# Doppler’s Effect of Light

## Doppler’s Effect of Light

The phenomenon of apparent change in frequency of the light due to relative motion between the source of light and the observer is called Doppler’s effect. If $$\nu$$ = actual frequency, $$\nu ‘$$ = apparent frequency, $$v=$$ speed of source with respect to the stationary observer, $$c=$$ speed of light.

1) Source of light moves towards the stationary observer: When a light source is moving towards an observer with a relative velocity v then the apparent frequency is greater than the actual frequency of light. Thus apparent wavelength is lesser than the actual wavelength.

$$\nu ‘=\nu \sqrt{\frac{\left( 1+v/c \right)}{\left( 1-v/c \right)}}$$ and $$\lambda ‘=\lambda \sqrt{\frac{\left( 1+v/c \right)}{\left( 1-v/c \right)}}$$

For$$v<<c$$ :

i) Apparent frequency, $$\nu ‘=\nu \left( 1+\frac{v}{c} \right)$$

ii) Apparent wavelength, $$\lambda ‘=\lambda \left( 1-\frac{v}{c} \right)$$

iii) Doppler’s shift: Apparent wavelength < Actual wavelength, so spectrum of the radiation from the source of light shifts towards the violet end of spectrum. This is called violet shift.

Doppler’s shift, $$\Delta \lambda =\lambda \times \frac{v}{c}$$

iv) The fraction decrease in wavelength = $$\frac{\Delta \lambda }{\lambda }=\frac{v}{c}$$

2) Source of light moves away from the stationary observer: In this case, $$\nu ‘<\nu$$ and $$\lambda ‘>\lambda$$

$$\nu ‘=\nu \sqrt{\frac{\left( 1-\frac{v}{c} \right)}{\left( 1+\frac{v}{c} \right)}}$$ and $$\lambda ‘=\lambda \sqrt{\frac{\left( 1-\frac{v}{c} \right)}{\left( 1+\frac{v}{c} \right)}}$$

For$$v<<c$$ :

i) Apparent frequency, $$\nu ‘=\nu \left( 1-\frac{v}{c} \right)$$

ii) Apparent wavelength, $$\lambda ‘=\lambda \left( 1+\frac{v}{c} \right)$$

iii) Doppler’s shift: Apparent wavelength > Actual wavelength, so spectrum of the radiation from the source of light shifts towards the red end of spectrum. This is called red shift.

Doppler’s shift, $$\Delta \lambda =\lambda \times \frac{v}{c}$$

iv) The fractional increase in wavelength = $$\frac{\Delta \lambda }{\lambda }=\frac{v}{c}$$

3) Applications of Doppler Effect:

i) Determination of speed of moving bodies in RADAR and SONAR.

ii) Determination of the velocities of stars and galaxies b spectral shift.

Iii) Determination of rotational motion of sun.

iv) Explanation of width of spectral lines.

v) Tracking of satellites.

vi) In medical sciences in echo cardiogram, solography etc.