Light coming from a star is observed to have a wavelength of $3737 \ \mathring{A}$,while its real wavelength is $3700 \ \mathring{A}$. The speed of the star relative to the earth is (Speed of light $c = 3 \times 10^8 \ m/s$).

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?

$A$ rocket is moving away from the earth at a speed of $6 \times 10^7 \ m/s$. The rocket has blue light in it. What will be the wavelength of light recorded by an observer on the earth in $\mathring A$? (Wavelength of blue light $\lambda = 4600 \ \mathring A$)

Light from the constellation Virgo is observed to increase in wavelength by $0.4\%$. With respect to Earth,the constellation is:

The Doppler effect in sound,in addition to the relative velocity between the source and the observer,also depends on the individual motion of the source and the observer relative to the medium. However,the Doppler effect in light depends only on the relative velocity between the source and the observer. The reason for this is:

If a source of light is moving away from a stationary observer,then the frequency of light wave appears to change because of