question_answer

If the critical angle for total internal reflection from a medium to vacuum is \[30{}^\circ \], then velocity of light in medium will be

A)  \[\text{1}.\text{5}\times \text{1}{{0}^{\text{8}}}\text{ m}/\text{s}\]    

B)  \[\text{2}\times \text{l}{{0}^{\text{8}}}\text{ m}/\text{s}\]

C) \[\text{3}\times \text{l}{{0}^{\text{8}}}\text{m}/\text{s}\]                        

D)  \[\text{5}\times \text{l}{{0}^{\text{8}}}\text{m}/\text{s}\]

Correct Answer: A

Solution :

                 The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is \[{{90}^{o}}\].                                 \[_{1}{{n}_{2}}=\frac{1}{\sin C}\]                              ?. (i) Also,      \[_{1}{{n}_{2}}=\frac{c}{v}\]                                       ? (ii) From Eqs. (i) and (ii), we get                 v = c sin C Given,   \[C={{30}^{o}}\],              \[c=3\times {{10}^{8}}\,m/s\] \[\therefore \]  \[v=3\times {{10}^{8}}\times \sin {{30}^{o}}\]                 \[v=3\times {{10}^{8}}\times 0.5\]                 \[=1.5\times {{10}^{8}}m/s\]