Question

The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of indicate $2A$ 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 :

• A. $2\sin A$
• B. $2\cos A$
• C. $\frac{1}{2}\cos A$
• D. $\tan A$

Answer 1

The correct option is B $2\cos A$

For light to return through same path, $r_2=0°$ (angle from normal)

$\therefore A=r_1+r_2\therefore r_1=A$

Use Snell's law,

$1\times \sin 2A=\mu \times \sin r_{1}or2\sin A\cos A=\mu \times \sin A\therefore \mu =2\cos A$