question_answer

A ray of light propagates from glass (refractive index\[=\frac{3}{2})\] to water (refractive index\[=\frac{4}{3}).\]                                                                        The value of the critical angle is:

A) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]                

B)        \[{{\sin }^{-1}}\left( \sqrt{\frac{9}{8}} \right)\]

C)        \[{{\sin }^{-1}}\left( \frac{8}{9} \right)\]                

D)        \[{{\sin }^{-1}}\left( \frac{5}{7} \right)\]

Correct Answer: B

Solution :

The angle of incidence in denser medium for which the angle of refraction in rarer medium is \[{{90}^{o}}\] is called the critical angle (C). \[{{\mu }_{w}}\]and\[{{\mu }_{g}}\]are refractive indices for rarer (water) and denser (glass) media, then                                 \[\frac{\sin C}{\sin {{90}^{o}}}=\frac{{{\mu }_{w}}}{{{\mu }_{g}}}\]                 \[\Rightarrow \]               \[\sin C=\frac{4/3}{3/2}=\frac{8}{9}\]                 \[\Rightarrow \]               \[C={{\sin }^{-1}}\left( \frac{8}{9} \right)\] Note: The critical angle for water-air, glass-air and diamond-air interfaces are \[{{49}^{o}},{{42}^{o}}\] and \[{{24}^{o}},\] respectively.