question_answer

Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index is placed on face AC of the prism. The prism is made of glass of refractive index 3/2. The limits of \[\mu \] for which total internal reflection takes place on face AC is

A) \[\mu >\frac{3\sqrt{3}}{2}\]                  

B) \[\mu >\sqrt{3}\]           

C) \[\mu <\frac{3\sqrt{3}}{4}\]      

D)        \[\mu <\frac{3\sqrt{3}}{8}\]      

Correct Answer: C

Solution :

                                Total internal reflection takes place when angle of incidence is greater than critical angle,         Here, \[{{\mu }_{l}}=\mu ,{{\mu }_{g}}=\frac{3}{2}\] We know, \[\sin C=\frac{{{\mu }_{l}}}{{{\mu }_{g}}}=\frac{\mu }{3/2}=\frac{2\mu }{3}\]                       ?(i) Light suffers total internal reflection, \[i>C\]or \[{{60}^{o}}>C\] \[\Rightarrow \sin {{60}^{o}}>\sin C\Rightarrow \frac{\sqrt{3}}{2}>\frac{2\mu }{3}\] \[\therefore \]      \[\mu <\frac{3\sqrt{3}}{4}\]