1. Not finding help here? Sign up for a free 30min 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!

Diffraction grating and wavelengths

  1. Mar 25, 2009 #1
    diffraction grating URGENT

    1. The problem statement, all variables and given/known data

    A spectrometer is used to analyze a light source. The screen-to-grating distance is 50.0 cm and the grating has 5000 slits/cm. Spectral lines are observed at the following angles: 12.98, 19.0, 26.7, 40.6, 42.4, 63.9 and 77.6. How many different wavelengths are present in the spectrum of this light source? FInd each of the wavelengths.


    2. Relevant equations

    d*sinthetha =m*lambda

    d=0.0002cm

    The thing I am really confused about is the value "m". Which values would I use for this question, because I know m=0,+/-1,+/-2 etc..

    I just don't understand which values to use.
    3. The attempt at a solution
     
  2. jcsd
  3. Mar 25, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    Re: diffraction grating URGENT

    Find the sin( theta) of all the angles.
    For same d and lambda, some sin(theta) must be equal to m*sin(12.98). Find m values. Repeat the same thing for other wavelengths.
     
  4. Mar 25, 2009 #3
    Re: diffraction grating URGENT

    since there are 7 different angles, does that mean there will be seven different wavelengths?
     
  5. Mar 25, 2009 #4
    Re: diffraction grating URGENT

    I do not understand what you are trying to say here.

    I know d, I do not know λ or m. How can I solve for two unknowns here? Your statement is very confusing.
     
  6. Mar 25, 2009 #5

    rl.bhat

    User Avatar
    Homework Helper

    Re: diffraction grating URGENT

    No. Not necessarily. Find the sine of all angles.
     
  7. Mar 25, 2009 #6
    Re: diffraction grating URGENT

    I still don't really understand how to find the values of m.. For some reason this is really confusing
     
  8. Mar 25, 2009 #7

    rl.bhat

    User Avatar
    Homework Helper

    Re: diffraction grating URGENT

    Will you please write down sine values of all the angles. Then I will tell you how to find m.
     
  9. Mar 25, 2009 #8
    Re: diffraction grating URGENT

    sin12.98=0.2246
    sin19=0.3257
    sin26.7=0.4493
    sin40.6=0.6508
    sin42.4=0.6743
    sin63.9=0.8980
     
  10. Mar 25, 2009 #9

    rl.bhat

    User Avatar
    Homework Helper

    Re: diffraction grating URGENT

    sin12.98=0.2246
    sin19=0.3257
    sin26.7=0.4493
    sin40.6=0.6508
    sin42.4=0.6743
    sin63.9=0.8980
    These four belong to the same wavelength. Because other three are multiple of 0.2246. And the remaining two belong to another wavelength.
     
  11. Mar 25, 2009 #10
    Re: diffraction grating URGENT



    Alright, so there is a total of 3 different wavelengths? I think I got that.

    However, when calculating the wavelengths, would sin12.98, have m=1
    would sin 19 have m=1 too?
    same goes for sin40.9, m=1?
     
  12. Mar 26, 2009 #11
    Re: diffraction grating URGENT

    Sorry for intruding here again (I am working on the same problem) but I think that 12.98/19=1, 26.7/40.6=2, 42.4/77.6=3 and 63.9=4

    ????


    edit: I have checked it out, and as far as I can tell this is correct.
     
    Last edited: Mar 26, 2009
  13. Mar 26, 2009 #12

    rl.bhat

    User Avatar
    Homework Helper

    Re: diffraction grating URGENT

    For last one m = 2
    And for 77.6 degree, m=3.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook