How is the color shift referenced above related to the motion of galaxies?
A) Red light travels faster so it reaches Earth from distant galaxies before other light waves.
B) Red light has a higher frequency so these are the only waves able to reach Earth from distant galaxies.
C) Red light has longer wavelengths so these are the only waves of the visible spectrum that are able to reach Earth without interference.
D) Red light has longer wavelengths so light waves from galaxies traveling away from Earth appear to shift to the red end of the visible spectrum.

Spectral lines¹ will be shifted to the blue part of the spectrum² if the source of the observed light is moving toward the observer, or to the red part of the spectrum when is moving away from the observer (that is known as the Doppler effect).

See that shift to the red part of the spectrum in the case of galaxies is a clear prove of the expansion of the universe.

Due to that shift the velocity of the galaxy can be determined by means of Doppler velocity.

[tex]v = c\frac{\Delta \lambda}{\lambda_{0}}[/tex] (1)

Where [tex]\Delta \lambda[/tex] is the wavelength shift, [tex]\lambda_{0}[/tex] is the wavelength at rest, v is the velocity of the source and c is the speed of light.

The redshift can be defined in analytic way by means of equation 1 in the following way:

[tex]v = c(\frac{\lambda_{measured}-\lambda_{0}}{\lambda_{0}})[/tex]

[tex]\frac{v}{c} = \frac{\lambda_{measured}-\lambda_{0}}{\lambda_{0}}[/tex]

[tex]z = \frac{\lambda_{measured}-\lambda_{0}}{\lambda_{0}}[/tex] (2)

Where z is the redshift.

Hence, the redshift represents this shift of the spectral lines to red part in the spectrum of a galaxy or any object which is moving away.

Summary:

In equation 2 [tex]\lambda_{0}[/tex] represents the value in wavelengths that the spectral line will have if there is no Doppler effect present (at rest).

Therefore, in that way is easy to denote the shift of different spectral lines.

Key terms:

¹Spectral line: Part in the spectrum that denotes the absorption or emission of light due to an specific element. Spectral lines will be shifted to the blue part of the spectrum if the source of the observed light is moving toward the observer, or to the red part of the spectrum when is moving away from the observer (that is known as the Doppler effect).

²Spectrum: Decomposition of light in its characteristic wavelengths (colors).