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 :
minimum on the axis of the beam
Solution :
The speed of light $$(c)$$ in a medium of refractive index $$\left( \mu \right)$$ is given by
$$\mu = \frac{{{c_0}}}{c},$$
where $${{c_0}}$$ is the speed of light in vacuum
$$\eqalign{
& \therefore \,\,c = \frac{{{c_0}}}{\mu } \cr
& = \frac{{{c_0}}}{{{\mu _0} + {\mu _2}\left( I \right)}} \cr} $$
As $$I$$ is decreasing with increasing radius, it is maximum
on the axis of the beam. Therefore, $$c$$ is minimum on the
axis of the beam.