PQR is an isosceles prism in which point ‘S’ is the mid point of the face PQ. The refractive index of the prism is $\sqrt{3}$ and its face QR is silvered. ‘O’ is a point source. A light ray has been sent from the source ‘O’ to point ‘S’ in such a way that it comes back to point ‘O’. It is given that $P R = \frac{20}{\sqrt{3} + 1} c m$ . Find the distance (in cm) of the source ‘O’ from the point ‘P’.

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answer is 5.

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Detailed Solution

$1 \times \sin i = \sqrt{3} \times \sin 30^{0} i = 60^{0} \tan 75^{0} = \frac{S N}{d / 4} \dots \dots (i) \tan 45^{0} = \frac{S N}{x + \frac{d}{4}} \dots \dots . (i i)$

From (i) and (ii)

$x = \frac{d}{4} (\sqrt{3} + 1)$

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