 60

Solution

At minimum deviation

i = e

and

r_{1} = r_{2} = \frac{A}{2}

. Given

δ_{min} = A

, and

δ_{min} = 2 i - A

, so

2 i - A = A \Rightarrow i = A

.
Snell's law:

sin i = μ sin \frac{A}{2}

, i.e.

sin A = 3 sin \frac{A}{2}

2 sin \frac{A}{2} cos \frac{A}{2} = 3 sin \frac{A}{2} \Rightarrow cos \frac{A}{2} = \frac{3}{2} \Rightarrow \frac{A}{2} = 3 0^{\circ}

.
So

A = 6 0^{\circ} .

JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Integer answer

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