Four Slit Diffraction

Note: This problem is from a tutorial assignment, which we do before reading the corresponding chapter, so I’m not supposed to use a lot of math or equations in my justifications.

Suppose that the 2 rightmost slits are covered. The diagram below shows the direction to point M, a point on a distant screen where there is a first interference minimum due to the leftmost two slits.

___/ ___/ ___ ___ ___ (slits are all the same width and are evenly spaced)

1) Would the light that passes through the rightmost pair of slits alone (only slits 3 and 4) also yield a first minimum at M?

I think they would because the path length difference between 1 and 2 is the same as 3 and 4, and if 1 and 2 alone yield a minimum, 3 and 4 should yield a minimum as well.

2) Would the light that passes through all 4 slits yield an interference minimum at point M? If so, determine the order of the minimum.
Again, I think the answer is yes…But I’m not sure. My reasoning is that 1 and 2 yield a minimum and 3 and 4 yield a minimum, so all together they should still yield a minimum. I’m not sure how to determine what order minimum it should be though. Is it just that since each pair of slits yields a first order minimum, then together they still yield a first order minimum>

Am I thinking about this correctly? I’m getting kind of tripped up because if 1 and 2 yield a min, shouldn’t 1 and 3 yield a max (along with 2 & 4)? If there are any big misconceptions I’m having, I would greatly appreciate someone identifying what they are.

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