A) \[8\times {{10}^{-10}}s\]
B) \[16\times {{10}^{-11}}s\]
C) \[2\times {{10}^{-11}}s\]
D) \[4\times {{10}^{-11}}s\]
Correct Answer: D
Solution :
From Huygens principle \[\mu =\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{speed\text{ }of\text{ }light\text{ }in\text{ }vacuum\,\,({{v}_{0}})}{speedotlightinmedium({{v}_{m}})}\] \[\Rightarrow \] \[{{v}_{m}}=\frac{{{v}_{0}}}{\mu }=\frac{3\times {{10}^{8}}}{3}={{10}^{8}}m/s\] Time taken \[=\frac{distance}{speed}\] \[t=\frac{4\times {{10}^{-3}}}{{{10}^{8}}}\] \[t=4\times {{10}^{-11}}s\]. Alternative: Time taken by the light to cross a glass slab of thickness d and refractive index a is \[t=\frac{\mu \,d}{c}\] where c is the speed of light. Given, \[\mu =3,\,\,d=4\,mm=4\times {{10}^{-3}}m\], \[c=3\times {{10}^{8}}m/s\] \[\therefore \] \[t=\frac{3\times 4\times {{10}^{-3}}}{3\times {{10}^{8}}}=4\times {{10}^{-11}}s\]
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