question_answer

An isosceles prism of angle 120° has a refractive index of 1.44. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerging from the opposite faces                                  [IIT-JEE 1995]

A)            Are parallel to each other

B)            Are diverging

C)            Make an angle \[2{{\sin }^{-1}}\,(0.72)\] with each other

D)            Make an angle \[2\,\{{{\sin }^{-1}}(0.72)-{{30}^{o}}\}\] with each other

Correct Answer: D

Solution :

                   At point A. \[\frac{\sin {{30}^{o}}}{\sin r}=\frac{1}{1.44}\] \[\Rightarrow r={{\sin }^{-1}}(0.72)\,\,\text{also}\,\,\angle BAD=180{}^{o}-\,\angle r\] In rectangle ABCD, Ð A + Ð B + Ð C + Ð D = 360° Þ \[(180{}^\circ -r)+60{}^\circ +(180{}^\circ -r)+\theta =360{}^\circ \] \[\Rightarrow \theta =2\,[\sin {}^{-1}(0.72)-30{}^{o}]\]