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# The cross section of glass prism has the form of an isosceles triangle . One of equal face is silvered. A ray of light incident normally on other equal face and after being reflected twice, emerges through base of prism along normal. That the angle of prism is :-

$(a)\;30^{\circ} \\ (b)\;36^{\circ} \\ (c)\;52^{\circ} \\ (d)\;60^{\circ}$

From figure,
$\alpha= 90^{\circ} -A$
$i= 90^{\circ} - \alpha=A$
Also $\beta =90^{\circ} -2i^{\circ}=90^{\circ}-2A$
and $y= 90^{\circ} - \beta =2A$
Thus, $y= r=2A$
From geometry $A+ y+y =180^{\circ}$
or $A= \large\frac{180}{5}$$=36^{\circ}$
Hence b is the correct answer.

edited Jul 22, 2014