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!

Intensity in double slit interference

  1. Mar 21, 2014 #1
    I'm a little confused about a small detail when finding the intensity over the screen, as some notes I'm using happen to calculate the same thing twice, with a slight difference the second time.

    Each method does the following
    Call the electric field at any point E so we have
    E=E0ei(kx1-wt)+E0ei(kx2-wt) with x1,x2 the paths from each of the two slits to a point on the screen.
    Write each path in terms of a common path x starting midway between the slits, so x1 and x2 both have a path length difference of δ/2 relative to x. Let x1 be the shorter path.
    Then x1=x-δ/2 and x2=x+δ/2, and
    E=E0ei(kx-kδ/2-wt)+Eoei(kx+kδ/2-wt).
    Factoring out the common terms gives
    E=E0ei(kx-wt)[2cos(kδ/2)].

    This is where this issue is. First it says that the intensity is proportional to E*E whilst later it says it is proportional to E*E/2.

    This would give either
    4E02cos2(kδ/2)->I=4I0cos2(kδ/2), or
    2E02cos2(kδ/2)->I=2I0cos2(kδ/2).
    Now the first of these is the expression I always see, so must be right.

    I'm a little confused by this. I feel like I might be missing something with regards to time averaging the time varying term as in the E*E/2 method. Can somebody clear this up, thanks :)
     
    Last edited: Mar 21, 2014
  2. jcsd
  3. Mar 21, 2014 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The intensity is proportional to both E2 and E2/2 .The intensity of the incident light is I0= K E02. The intensity of the diffracted light is I=K [2cos(δ/2)E0]2=[2cos(δ/2)]2 KE02, that is I=4cos2(δ/2) I0.

    ehild
     
  4. Mar 21, 2014 #3
    Why not:

    The intensity is proportional to both E2 and E2/2 .The intensity of the incident light is I0= K E02. The intensity of the diffracted light is I=0.5K [2cos(δ/2)E0]2=0.5[2cos(δ/2)]2 KE02, that is I=2cos2(δ/2) I0.
     
  5. Mar 21, 2014 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    In that case, I0=0.5K E02. Be consistent.

    ehild
     
  6. Mar 21, 2014 #5

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    In the second line, you replaced ##E_0^2## by ##I_0##, but it should be ##2(E_0^2/2) = 2 I_0##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Intensity in double slit interference
Loading...