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

[NCyellow]

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.

 

[Redbelly98]

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