Question

An isosceles glass prism having refractive index $\mu$ has one of its faces coated with silver. A ray of light is incident normally on the other face(which is equal to the silvered face). The ray of light is reflected twice on the same sized faces and then emerges through the base of the prism perpendicularly. The angles of the prism are:

• A. ${40}^o,{70}^o,{70}^o$
• B. ${50}^o,{65}^o,{65}^o$
• C. ${36}^o,{72}^o,{72}^o$
• D. Data insufficient

Answer 1

The correct option is C ${36}^o,{72}^o,{72}^o$

$\alpha ={90}^{\circ }-A$

$i={90}^{\circ }-\alpha =A$

$\beta ={90}^{\circ }-2i^{\circ }={90}^{\circ }-2A$

and$y={90}^{\circ }-\beta =2A$

Thus,$y=r=2A$

From geometry,

$A+y+y={180}^{\circ }$

or$A=\frac{180}{5}={36}^{\circ }$

Answer C.