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!

Phase difference

  1. May 15, 2008 #1
    1. The problem statement, all variables and given/known data
    For single-slit diffraction, calculate the first three values of [tex]\phi[/tex] (the total phase difference betweenrays from each edge of the slit) that produce subsidiary maximu by

    a) using the phasor model

    b) setting [tex]\frac{dI}{d\phi} = 0[/tex], where I is given by [tex]I = I_0 \cdot (\frac{sin(\frac{1}{2} \cdot \phi)}{\frac{1}{2} \cdot \phi})^2[/tex]

    2. Relevant equations


    3. The attempt at a solution

    I attempted to do part b first as I already knew the answers from part a (fairly straight forward) and was using them to check my answer.

    I realized that even though I had used the exact described method, my answer was completely different as my values for phi ended up as:

    1) [tex]\pi[/tex]
    2) The first non-zero solution to [tex]tan(\frac{\phi}{2}) = \frac{\phi}{2}[/tex]
    3) [tex]2 \cdot \pi[/tex]
  2. jcsd
  3. May 16, 2008 #2
    The equation for the intensity with single slit diffraction is

    [tex] \frac { \frac {\pi d} {\lambda} sin(\phi) } { \frac {\pi d} {\lambda} } [/tex]

    your equation is produced if [itex] d = \frac {\lambda} { 2 \pi} [/itex]. d is obviously too small here to get destructive interference at any angle. For the light to go through the slit and reach the screen you need [itex] \frac {- \pi} {2} < \phi < \frac {\pi} { 2 } [/itex]
  4. May 16, 2008 #3
    Err. The equation for the intensity is given in the problem and d is not involved.
  5. May 17, 2008 #4


    User Avatar
    Homework Helper

    Hi Math Jeans,

    When you take the derivative and set it to zero, you find the minima and maxima. The third values you found (2 pi) is a minima (it makes [itex]I[/itex] to be zero); the maxima are found by using your expression [tex]tan(\frac{\phi}{2}) = \frac{\phi}{2}[/tex] and finding the first three non-zero solutions.

    I did not see how you got the first answer (pi); I don't believe it makes the derivative zero. If you still get it as an answer would you post your expression for the derivative?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Phase difference
  1. Phase Difference (Replies: 21)

  2. Phase difference! (Replies: 1)

  3. Phase Difference (Replies: 3)

  4. Phase difference. (Replies: 2)

  5. Phase difference (Replies: 5)