A) \[~\text{2}.\text{12 }\times \text{ 1}{{0}^{\text{1}0}}\text{ cm}.{{\text{s}}^{-\text{1}}}\]
B) \[\text{2}.\text{52 }\times \text{ 1}0\text{ cm}.{{\text{s}}^{-\text{1}}}\]
C) \[2.21\times {{10}^{10}}cm.{{s}^{-1}}\]
D) \[\text{2}.\text{82 }\times \text{ 1}{{0}^{\text{1}0}}\text{ cm}.{{\text{s}}^{-\text{1}}}\]
Correct Answer: B
Solution :
\[\mu =\frac{\sin \left( \frac{A+{{\delta }_{m}}}{2} \right)}{\sin A/2}\] \[=\frac{\sin \left\{ \left( \frac{60+30}{2} \right) \right\}}{\sin (60/2)}=\frac{\sin {{45}^{o}}}{\sin {{30}^{o}}}\] \[=\frac{1/\sqrt{2}}{1/2}=\sqrt{2}\] \[\mathbf{=1}\mathbf{.414}\] Velocity in glass\[=\frac{Velocity\,\,in\,\,vacuum}{\mu }\] \[=\frac{3\times {{10}^{10}}}{1.414}\] \[\mathbf{=2}\mathbf{.12\times 1}{{\mathbf{0}}^{\mathbf{10}}}\mathbf{cm/sec}\mathbf{.}\]
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