Most stars and galaxies are moving farther away from us, but there are exception

Question

Most stars and galaxies are moving farther away from us, but there are exceptions. Using a telescope, a diffraction grating and a digital camera, a very precise amateur astronomer analyses the spectrum of light from Sirius (the brightest star in the sky, and a neighbor to our solar system). A hydrogen absorption line at a wavelength of ?’ = 656.26 nm is detected. This is blue-shifted slightly from the value of ? = 656.28 nm which would be measured in a lab on Earth (See chapter 31 for a discussion of the absorption spectrum of hydrogen, but you don’t need to in order to solve this problem). Based on this measurement, and using c = 2.9979 x 108 m/s, (a) what would you conclude is the relative velocity between Sirius and the Sun? (b) Are they approaching or receding from each other? (c) If, while stargazing, you could inspect one ray of blue light (? = 475.0 nm) coming from Sirius, how many wavelengths (to the nearest whole number) would you count along one millimeter of its direction of travel?

****My question is on part c. I am unsure how to incorporate the 1 mm into the problem? What equation do I start with? Any help would be greatly appreciated!
Thanks!

Explanation / Answer

The wavelength of the blue ray is = 475 nm The number of wavelengths that would account along one mm distance is n = 1 mm / 475 nm n = 2105

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