How does the wavelength of light we observe from those galaxies compare with its original wavelength when it was emitted?

The most distant galaxies observed to date have a redshift of approximately z =7.

The wavelength of light we observe from distant galaxies is typically longer (redshifted) than its original wavelength when it was emitted due to the expansion of the universe. This phenomenon is known as cosmic redshift. As the universe expands, the space between galaxies also expands causing light from distant galaxies to stretch as it travels towards us. This stretching causes the observed wavelength to appear longer (i.e., more red) than its original wavelength, which is what we call redshift.

The redshift (z) can be used to calculate the ratio of the observed wavelength (λ_observed) to the emitted wavelength (λ_emitted). The relationship is given as:

1 + z = λ_observed / λ_emitted

Given a redshift of z = 7, we can calculate the ratio:

1 + 7 = 8 = λ_observed / λ_emitted

This means that the observed wavelength of light from galaxies with a redshift of 7 is 8 times longer than the wavelength of the light when it was emitted.

To compare the observed wavelength of light from galaxies with their original wavelength when emitted, we need to understand the concept of redshift. Redshift is a phenomenon that occurs when light waves are stretched as the source moves away from the observer. It is commonly observed in astronomical objects moving away from us due to the expansion of the universe.

The redshift parameter, denoted by "z," is a measure of how much the wavelength of the observed light has been stretched relative to its original wavelength. A redshift of z = 0 means no stretching, while higher values indicate greater stretching.

In the case of distant galaxies, the redshift value tells us how much the light from those galaxies has stretched since it was emitted. A redshift of z = 7 indicates that the observed wavelength of the light from those galaxies is approximately seven times longer (or "redder") than its original wavelength when it was emitted.

To calculate the actual change in wavelength, we use the formula:

λ_observed = (1 + z) * λ_emitted,

where λ_observed is the observed wavelength, λ_emitted is the original (emitted) wavelength, and z is the redshift.

For example, if the original wavelength of a galaxy's light was λ_emitted = 500 nm (nanometers), then the observed wavelength would be:

λ_observed = (1 + 7) * 500 nm = 4000 nm.

Therefore, the observed wavelength of light from galaxies with a redshift of z = 7 would be approximately 4000 nm, which is seven times longer than its original wavelength when emitted.

The redshift of a galaxy is a measure of how its light has been stretched or shifted towards longer wavelengths as it travels through the expanding universe. This shift in wavelength is due to the Doppler effect and is caused by the motion of the galaxy away from us. The higher the redshift value (z), the greater the shift in wavelength.

In the case of galaxies with a redshift of approximately z = 7, the observed light from these galaxies has been significantly stretched towards longer wavelengths. This indicates that the original wavelength of the light emitted by these galaxies was shorter than what we currently observe.

To put it simply, as light from these distant galaxies travels through space, it gets "stretched" due to the expansion of the universe, causing the observed wavelength to be longer (redshifted) compared to its original emitted wavelength. The higher the redshift value, the greater the stretching of the light and the more significant the change in wavelength from its emission point.