The refractive index of a transparent liquid filled in an equilateral hollow prism is . The angle of minimum deviation for the liquid will be _____ . [2023]

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Solution

Q.
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 _____ $°$ . [2023]

Ans.
(30)

$As μ = \frac{\sin (\frac{D_{\min} + A}{2})}{\sin (\frac{A}{2})}$

$\sqrt{2} = \frac{\sin (\frac{D_{\min} + 60}{2})}{\sin (\frac{60}{2})}$

$\Rightarrow \frac{1}{\sqrt{2}} = \sin (\frac{D_{\min} + 60}{2})$

$\Rightarrow \frac{D_{\min} + 60}{2} = 45 \Rightarrow D_{\min} = 30$

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