Interference: Equation versus Reality

I’m a physics teacher and I got stumped by a question: On the AP Physics exam there is an equation X=m(lamda)L/d. Its the distance between the central band and the mth order band. It obviously assumes the distance between each band is the same. I’ve seen pictures online (and tried it myself with a diffraction grating and laser) and the larger the m order band the more apart they are. Why is this discrepancy?

My suggestion is to go and understand the derivation of the formula and you’ll have your answer. There are assumptions behind the formula. I’m surprised that your AP teacher did not know the answer.

It’s a small-angle approximation.

Can I ask a yes or no question. Is there ever a situation with interference patterns where the distance between ALL bands (0 to 1, 1 to 2, 2 to 3 and so on) are constant?

As measured how? Along the wall?

The answer is the same as above - the small angle approximation.

I’m sure you could design a ‘wall’ that was curved appropriately so you could measure a constant distance between bands, even without the approximation. It’d be hella tricky, but I’m sure it could be done.

For what it’s worth, we did the same experiment in high school, and got nearly constant distances between bands (for the first few bands, and for small angles). Just remember that the distance between bands must be negligible compared to the distance from the diffraction grating to the wall for this to work.