According to Doppler Effect, an observer at rest will perceive a shift in the wavelength or frequency of the radiation emitted by a source in movement.This shift is given by the formula:
[tex] \frac{ \lambda - \lambda_{0} }{ \lambda_{0} } = \frac{-v}{c} [/tex]
where:
[tex] \lambda[/tex] = observed wavelength
[tex] \lambda_{0}[/tex] = wavelength at rest
v = speed of source (positive if towards the observer, negative if away from the observer)
c = speed of light
Therefore, we can solve for the observed wavelength:
[tex]\lambda = \lambda_{0} (\frac{-v}{c}) + \lambda_{0} \\ \lambda = \lambda_{0} (1 - \frac{v}{c})[/tex]
Substituting the given data:
[tex]\lambda = 656.46 (1 - \frac{300}{299792})[/tex]
= 655.80 nm
Hence, the observed wavelength of the line would be 655.80 nm. Note that this value is smaller than the one at rest, which means that we have a blue-shift, as expected for an approaching source.
