question_answer

The angle of a prism is A and 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 second (silvered) surface. The refractive of the material of the prism is

A)  2 sin A                       

B)  \[2\cos A\]      

C)       \[\left( \frac{1}{2} \right)\cos A\]       

D)      \[\tan A\]

Correct Answer: B

Solution :

The refracted ray BC will retrace its path if it falls normally on the silvered face PQ of the prism, i.e.,\[\angle PCB={{90}^{o}}\] \[\therefore \]\[\alpha ={{90}^{o}}-A\] \[\therefore \]\[r=90-\alpha =90-(90-A)=A\] Now, \[\mu =\frac{\sin i}{\sin r}=\frac{\sin 2A}{\sin A}=2\cos A\] Hence, the correction option is (b).