The angle of a prism is A. One of its refract | vedclass

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(B) For the light ray to retrace its path after reflection from the silvered surface,it must strike the silvered surface normally (at an angle of inci

Vedclass · Accepted Answer

$2 \cos A$

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(B) For the light ray to retrace its path after reflection from the silvered surface,it must strike the silvered surface normally (at an angle of incidence $0^{\circ}$). From the geometry of the prism,the angle of refraction $r$ at the first surface is related to the prism angle $A$ by $r = A$. Applying Snell's law at the first surface: $1 \cdot \sin i = \mu \cdot \sin r$ Given that the angle of incidence $i = 2A$ and the angle of refraction $r = A$,we substitute these values: $\sin(2A) = \mu \sin A$ Using the trigonometric identity $\sin(2A) = 2 \sin A \cos A$: $2 \sin A \cos A = \mu \sin A$ Dividing both sides by $\sin A$ (assuming $A 
eq 0$): $\mu = 2 \cos A$

The angle of a prism is $A.$ One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is

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