If a star emitting light of wavelength $5000\,\mathring{A}$ is moving towards Earth with a velocity of $1.5 \times 10^6\,\text{m/s}$,then the shift in the wavelength due to Doppler's effect will be......$\mathring{A}$

$A$ star is moving towards the earth with a speed of $4.5 \times 10^6 \ m/s$. If the true wavelength of a certain line in the spectrum received from the star is $5890 \ \mathring A$,its apparent wavelength will be about........$\mathring A$ $[c = 3 \times 10^8 \ m/s]$

If a star is moving towards the Earth,then the spectral lines are shifted towards:

Due to the Doppler effect, the shift in wavelength observed is $0.1 \text{ Å}$ for a star producing a wavelength of $6000 \text{ Å}$. The velocity of recession of the star will be: (in $\text{ km/s}$)

$A$ light source approaches the observer with velocity $0.8 c$. The Doppler shift for the light of wavelength $5500 \ \mathring{A}$ is.....$\mathring{A}$.

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?