First slide

Prism

Question

A ray of monochromatic light is incident on one refracting face of a prism of angle 75°. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is $\sqrt{2}$ , the angle of incidence (in degree) on the first face of the prism is

Moderate

Solution

From figure
$A = r_{1}^{} + c = r_{1}^{} + \sin^{- 1} (\frac{1}{μ}) \Rightarrow r_{1} = 75 - \sin^{- 1} (\frac{1}{μ}) \Rightarrow r_{1} = 75 - 45 = 30^{\circ} From Snell ’ s law At B μ = \frac{\sin i}{\sin r_{1}} \Rightarrow \sqrt{2} = \frac{\sin i}{\sin 30^{\circ}} \Rightarrow i = 45^{\circ}$

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