Question

Ray diagram for incident ray on a prism is shown in figure. Find X and minimum deviation produced by incident ray.

• A. ${90}^o$, ${30}^o$
• B. ${90}^o$, ${60}^o$
• C. ${60}^o$, ${90}^o$
• D. ${90}^o$, ${120}^o$

Answer 1

The correct option is D ${90}^o$, ${120}^o$



Condition of grazing emergence :
sin ${\theta }_C=\frac{1}{n}=\frac{1}{2}$
${\theta }_C={30}^o$
$\alpha +{\theta }_C={60}^o$
$\alpha ={30}^o$
sinX = n$\lambda$ ;
given n=2
$1\times sinX=n\times sin\alpha$ (where, $n=2$)
Hence, X$={90}^o$
For minimum deviation, i = e, and in that case, ${\delta }_m=2i-A=2\times {90}^0-{60}^0={120}^o$