An initially parallel cylindrical beam travels in a medium of refractive index μ(I) = μ₀ +μ₂I , where μ₀ and μ₂ are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. 

As the beam enters the medium, it will

• travel as a cylindrical beam

• diverge

• converge

• diverge near the axis and converge near the periphery.

Let us list some of the factors which could possibly influence the speed of wave propagation:
(i) nature of source.
(ii) direction of propagation. 
(iii) motion of source and/or observer.
(iv) wave length.
(v) intensity of the wave.
On which of these factors, if any, does
(a) the speed of light in vacuum,
(b) the speed of light in a medium (say, the glass or water) depend?

For sound waves, the Doppler formula for frequency shift differs slightly between the two situations:
(i) source at rest; observer moving, and
(ii) source moving; observer at rest.
The exact Doppler formulas for the case of light wave in vacuum, are however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?