One face of the glass prism is silver polishe | vedclass

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(B) Given: Angle of incidence $i = 45^{\circ}$,Prism angle $A = 30^{\circ}$.Since the ray retraces its path after reflection from the silvered face,it

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$\sqrt{2}$

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(B) Given: Angle of incidence $i = 45^{\circ}$,Prism angle $A = 30^{\circ}$.Since the ray retraces its path after reflection from the silvered face,it must strike the silvered face normally (at $90^{\circ}$).In the triangle formed by the ray and the prism sides,the angle at the silvered face is $90^{\circ}$ and the prism angle is $30^{\circ}$.Therefore,the angle of refraction $r$ at the first face is $r = 180^{\circ} - 90^{\circ} - 30^{\circ} = 60^{\circ}$ is incorrect based on the geometry shown. Looking at the triangle,the angle of refraction $r$ is $r = 90^{\circ} - 60^{\circ} = 30^{\circ}$.Using Snell's Law: $\mu = \frac{\sin i}{\sin r} = \frac{\sin 45^{\circ}}{\sin 30^{\circ}}$.$\mu = \frac{1/\sqrt{2}}{1/2} = \frac{2}{\sqrt{2}} = \sqrt{2}$.

One face of the glass prism is silver polished. $A$ light ray falls at an angle of $45^{\circ}$ on the other face. After refraction,it is subsequently reflected from the silvered face and then retraces its path. The refracting angle of the prism is $30^{\circ}$. The refractive index of the prism is

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