An equilateral glass prism kept on a table has refractive index $μ = \sqrt{2}$ . The prism is illuminated by a narrow laser beam of power $p_{0}$ and the wavelength $λ$ such that refracted beam inside the prism is parallel to the base of prism. The change in weight of the prism due to the incident laser beam is $\frac{n \sqrt{2} P_{0}}{C}$ [C is speed of light] Find n.

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answer is 1.86.

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Detailed Solution

The prism is in the minimum deviation position hence angle of incidence is $45^{\circ}$ .
Change in momentum of a photon is $2 P \cos 15^{\circ}$ in the vertically downward direction force on the prism $F = (Δ P) (\frac{n u m b e r o f p h o t o n s}{t i m e})$
$F = \frac{2 P_{0}}{C} \cos 15^{\circ}$ . Hence $n = 1.866$

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