# Doppler Effect A to Z

In 1842, Christian J.Doppler, an Austrian phisicist pointed out that when a light source approaches an observer, the waves are crowded together and the lengths of the waves are decreased. Similarly, when the source recedes from the observer, the waves spread out and the wavelengths are increased. This phenomenon is known as Doppler Effect. The same effect is observed when the source is stationary and the observer is moving.In actual practice the relative motion along the line of sight, that is, the radial component of motion between the source and the observer is considered. Since the velocity of light is constant, the frequency of radiation from an approaching source increases while that form of a receding source decreases. The entire spectrum of the source will thus be shifted towards the red. The shift is called Doppler Shift. The amount of shift will depend on the radial velocity of the source and also on the frequency observed which is given by the formula:-

\frac{\triangle\lambda}{\lambda}=\frac{v_r}{c}

where \lambda is the natural wavelength observed, \triangle\lambda is the shift in wavelength due to radial velocity v_r of the source. v_r is taken as positive when the source recedes from the observer and as negative when the source approaches the observer. c is the velocity of light. The stated formula applies for velocities of objects very much less than the velocity of light. For objects with velocities comparable to that of light, the modified relativistic formula is:-

\sqrt\frac{1+v_rlc}{1-v_rlc}=\frac{\lambda+\triangle\lambda}{\lambda}

Although the radial motion of the source causes a doppler shift of the entire spectrum, this shift is difficult to measure in continuous spectrum.But the shift in the position of spectral lines can be measured by matching with the unshifted lines superimposed on the spectrum which are produced in the laboratory by applying spark to some element or elements. After the shift of any known line has been measured in the spectrum of the source, the first equation can be used to calculate the radial velocity of the source. Applying the process the radial component of motions of the heavenly bodies has been measured. In particular, this has been done for thousands of stars & hundreds of distant galaxies. The same principle is used to calculate the rotational velocities of stars and the thermal states of the stellar atmospheres and other radiating gaseous astronomical bodies, as we shall discuss later.

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Here is a pdf for the Doppler Effect . Doppler Effect