question_answer

A ray of light is incident on a glass sphere of refractive index 3/2. What should be the angle of incidence so that the ray which enters the sphere does not come out of the sphere?

A) \[te{{n}^{-1}}(2/3)\]    

B) \[{{60}^{0}}\]

C) \[{{90}^{0}}\]            

D) \[{{30}^{0}}\]

Correct Answer: C

Solution :

[c] \[\angle ABO=\angle OAB={{\theta }_{c}}\] \[\sin {{\theta }_{c}}=\frac{1}{\mu }=\frac{2}{3}\] Applying snell's law at A \[\frac{\sin i}{\sin {{\theta }_{C}}}=\frac{3}{2}\] \[\sin i=\left( \frac{3}{2} \right)\left( \frac{2}{3} \right)=1\] Or \[i=90{}^\circ \]