Apparent wavelength of light coming from a star moving away from Earth is $0.02 \%$ more than its actual wavelength. The velocity of the star is ........ $km/s$.

The $6563 \ \mathring{A}$ line emitted by a hydrogen atom in a star is found to be red-shifted by $5 \ \mathring{A}$. The speed with which the star is receding from 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?

The $K$ line of singly ionised calcium has a wavelength of $393.3 \, nm$ as measured on Earth. In the spectrum of one of the observed galaxies,this spectral line is located at $401.8 \, nm$. The speed with which the galaxy is moving away from us will be..... $km/s$.

Write the formula for the Doppler shift for light.

The observed wavelength of light coming from a distant galaxy is found to be increased by $0.5\%$ as compared with that coming from a terrestrial source. The galaxy is