Brewer
Mar28-07, 06:10 AM
1. The problem statement, all variables and given/known data
Light is incident on the reflecting surface tilted at a blaze angle \gamma 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 \theta_i.
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 \theta (with respect to the screen normal) can be calculated as:
\Delta = z[sin(\theta + \gamma) - sin(\theta_i - \gamma)]
http://i54.photobucket.com/albums/g99/brewer86/blaze.jpg
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 \Delta, as shown below.
http://i54.photobucket.com/albums/g99/brewer86/blaze2.jpg
Now from this I can see that \Delta = zsin\phi, so this indicates to me that I have find \phi in terms of the other angles (or sin\phi 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 z[sin(\theta + \gamma) - sin(\theta_i - \gamma)] = zsin\phi, 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?
Light is incident on the reflecting surface tilted at a blaze angle \gamma 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 \theta_i.
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 \theta (with respect to the screen normal) can be calculated as:
\Delta = z[sin(\theta + \gamma) - sin(\theta_i - \gamma)]
http://i54.photobucket.com/albums/g99/brewer86/blaze.jpg
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 \Delta, as shown below.
http://i54.photobucket.com/albums/g99/brewer86/blaze2.jpg
Now from this I can see that \Delta = zsin\phi, so this indicates to me that I have find \phi in terms of the other angles (or sin\phi 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 z[sin(\theta + \gamma) - sin(\theta_i - \gamma)] = zsin\phi, 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?