Doppler effect for light is

Explanation

The apparent change in the observed frequency of an electro- magnetic radiation as a result of relative motion between the source of radiation and observer is called the Doppler effect in light.
According to the special theory of relativity, the apparent frequency of light measured by the observer for relative motion along the line-of-sight is given by`f=1+(v_(r)/(c))/(sqrt(1-(v_r/c)^2).f_0` (longitudinal Doppler effect) ... (1)
where `v_(r)` is the radial (or line-of sight) component of the velocity of the source relative to the observer, c is the speed of light in free space and `f_0` is the true frequency of the radiation. The plus sign in the numerator is used when `vecv_(r)` is towards the observer, and the minus sign when `vecv_(r)`, is away from the observer. Thus, fgtf_(0) when the source is moving towards the observer, and fltf_(0) when the source is moving away from the observer.
For v_(r)ltltc,
`f=f_o(1+f_(r)/c)` ..(2)
Therefore, the Doppler frequency shift is
`Deltaf=f-f_o=+f_o(v_r/c)` and `Deltaf/f_(o)=Deltaeta/eta_(o)=+(v_(r)/c)` where `eta` and `Deltaeta` are respectively wavelength and the Doppler shift in wavelength. If the source of radiation moves towards the observer (v_(r) is positive), `f gt f_(0) and etalteta_(0)`, i.e., the wavelength of a radiation in the visible region of the electromagnetic spectrum shifts towards the blue end of the spectrum and is said to be blueshifted. If the source moves away from the orver` (v_(r)` is negative),` fltf_(0)`, and `etagteta_(o) i.e., the wavelength of the radiation shifts towards the red end of the spectrum and is said to be redshifted.
An apparent shift toward longer wavelengths of spectral lines in the Hation emitted by a source caused by the source moving away from the abserver is called the Doppler redshift. An apparent shift toward shorter wavelengths of spectral lines in the radiation emitted by a source caused by motion between the source and the observer which decreases the distance hotween them is called the Doppler blueshift.