Question

An initially parallel cylindrical beam travels in a medium of refractive index$\mu \left(I\right)={\mu }_0+{\mu }_{2}I$ , where ${\mu }_0$ and ${\mu }_2$ are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The speed of light in the medium is

• A. minimum on the axis of the beam
• B. the same everywhere in the beam
• C. directly proportional to the intensity I
• D. maximum on the axis of the beam

Answer 1

The correct option is A minimum on the axis of the beam

Refractive index of the medium $\mu \left(I\right)={\mu }_o+{\mu }_{2}I$ where $I=\frac{k}{r^2}$,Where $r=$radius of the beam.

$⟹$ $\mu \left(I\right)={\mu }_o+\frac{{\mu }_{2}k}{r^2}$

Speed of light in the medium $v=\frac{c}{\mu \left(I\right)}$ where $c$ is the speed of light in vacuum

$⟹$ $v=\frac{c}{{\mu }_o+\frac{{\mu }_{2}k}{r^2}}$

As $r$ increases, the speed of light in the medium also increases.

Hence the speed of light in the medium is minimum on the axis of the beam.