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: C

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 \[\frac{\sin C}{\sin {{90}^{o}}}=\frac{{{\mu }_{w}}}{{{\mu }_{g}}}\] \[\Rightarrow \] \[{{\sin }^{-1}}\left( \frac{8}{9} \right)\] \[\Rightarrow \] \[C={{\sin }^{-1}}\left( \frac{8}{9} \right)\] Note: The critical angle for water-air, glass-air and diamond-air interfaces are \[{{49}^{o}},{{42}^{o}}\] and\[{{24}^{o}}\] respectively.