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,\[{{v}_{2}}=2u,\text{ }{{v}_{1}}=u,\text{ }i=30{}^\circ ,\text{ }\sin {{30}^{o}}=\frac{1}{2}\] \[\therefore \] \[\sin r=2\times \frac{1}{2}=1\] \[\Rightarrow \] \[r={{90}^{o}}\]You need to login to perform this action.
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