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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.

1. Stationary with respect t to the earth
2. Approching the earth with velocity of light
3. Receding from the earth with velocity of light
4. Receding from the earth with a velocity equal to \( 1.5 \times \) \( 10^{6} \mathrm{m} / \mathrm{s} \)

Correct answer: Receding from the earth with a velocity equal to \( 1.5 \times \) \( 10^{6} \mathrm{m} / \mathrm{s} \)

Solution

A 0.5% increase means the light is redshifted, so the galaxy is receding. Using the small-velocity Doppler approximation, \(v/c = 0.005\), giving \(v = 0.005\times 3\times10^8 = 1.5\times10^6\,\text{m/s}\).

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