How is resolving power of a microscope affected when (i) wavelength of illuminating radiations is decreased (ii) the diameter of objective lens is decreased? Justify.

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?