Light beam question

  1. Q: The grating equation tells you at what angles different colors of light will appear: d sin θ = mλ
    where d is the separation between the lines on the grating,
    m is an integer (i.e., m = 0, ±1, ±2, ±3, etc.) known as the diffraction order number,
    λ is the wavelength (with the same length units as d), and
    θ is the angle at which light with wavelength λ is diffracted.

    Make a sketch based on the figure below to show a narrow parallel beam of white light shining onto a grating with line separation d = 1150 nm. Show the angles for red and blue light for m = 0, +1, and –1 by drawing them in appropriate colors
    [​IMG]

    I am confused on how to start this problem. Suggestions on starting points are appreciated.
    Thanks.
     
  2. jcsd
  3. andrevdh

    andrevdh 1,724
    Homework Helper

    Since the wavelengths for the two colours are not given you should choose your own, maybe use [itex]\lambda_{red}=700\ nm,\ \lambda_{blue}=\ 500\ nm[/itex], and then work the diffraction angles out for the various orders for each of the two colours. It seems this is more a qualitative than quantitative question in spite of the given grating spacing.
     
  4. It does seem more like a qualitative question... however, you are given enough information to solve for the diffraction angles.

    You know:

    d*sin(theta) = m*lambda

    You are given (if you choose your blue and red wavelengths as Andre suggested) all variables except theta.

    It's a matter of transposing the equation so that you have:

    theta = something (it's up to you to work this out)

    and then applying it three times for each wavelength (m= 0 , +1 and -1)

    With this information, you can draw an accurate sketch, you should have 3 blue lines and three red lines....
     
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