Class 12 Physics Wave Optics Dopplers effect

Doppler’s effect

  • Doppler Effect is the shift in frequency of light when there is relative motion between the source and observer.
  • It is used to measure the speed of a receding object.
  • When the source is moving away from the observer then the wavefronts have to travel a greater distance to reach the observer.
  • When a star is moving away from the earth the wavelength in the middle of the visible region of the spectrum moves towards the red end of the spectrum.
  • As a result star looks more reddish when moves away from the earth.
  • This is known as red shift phenomenon.
  • When the waves are received from a sourcemoving towards the observer, there is an apparent decrease in wavelength. This is called blue shift.
  • The fractional change in frequency (Δν/ν)=(–vradial/c),
  • Where vradial= component of the source velocity along the line joining the
    • observer to the source; vradial is considered positive when the source moves away from the observer.
  • Thus, the Doppler shift can be expressed as:
  • (Δν/ν) = (–vradial/c);
  • It is valid when the speed of the source is small compared to that of light.

Problem:-

What speed should a galaxy move with respectto us so that the sodium line at 589.0 nm is observedat 589.6 nm?

Answer:-

Since νλ = c,

(Δ ν/ ν) =- (Δλ/λ) = (for small changes in ν and λ). For

Δλ = 589.6 – 589.0 = + 0.6 nm

We get [using (Δ v/v) =- (vradial/c)

(Δ ν/ ν) =- (Δλ/λ)=- (vradial/c)]

Or, vradial≅ +c(0.6/ 589.0) =+ 3.06 x105 ms-1

= 306 km/s

Therefore, the galaxy is moving away from us.

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