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Wave Optics

Question

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The 6563 Å H $α$ line emitted by hydrogen in a star is found to be red-shifted by 15A. Estimate the speed with which the star is receding from the Earth.

Solution

Given,

Wavelength of Hα line, λ = 6563 Å = 6563 \times 10^{- 10} m

Redshift,

λ' - λ = 15 Å = 15 \times 10^{- 10} m

Now, according to the formula,

λ' - λ = \frac{V_{s} λ}{c}

we have,

V_{s} = \frac{c}{λ} (λ' - λ)

= \frac{3.0 \times 10^{8}}{6563 \times 10^{- 10}} \times 15 \times 10^{- 10}

= 6.8566 \times 10^{5} {ms}^{- 1}

i.e.,

V_{s} = 6.86 \times 10^{5} {ms}^{- 1} .

therefore, the start is receding from the earth at a speed of 6.86

\times

10⁵ m/s.

Some More Questions From Wave Optics Chapter

Let us list some of the factors which could possibly influence the speed of wave propagation:
(i) nature of source.
(ii) direction of propagation.
(iii) motion of source and/or observer.
(iv) wave length.
(v) intensity of the wave.
On which of these factors, if any, does
(a) the speed of light in vacuum,
(b) the speed of light in a medium (say, the glass or water) depend?

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 wave 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?

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