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