question_answer

A ray of light is incident at \[{{60}^{{}^\circ }}\] on one face of a prism of angle \[{{30}^{{}^\circ }}\] and the emergent ray makes \[{{30}^{{}^\circ }}\] with the incident ray. The value of h is:

A) 1.732                           

B) 1.414      

C) 1.5                               

D) 1.33

Correct Answer: A

Solution :

[b] \[i=60,A=30,\delta =30\] \[i+e=A+\delta \] \[60+e=30+30\] \[e=0\] \[{{r}_{2}}=0\] \[{{r}_{1}}+{{r}_{2}}=A\] \[{{r}_{1}}=A={{30}^{{}^\circ }}\] \[\mu =\frac{Sin\,i}{Sin\,{{r}_{1}}}=\frac{Sin\,60}{Sin}=\frac{\sqrt{3}}{2\times \frac{1}{2}}=\sqrt{3}=1.732\]