A prism of refractive index 3 2 and refracting angle is 45 ° is placed in air. One of the two refracting surfaces of the prism is silvered and a ray of monochromatic light enters the prism from the ot

Question

A prism of refractive index 3 2 and refracting angle is 45 ° is placed in air. One of the two refracting surfaces of the prism is silvered and a ray of monochromatic light enters the prism from the other face at an angle θ . If the ray retraces its path, then what is the value of θ (in degree)?

TestHub · Accepted Answer

The monochromatic ray of light will retrace its path if it strikes the mirror perpendicularly.

Using Snell's law of refraction,

$1 \times \sin θ = μ \times \sin 45 °$

$\Rightarrow \sin θ = \sqrt{\frac{3}{2}} \times \sin 45 °$

$\sin θ = \sqrt{\frac{3}{2}} \times \frac{1}{\sqrt{2}} = \frac{\sqrt{3}}{2}$

$\Rightarrow θ = 60 °$

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