question_answer

A ray of light is incident on the surface of separation of a medium with the velocity of light at an angle \[45{}^\circ \] and is refracted in the medium at an angle \[30{}^\circ .\] Velocity of light in the medium will be (velocity of light in air \[=3\times {{10}^{8}}m/s\])

A) \[3.8\times {{10}^{8}}m/s\]

B)        \[3.38\times {{10}^{8}}m/s\]

C) \[2.12\times {{10}^{8}}m/s\]

D)        \[1.56\times {{10}^{8}}m/s\]

Correct Answer: C

Solution :

[c] Refractive index, \[\mu =\frac{\sin 45{}^\circ }{\sin 30{}^\circ }\] \[\mu =\frac{1}{\sqrt{2}}\times 2=\sqrt{2}\] Now, \[\mu \text{=}\frac{\text{Velocity}\,\,\text{of}\,\,\text{light}\,\,\text{in}\,\,\text{air}}{\text{Velocity}\,\,\text{of}\,\,\text{light}\,\,\text{in}\,\,\text{medium}}\text{=}\sqrt{\text{2}}\] Velocity of light in medium \[=3\times {{10}^{8}}\times \frac{1}{\sqrt{2}}=2.12\times {{10}^{8}}m/\sec \]