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.