115. assignment (diffraction grating in astrophysics)

An application of spectra produced by a diffraction grating is in astrophysics, where the Doppler shift of a particular galaxy can be measured to determine the velocity of the galaxy with respect to us. If the red hydrogen line in the galaxy's spectrum is observed at 674 nm instead of 658 nm, first think about whether that means the galaxy is moving toward us or away from us. Then, recalling that the Doppler equation for electromagnetic waves states that the magnitude of the shift in frequency associated with relative motion between a source and observer is |f ' - f | = vf/c, where f ' is the observed frequency and f is the frequency emitted by a stationary source, determine v, the relative speed of the galaxy with respect to us. Take the speed of light to be 3.00 x 10^8 m/s.

 

State the galaxy's velocity with respect to us, including a plus sign if the velocity Is directed away from us, and a minus sign if It is directed toward us. Note that the Doppler equation is valid as long as the speed is not too close (10% of c or higher) to the speed of light, and we can get away with applying it here.

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