$A$ rocket is moving away from the Earth at a speed of $0.2c$,where $c$ is the speed of light. It emits a signal of frequency $4 \times 10^7 \text{ Hz}$. What will be the frequency observed by an observer on the Earth?

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 time period of rotation of the sun is $25$ days and its radius is $7 \times 10^8 \ m$. The Doppler shift for the light of wavelength $6000 \ \mathring{A}$ emitted from the surface of the sun will be ...... $\mathring{A}$.

$A$ star emits light of $5500 \ \mathring{A}$ wavelength. If it appears blue to an observer on the Earth,it means:

$A$ galaxy is moving away from the Earth at a speed of $286 \, km/s$. The shift in the wavelength of a red line at $630 \, nm$ is $x \times 10^{-10} \, m$. The value of $x$,to the nearest integer,is........
[Take the value of speed of light $c$ as $3 \times 10^{8} \, m/s$]

$A$ star producing light of wavelength $6000 \ \mathring{A}$ moves away from the Earth with a speed of $5 \ km/s$. Due to the Doppler effect, the shift in wavelength will be $...... \ \mathring{A}$ $(c = 3 \times 10^8 \ m/s)$.