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 \[30{}^\circ \], then the angle of refraction will be :

A) \[30{}^\circ \]

B) \[45{}^\circ \]

C) \[60{}^\circ \]

D) \[90{}^\circ \]

Correct Answer: D

Solution :

                 From Snells law, refractive index\[(\mu )\]is given by \[\mu =\frac{\sin i}{\sin r}\]                        ???. (i) where\[i\]is angle of incidence and rot 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,\[{{v}_{2}}=2u,\text{ }{{v}_{1}}=u,\text{ }i=30{}^\circ ,\text{ }\sin {{30}^{o}}=\frac{1}{2}\] \[\therefore \]  \[\sin r=2\times \frac{1}{2}=1\] \[\Rightarrow \]               \[r={{90}^{o}}\]