Diffraction grating problem, missing orders, diffraction minimum and maximums.

AI Thread Summary
Missing orders in a diffraction grating occur when a diffraction minimum aligns with an interference maximum. When the slit separation d equals twice the slit width D, all even orders (m=2,4,6) are absent. Additionally, missing orders arise whenever the ratio d/D equals the ratio of two integers m1/m2. The discussion also touches on the scenario where the space between slits becomes negligible, leading to different diffraction patterns. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement


Missing orders occur for a diffraction grating when a diffraction minimum coincides with an interference maximum. Let D be the width of each slit and d the separation of slits. (a) show that if d = 2D, all even orders (m=2,4,6) are missing. (b) show that there will be missing orders whever d/D = m1/m2. where m1 and m2 are integers. (c) Discuss the case d + D, the limit in which the space between slits becomes negligible.


Homework Equations


sin(theta) = m(lamda)/d


The Attempt at a Solution


I figured out that in order for there to be a missing order m1 and m2 needs to coincide. However, setting m1D=m2d (m2 can't be 0), plugging in the given information d=2D, I simply get m2=m1/2. That did not seem to prove anything. Please give me some hints.
 
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You'll need to use the equation for diffraction from a single slit also.
 
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