The wavelength of light observed on the earth,from a moving star is found to decrease by $0.05\%$. Relative to the earth,the star is:

Due to the Doppler effect,the shift in wavelength observed is $0.1\;\mathring{A}$,for a star producing a wavelength of $6000\;\mathring{A}$. The velocity of recession of the star will be ....... $km/s$.

Assuming that the universe is expanding,if the spectrum of light coming from a star which is moving away from the Earth is tested,then in the wavelength of light:

In the spectrum of light of a luminous heavenly body,the wavelength of a spectral line is measured to be $4747 \ \mathring{A}$,while the actual wavelength of the line is $4700 \ \mathring{A}$. The relative velocity of the heavenly body with respect to the Earth will be (velocity of light is $3 \times 10^8 \ m/s$).

The wavelength of light from a star is $0.4\%$ more than the corresponding wavelength on the Earth. The velocity of the star with respect to the Earth is:

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 case of light travelling in a medium?