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Homework Help: Find the speed of a galaxy

  1. Feb 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Taking light collected by the telescope and shine it through a diffraction grating with a 765.5 lines/mm. Using the filter that just the brightest Helium II line. you cast the diffraction grating's diffracted pattern on a screen is 22.000cm away and there are 3 dots, m=-1, m=0 amd m=1. the distances between m=-1 and m=1 is 10.7314.

    find the speed of the galaxy moving away from us?

    2. Relevant equations

    d sin theta =m lambda
    y_m=Ltan lambda
    Doppler effect
    3. The attempt at a solution

    At first, I think I need to find the angel by using: y_m=Ltan lambda
    then I have: 0.22 tan theta _1 =0.107314/2 → theta=47.3972 degrees

    Since I have the angel, I can find the wavelength of the light by using: d sin theta =m lambda
    then I have: 1mm/765.5 sin (47.3972)= 1*lambda → lambda = 962 nm

    I get stuck at this step, can anyone give me a hit to get the answer?

  2. jcsd
  3. Feb 28, 2015 #2


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    You set this up correctly, but your answer for the angle θ is not correct.

    Think about how to use the Doppler effect to get the speed of the galaxy.
  4. Feb 28, 2015 #3
    λ=309nm, this is the initial wavelength.

    the equation of the Doppler effect is λ=λ'√(1+v_s/c)/(1-v_s/c)

    309nm is λ' , I dont't see how to get λ with the information I have.
  5. Feb 28, 2015 #4


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    What is the normal wavelength for the brightest He II line?
  6. Feb 28, 2015 #5
    I don't know, the question doesn't give me any information about that
  7. Feb 28, 2015 #6


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    Staff: Mentor

    Your text or notes will likely contain the value. If not it can be looked up online. The NIST site should have a table.
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