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: Slit diffraction with a beam of spatially distributed intensity

  1. Dec 6, 2008 #1
    1. The problem statement, all variables and given/known data

    I have the classic slit-diffraction experiment, where light is incident on two narrow slits on a screen and is diffracted to create a pattern of maxima and minima on the far surface. It is usually assumed that the light incident on the slits is uniform. In practice, the light generally varies a little bit, i.e. you have a spatial distribution of intensity rather than one intensity, so the intensity of the incident light through each slit is a little bit different.

    3. The attempt at a solution

    I started by summing the diffracted bits of electric field:

    E = E(0)e^i(kr - wt) + E(0)e^i(k(r + dsin(theta)) - wt) + E(0)e^i(k(r + 2dsin(theta)) - wt)...

    If all the E(0)'s are the same, they can be pulled out from the exponential, and then the exponential can be summed alone and a trig identity used to change it into an equation with sines instead of e^1(thing)'s. If they're all different...

    E = Ae^i(kr - wt) + Be^i(k(r + dsin(theta)) - wt) + Ce^i(k(r + (N-1)dsin(theta)) - wt)

    let (phi) = kdsin(theta)

    E = e^i(kr - wt)*(A + Be^i(phi) + Ce^i2(phi))

    and I can't get it to simplify any more than that. Is there a way to get this into a form with sines and cosines? Failing that, is there a way to graph this as-is to get the distribution pattern? I haven't been able to find any graphing software that'll play nice with e^i factors.
  2. jcsd
  3. Dec 6, 2008 #2


    User Avatar
    Homework Helper

    Don't you need to make those r's into (r-r0)'s (vectorwise)? You refer to a 2-slit problem in your problem statement, but in your solution you are dealing with multiple slits. You should take the real part of the result, which will be a sum of products of sines and cosines.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook