question_answer

Light is incident normally on face AB of a prism as shown in figure; A liquid of refractive index \[\mu \] 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) \[\mu >\frac{3}{4}\]     

B) \[\mu <\frac{3}{4}\]

C) \[\mu >\sqrt{3}\]           

D) \[\mu <\frac{\sqrt{3}}{2}\]

Correct Answer: C

Solution :

[c] Critical angle between glass and liquid face is \[\sin {{\theta }_{c}}=\frac{3/2}{\mu }=\frac{3}{2\mu }\]                       ...(1) Angle of incidence at face AC is \[60{}^\circ \] i.e., \[i=60{}^\circ \] For total internal reflection to take place \[i>{{\theta }_{c}}\] Or \[\sin i>\sin {{\theta }_{c}}\] Or \[\sin 60{}^\circ >\frac{3}{2\mu }\]or \[\frac{\sqrt{3}}{2}>\frac{3}{2\mu }\] Or \[\mu >\sqrt{3}\]