question_answer

A glass prism of refractive index \[\text{1}\text{.5}\] is immersed in water of refractive index 4/3. A ray of light incident normally on face AB is totally reflected at face AC if

A)  \[\sin \theta >\frac{8}{9}\]                          

B)  \[\sin \theta <\frac{8}{9}\]

C)  \[\sin \theta =\frac{1}{\sqrt{2}}\]           

D)         None of these

Correct Answer: A

Solution :

 Angle of incidence at face \[AC\] is\[\theta \]. Since the ray suffers total internal reflection, \[\theta \] must be greater than critical. \[\Rightarrow \]               \[\sin \theta >\sin C\]                 \[\sin \theta >\sin ({{\sin }^{-1}}\frac{1}{\mu })\] Now, for water-glass interface,\[\mu =\frac{{{\mu }_{g}}}{{{\mu }_{w}}}=\frac{9}{8}\]