question_answer

A ray of light makes normal incidence on the diagonal face of a right angled prism as shown in figure If\[\theta =37{}^\circ \], then the angle of deviation is \[(sin37{}^\circ \,3/5)\]            

A)  \[{{53}^{o}}\]                                

B)  \[{{127}^{o}}\]

C) \[106{}^\circ \]                                 

D) \[90{}^\circ \]

Correct Answer: B

Solution :

The ray gets totally internally reflected at face AB as \[90{}^\circ -\theta >{{\theta }_{c}}={{\sin }^{-1}}\left( \frac{1}{\mu } \right)=37{}^\circ \] At face BC, it emerges out at grazing angle as shown in figure. The angle of deviation is \[\delta =180{}^\circ -(90{}^\circ -\theta )=90{}^\circ -\theta \] \[=90{}^\circ +37{}^\circ =127{}^\circ \]