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

NCyellow

1. The problem statement, all variables and given/known data
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.


2. Relevant equations
sin(theta) = m(lamda)/d


3. 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.

Redbelly98

You'll need to use the equation for diffraction from a single slit also.