question_answer

A rectangular glass wedge is partially dipped in water \[\left( {{n}_{\text{glass}}}=\frac{3}{2} \right).\]A beam of light entering face AB normally reaches entirely to AC.

Now, value of angle a must be

A) less than \[60{}^\circ \] 

B) less than \[30{}^\circ \]

C) more than \[60{}^\circ \]           

D) between\[30{}^\circ \]to \[60{}^\circ \]

Correct Answer: C

Solution :

Beam reaches AC, if TIR occurs at BC.

From geometry of figure, angle of incidence over face \[BC=\alpha .\]

For beam to reach AC,

\[\sin \alpha >\frac{{{n}_{2}}}{{{n}_{1}}}\]

where, \[{{n}_{2}}=\]refractive index of water \[=\frac{4}{3}\] and \[{{n}_{1}}=\]refractive index of glass \[=\frac{3}{2}.\]

\[\therefore \]\[\sin \alpha >\frac{\frac{4}{3}}{\frac{3}{2}}\]\[\Rightarrow \]\[\sin \alpha >\frac{8}{9}=0.89\]

\[\therefore \]\[\alpha >60{}^\circ \]

\[\therefore \]\[\sin 60{}^\circ \approx 0.86\]