Question

During refraction of light through a glass prism of prism angle 60 degree, the refracted ray inside the prism is parallel to prism base. What is the angle of incidence if refractive index of material of prism is 1.732 ?. Single choice.

Answer 1

Dear Student
The condition for minimum deviation through a prism is that angle of incidence (i) is equal to angle of emergence ( e). In that case, the refracted ray becomes parallel to the base of the prism.
So applying condition of minimum deviation
$$\begin{gathered} \mu =\frac{\sin \left({\displaystyle \frac{A+{\delta }_m}{2}}\right)}{Sin{\displaystyle \frac{A}{2}}} \\ 1.732=\frac{\sin \left({\displaystyle \frac{60+{\delta }_m}{2}}\right)}{Sin{\displaystyle \frac{60}{2}}}=\frac{\sin \left({\displaystyle \frac{60+{\delta }_m}{2}}\right)}{Sin{\displaystyle 30}}=2\sin \left(\frac{60+{\delta }_m}{2}\right) \\ \sin \left(\frac{60+{\delta }_m}{2}\right)=\frac{1.732}{2}=0.866=\sin 60 \\ \left(\frac{60+{\delta }_m}{2}\right)=60 \\ 60+{\delta }_m=120 \\ {\delta }_m=60 \\ Nowconditionofminimumdeviation \\ i=\frac{A+{\delta }_m}{2}=\frac{60+60}{2}={60}^o \end{gathered}$$
Regards