Write the formula for Doppler shift for light."

Explanation

When the source of light and the observer are in relative motion then the frequency of light is different than the frequency experienced by observer. This is known as the Doppler effect.
For example : If there is no medium and the source moves away from the observer, then later wavefronts have to travel a greater distance to each the observer and hence take a longer time. The time taken between the arrival of two successive wavefronts is hence longer at the observer than it is at the source. Thus, when the source moves away from the observer the frequency as measured by the source will be smaller. This is known as the Doppler effect.
The increase in wavelength due to Doppler effect as red shift since a wavelength in middle of the visible region of the spectrum moves towards the red end of the spectrum.
When waves are received from a source moving towards the observer there is an apparent decrease in wavelength this is referred to as blue shift. In the case of visual light, the frequency increases when the source is coming closer to the observer and the frequency decreases as it goes away.
Second method : In the case of visual light, the frequency decreases, means the frequency of light comes closer to red light then this phenomenon is called red shift and if frequency increases means the frequency of light comes closer to blue light, then this phenomenon is called blue shift.
General equation for Doppler effect for sound is `(v_(L))/(v+v_(L))=(v_(S))/(v+v_(S))` where `v_(L)` and `v_(S)` are the frequencies experience by observer and emitted by source respective
v = velocity of sound
`v_(L)=` velocity of observer
`v_(S)=` velocity of source
In case of light, velocity of light c instead velocity of sound v and frequency of source is and frequency experienced by observer is then,
`(v_(L))/(c+v_(L))=(v_(S))/(c+v_(S))`
`:.(v_(L))/(v_(S))=(c+v_(L))/(c+v_(S))`
but if observer is stationary then `v_(L)=0`
`:.(v_(L))/(v_(S))=(c)/(c+v_(S))`
`:.` Fractional change in frequency,
`=(v_(L)-v_(S))/(v_(S))=(c-c-v_(S))/(c+v_(S))`
`:.(Deltav)/(v_(S))=-(v_(S))/(c+v_(S))" "["":.v_(L)-v_(S)=Deltav]`
`:.(Deltav)/(v_(S))=-(v_(S))/(c)" "["":.v_(S)` is neglected compare to c in denominator]
`:.Deltav=-(v_(S))/(c)xxv_(S)` which is the formula for Doppler shift.
When source moves away from observer, `v_(S)` is considered as positive.
This formula is true when the speed of source is lower than that of light.
The direction of motion of celestial bodies can be determined using this.