question_answer

A ray of light is incident at the surface of separation of a medium with velocity of light at an angle 45° and is refracted in the medium at an angle 30°. Velocity of light in the medium will be:                     [BHU PMT-2002]

A)                  \[1.1\,\text{eV}\]                          

B)                  \[1.5\,\text{eV}\]

C)                  \[2.0\,\text{eV}\]                          

D)                  \[\text{1}0.\text{2 eV}\]

Correct Answer: C

Solution :

                 Key Idea: Since angle of incidence is greater than angle of refraction ray of light bends towards the normal.                 When a ray of light travels from a rarer to a denser medium it bends towards the normal. From Snell?s law                                 Where \[\mu \] is refractive index of the medium, \[i\]is angle of incidence and \[r\] is angle of refraction.                 Given, \[i={{45}^{\circ }}\], \[r={{30}^{\circ }}\]                 \[\therefore \]  \[\mu =\frac{\sin \,\,{{45}^{\circ }}}{\sin \,\,{{30}^{\circ }}}=\frac{1}{\sqrt{2}}\times 2\]                 Also \[\mu =\frac{\text{velocity in air vacuum}}{\text{velocity in medium}}=\frac{3\times {{10}^{8}}}{{{v}_{m}}}\]                 \[\Rightarrow \]               \[{{v}_{m}}=\frac{3\times {{10}^{8}}}{1.414}=2.12\times {{10}^{8}}\,\,m/s\]                 Note: Velocity of light is less in the denser medium, compared to rarer medium.