The refractive index of a transparent liquid filled in an equilateral hollow prism is $\sqrt{2}$. The angle of minimum deviation for the liquid will be ______°.

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Geometrical Optics

The refractive index of a transparent liquid filled in an equilateral hollow prism is

2

. The angle of minimum deviation for the liquid will be ______°.

Answer: 30

Solution

For an equilateral prism

A = 6 0^{\circ}

, and at minimum deviation

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

. With

μ = 2

sin (\frac{6 0 ^{\circ} + D _{m}}{2}) = 2 sin 3 0^{\circ} = \frac{1}{2}

, so

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

. The angle of minimum deviation is

3 0^{\circ}

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Integer answer

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