question_answer

A wave has velocity u in medium P and velocity \[2u\] in medium Q. If the wave is incident in medium P at an angle \[{{30}^{o}},\]then the angle of refraction will be

A)  \[{{30}^{o}}\]          

B)  \[{{45}^{o}}\]

C)  \[{{60}^{o}}\]          

D)  \[{{90}^{o}}\]

Correct Answer: D

Solution :

From Snell?s law, refractive index \[(\mu )\] is given by \[\mu =\frac{\sin \,i}{\sin \,r}\] ??(i) where i is angle of incidence and r of refraction. Also,           \[\mu =\frac{{{v}_{1}}}{{{v}_{2}}}\]    ??(ii) Equating Eqs. (i) and (ii), we get \[\mu =\frac{\sin i}{\sin r}=\frac{{{v}_{1}}}{{{v}_{2}}}\] \[\Rightarrow \] \[\sin r=\frac{{{v}_{2}}}{{{v}_{1}}}.\,\sin \,i\] Given, \[{{v}_{2}}=2u,\,{{v}_{1}}=u,\,i={{30}^{o}},\,\sin \,{{30}^{o}}=\frac{1}{2}\] \[\therefore \] \[\sin \,\,r=2\times \frac{1}{2}=1\] \[\Rightarrow \] \[r={{90}^{o}}\]