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THE DOPPLER EQUATION FOR LIGHT
delta(lambda) / (lambda) = v / c The Doppler equation reveals the motion of an object, either away or toward the observer. Large motions produce large shifts. The numerator on the left hand side is the difference between the observed wavelength and the rest wavelength; if that value is negative, then the motion is toward the observer; if positive, the motion is away from the observer. The denominator is the rest wavelength of the observed light. The velocity of that motion is given as the numerator on the right hand side; the denominator there is the speed of light. When the velocity v approaches the speed of light, we must take special relativity into account. In that case, we use the "relativistic Doppler equation": 1 + v/c delta(lambda) / (lambda) = sqrt(-------) - 1 1 - v/c This version is important when computing, for example, distances to faraway quasars using the velocity they are moving away from us due to the expansion of the universe. In that case, we use the letter "z" to denote the ratio delta(lambda) / (lambda), and call that ratio "redshift." |