The refractive index of the materiel of a prism is 2 and the angle of the prism is 30 o . One of the two refracting surface of the prism is made a mirror inwards, by silver coating. A beam of monochro

Question

The refractive index of the materiel of a prism is 2 and the angle of the prism is 30 o . One of the two refracting surface of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is

TestHub · Accepted Answer

by principle of reversibility, the beam will return its path when it strikes the mirror perpendicularly

$r_{2} = 0, r_{1} = A = 30^{o}$
$∴ r_{1} + r_{2} = A$ in a prism
Applying Snell's law at P $\sin i = \sqrt{2} \sin 30^{o} = \sqrt{2} \times \frac{1}{2} = \frac{1}{\sqrt{2}}$

$∠ i = 45^{o}$

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