1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Basic diffraction grating question

  1. Sep 15, 2010 #1
    This is an intro lab-based question.

    1. The problem statement, all variables and given/known data
    I took a 650 nm red laser and shined it through a diffraction grating that claimed it had 13500 lines/inch, which comes to 5315 lines/cm in civilized people units. The grating was placed 30 cm away from a piece of paper on the wall. The distance between the central maximum (m=0) and the m=1 maximum was measured to be 4.1 cm. I'm trying to verify that the number of lines per cm is in fact around 5315.

    2. Relevant equations
    The grating equation, d sin(theta) = m(lambda)

    3. The attempt at a solution
    m=1 for the first maximum, and rearranging the equation, d = lambda/sin(theta). d equals the spacing between each slit, which is just 1/N, where N is the number of lines per cm. sin(theta) is 4.1/sqrt(30^2 + 4.1^2) = 0.1354. So, N = sin(theta)/lambda = 0.1354/(6.5 x 10^-5 cm) = 2080 lines/cm, to 3 s.f.

    I find that answer odd - did I make some really basic mistake, or does the grating really have 2.5 times fewer lines than it claims it does? If I were to go the other way and assume N was right, I'd get an ultraviolet wavelength, and I double-checked my measurements. Can anybody spot my goof?
  2. jcsd
  3. Sep 15, 2010 #2


    User Avatar
    Homework Helper

    Your calc looks good.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook