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 waves 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 the case of light travelling in a medium?
The Doppler formula differs slightly between the two situations because the sound waves can travel only through the medium. The motion of the observer relative to the
medium is different in both cases. Hence, the doppler formula is different.
Light waves can propagate in vacuum. In the vacuum, the speed of light does not depend on the motion of the observer and the source.
When light travels in the medium, the doppler formula for the two cases will be different.