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Relativistic Doppler Effect (Light) Calculator

Compute the observed wavelength and frequency shift plus redshift z of light from a moving source using the relativistic Doppler effect.

Input

Enter the source wavelength or frequency and the relative speed (fraction of light, beta) to get the observed values and redshift z from the relativistic Doppler effect.

Input quantity

Choose whether to enter the source wavelength or frequency.

nm

Wavelength when the source is at rest (for example hydrogen H-alpha is about 656 nm).

× c

Relative speed divided by the speed of light, v / c. Enter a value from 0 up to but not including 1.

Direction of motion

Recession gives a redshift; approach gives a blueshift.

Result

Observed wavelength

725.545945nm

Observed frequency: 413.195691 THz

Redshift z

0.105542

Shift type

Redshift

Doppler factor

0.904534

Source wavelength

656.281 nm

Wavelength shift

69.264945 nm

SourceObservedToward red725.545945 nm

For recession f_obs = f_src × sqrt((1 − beta) / (1 + beta)); approach uses the reciprocal. Wavelength varies oppositely via lambda = c / f, and z = (lambda_obs − lambda_src) / lambda_src.

How it works

  • Uses the line-of-sight relativistic Doppler effect. For recession f_obs = f_src × sqrt((1 − beta) / (1 + beta)); for approach use the reciprocal. Here beta is the speed ratio v / c.
  • Wavelength changes opposite to frequency. Recession stretches the wavelength (redshift); approach shortens it (blueshift).
  • Redshift is defined as z = (lambda_obs − lambda_src) / lambda_src, positive for recession and negative for approach.
  • The speed of light is taken as c = 299792458 m/s. Wavelength input is in nanometers (nm) and frequency input is in terahertz (THz).
  • Enter beta in the range from 0 up to but not including 1.

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