Question

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?

Answer 1

(a) source at rest, $v_s=0$

observer moving, $v_o\neq0$

so, The Doppler's formula for frequency is given by, $f=f_0\left(\frac{v\pm v_o}{v}\right)$, here v is speed of sound.

(b) source moving, $v_s\neq0$

observer rest, $v_0=0$

so, the Dropper's formula for the frequency is given by, $f=f_0\left(\frac{v}{v\pm v_s}\right)$

in case of light wave travelling in vaccum, the above two cases are identical because the speed of light in vaccum is independent of the motion of observer and the motion of the source.

but when light travels in a medium, the above two cases are not identical because the speed of light in a medium depends on refractive index of that medium.

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