JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Geometrical Optics

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to

6 0^{\circ}

. The refractive index of the prism material is

2

. The angle of incidence (in degrees) is ______.

Answer: 45

Solution

At minimum deviation the ray passes symmetrically through the prism, so the angle of incidence equals the angle of emergence and

δ_{m} = 2 i - A

. The prism relation is

μ = \frac{sin ( \frac{A + δ _{m}}{2} )}{sin ( \frac{A}{2} )}

. With

A = 6 0^{\circ}

and

μ = 2

sin (\frac{6 0 ^{\circ} + δ _{m}}{2}) = 2 sin 3 0^{\circ} = \frac{2}{2}

, so

\frac{6 0 ^{\circ} + δ _{m}}{2} = 4 5^{\circ}

and

δ_{m} = 3 0^{\circ}

. Then

i = \frac{A + δ _{m}}{2} = \frac{6 0 ^{\circ} + 3 0 ^{\circ}}{2} = 4 5^{\circ}

. The angle of incidence is

4 5^{\circ}

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Integer answer

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