A rectangular cavity ABCD is carved inside an equilateral prism PQR of refractive index $(\frac{8}{5})$ as shown in figure. If $δ_{\min}$ is the deviation in a ray entering at face PQ and emerging at face PR, without passing through AB or CD, then which of the following is/are correct.

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The minimum deviation $δ_{\min} = 46^{0}$

If the cavity is filled with a liquid of refractive index $μ = 2$ , then $δ_{\min} = 23^{0}$

If the cavity is filled with water $(μ_{w} = 4 / 3)$ , the $δ_{\min} = 46^{0}$

There is no effect of cavity of the value of $δ_{\min}$

answer is A, B, C.

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Detailed Solution

The deviation produced by ABCD is zero. Hence the cavity will not have any effect on the deviation.

$μ = \frac{\sin (\frac{δ_{\min} + A}{2})}{\sin (\frac{A}{2})} = \frac{8}{5} \sin (\frac{δ_{\min} + A}{2}) = (\frac{8}{5}) \sin (\frac{60^{0}}{2}) δ = 46^{0}$

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