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!

Optics - diffraction gratings and blaze angles

  1. Mar 28, 2007 #1
    1. The problem statement, all variables and given/known data
    Light is incident on the reflecting surface tilted at a blaze angle [tex]\gamma[/tex] with respect to the horizontal non-reflecting screen as shown in the figure (below). The angle of incidence with respect to the screen normal is [tex]\theta_i[/tex].

    Consider two points along the reflecting surface with the distance z between them. Show that the path difference between the waves incident at these two points and then diffracted in the direction with the angle [tex]\theta[/tex] (with respect to the screen normal) can be calculated as:

    [tex]\Delta = z[sin(\theta + \gamma) - sin(\theta_i - \gamma)][/tex]

    2. Relevant equations
    I'm not sure - I think maybe simple geometry and tig can be used.

    3. The attempt at a solution
    I've drawn a diagram (not here) with the setup of the question, and all rays and important lines on it. From this I have extracted a triangle with base z (which is also the hypotenuse), and the longer of the two sides is [tex]\Delta[/tex], as shown below.

    Now from this I can see that [tex]\Delta[/tex] = zsin[tex]\phi[/tex], so this indicates to me that I have find [tex]\phi[/tex] in terms of the other angles (or sin[tex]\phi[/tex] in terms of the sine's of the other angles). However I am struggling to do this, I can't see a relationship, unless I think of vector addition, and say that [tex]z[sin(\theta + \gamma) - sin(\theta_i - \gamma)] = zsin\phi[/tex], which I think is correct. Then is sufficient to say that I found this out from the diagram and geometry? Or do you believe that the question is looking for more of an algebraic approach to the solution?
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Optics - diffraction gratings and blaze angles
  1. Optics problem (Replies: 0)

  2. Optics question (Replies: 0)

  3. Optics: Telescopes (Replies: 0)

  4. Help with optics (Replies: 0)