question_answer

An isosceles prism of angle \[120{}^\circ \] has a refractive index 1.44. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerge from the opposite faces

A) are parallel to each other     

B) are diverging                     

C) make an angle \[2\left[ si{{n}^{-1\text{ }}}\left( 0.72 \right)-30{}^\circ  \right]\] with each other                     

D) make an angle \[2\text{ }si{{n}^{-1}}(0.72)\]  with each other

Correct Answer: C

Solution :

[c] Applying Snell?s law at P, \[\mu =\frac{\sin r}{\sin 30{}^\circ }\] \[\sin r=\frac{1.44}{2}=0.72\] \[\therefore \delta =r-30{}^\circ ={{\sin }^{-1}}\left( 0.72 \right)-30{}^\circ \] \[\therefore \]The rays make an angle of \[2\delta =2\,[{{\sin }^{-1}}(0.72)-30{}^\circ ]\] with each other.