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We measure distances in universe by the units of light year/s or parsec. Which means distance traveled by light in one year equals one light year. Thus the lights we receive from the distant stars or galaxies are coming from many light years away.

So how do we know the age of the light so that we determine the distance it has traveled to reach earth ?

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We actually measure the distance, and infer the age of the light from the distance. There are many answers on the site discussing how cosmological distances are measured.

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    $\begingroup$ This is not entirely true. We can measure the age of light from standard candles directly by measuring the redshift of the light, which tells us how long it has been travelling. That is also where some distance measurements come from. $\endgroup$ – Jim Jul 18 '14 at 15:31
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    $\begingroup$ And not just standard candles but also Hydrogen emission spectra, and similar sources where we know the expected spectral pattern $\endgroup$ – Jim Jul 18 '14 at 15:32
  • $\begingroup$ Addendum: the redshift distance from standard candles is also backed up with luminosity distance, which is not inferred from age of light. I don't want people thinking I forgot about luminosity distance $\endgroup$ – Jim Jul 18 '14 at 15:33
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    $\begingroup$ Red shift is due to relative source-observer speed, not age or distance! $\endgroup$ – Michael Jul 18 '14 at 15:33
  • $\begingroup$ @Michael from the expansion of the universe, the longer a ray of light travels through the universe, the more the neighbouring peaks expand apart, thus redshifting $\endgroup$ – Jim Jul 18 '14 at 15:34

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