question_answer

A glass prism \[(\mu \]= 1.5) is dipped in water \[(\mu \]= 4/3) as shown in figure. A light ray is incident normally on the surface AB. It reaches the surface BC after totally reflected, if  [IIT JEE 1981; MP PMT 1997]

A)            sin\[\theta \] \[\ge \] 8/9

B)            2/3 < sin\[\theta \]< 8/9

C)            sin \[\theta \] \[\le \]  2/3

D)            It is not possible

Correct Answer: A

Solution :

                   For TIR at AC                    \[\theta >C\]                \[\Rightarrow \sin \theta \ge \sin C\]                    \[\Rightarrow \sin \theta \ge \frac{1}{_{w}{{\mu }_{g}}}\]            \[\Rightarrow \sin \theta \ge \frac{{{\mu }_{w}}}{{{\mu }_{g}}}\]\[\Rightarrow \sin \theta \ge \frac{8}{9}\]