Interference patterns do not have an infinite number of lines, since there is a limit to how big m can be. What is the highest-order constructive interference possible with the system described in the preceding example?

Strategy and Concept

The equation d sin θ= mλ (for m = 0, 1, -1, 2, -2, ...) describes constructive interference. For fixed values of d and A, the larger m is, the larger sin is. However, the maximum value that sin can have is 1, for an angle of 90°. (Larger angles imply that light goes backward and does not reach the screen at all.) Let us find which m corresponds to this maximum diffraction angle.