In a laboratory, light from a particular spectrum line of helium passes through

Question

In a laboratory, light from a particular spectrum line of helium passes through a diffraction grating and the second-order maximum is at 18,9 degrees from the center of the central bright fringe. The same grating is then used for light from a distant galaxy that is moving away from the earth with a speed of 2.65e7 m/s. For the light from the galaxy, what is the angular location of the second-order maximum for the same spctral line as was observed in the lab?

Please explain clearly with details so that I can follow.

Explanation / Answer

lambda' = lambda *sqrt( (1 + v/c)/(1 - v/c)

lambda' = lambda *sqrt( (1 + 2.65E7/3E8)/(1 - 2.65E7/3E8))= 1.0926 lambda

lambda' = lambda *sqrt( (1 + 0.883)/(1 - 0.883))= 1.0926 lambda

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