Imagine that you have obtained spectra for several galaxies and have measured the observed wavelength of a hydrogen emission line that has a rest wavelength of 656.3 nanometers. here are your results: galaxy 1: observed wavelength of hydrogen line is 660.0 nanometers. galaxy 2: observed wavelength of hydrogen line is 665.8 nanometers. galaxy 3: observed wavelength of hydrogen line is 682.7 nanometers. calculate the redshift, z, for each of these galaxies.

Galaxy 1:

z = 0.0056

Galaxy 2:

z = 0.014

Galaxy 3:

z = 0.040

Explanation:

Spectral lines will be shifted to the blue part of the spectrum¹ 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). The source in this particular case is represented for each of the galaxies of interest.

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. That is a direct confirmation of how the universe is in an expanding accelerated motion.

The redshift can be defined in analytic way by means of the Doppler velocity:

 (1)

Where is the wavelength shift, is the wavelength at rest, v is the velocity of the source and c is the speed of light.

 (2)

Where z is the redshift.

For the case of Galaxy 1:

Where and .

For the case of Galaxy 2:

Where and .

For the case of Galaxy 3:

Where and .

Key terms:

¹Spectrum: Decomposition of light in its characteristic colors (wavelengths).

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

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