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 ___________ °. Numerical answer type. Work it out, then open the answer.

Answer: 30. μ = (sin (A+δm)/(2))/(/2) with A = 60° (the thin glass walls do not matter). sin (60°+δm)/(2) = √(2)×1/2 = 1/√(2) ⇒ (60°+δm)/(2) = 45° δm = 30°, so the answer is 30.

The refractive index of a transparent liquid filled in an equilateral… | JEE Main 2023 (15 Apr, Shift 1)

Q45JEE Main 2023 · 15 APR · SHIFT 1Medium

Prism, Dispersion & Scattering

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 ___________ ${}^\circ$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 30

$\mu = \dfrac{\sin\frac{A+\delta_m}{2}}{\sin\frac{A}{2}}$ with $A = 60^\circ$ (the thin glass walls do not matter).
$\sin\frac{60^\circ+\delta_m}{2} = \sqrt{2}\times\frac{1}{2} = \frac{1}{\sqrt{2}} \Rightarrow \frac{60^\circ+\delta_m}{2} = 45^\circ$
$\delta_m = 30^\circ$ , so the answer is 30.

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