What is the Doppler effect for light? Derive the formula for the Doppler shift.

(N/A) The Doppler effect for light is the change in the observed frequency (or wavelength) of light due to the relative motion between the source of light and the observer.
When the source moves away from the observer,the wavefronts have to travel a greater distance,leading to a longer time interval between the arrival of successive wavefronts. This results in a decrease in the observed frequency and an increase in wavelength,known as 'red shift'.
When the source moves towards the observer,the wavefronts arrive at shorter intervals,leading to an increase in observed frequency and a decrease in wavelength,known as 'blue shift'.
For light,the Doppler shift formula is given by:
$\Delta \nu = -\nu \frac{v_{radial}}{c}$
where $\Delta \nu$ is the change in frequency,$\nu$ is the original frequency,$v_{radial}$ is the relative velocity of the source along the line of sight,and $c$ is the speed of light.
The fractional change in frequency is:
$\frac{\Delta \nu}{\nu} = -\frac{v_{radial}}{c}$