**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.