How Does Slit Separation Impact Interference Patterns in Physics?

[taliaroma]

Homework Statement

What is the difference between the pattern resulting from
-2 slits, each 0.02mm wide, separated by 0.2mm AND
-2 slits, each 0.02 mm wide, separated by 0.4 mm

Homework Equations

lambda = 2yd / (2m-1)D, m = 1,2,3, etc.
D = distance from screen (where pattern is displayed) and slit
d=distance between slits

The Attempt at a Solution

I said that the distance between the dark bands would decrease, to which my TA responded "which dark bands?" I'm not quite sure what he's getting at, and what the actual answer to this question is.

 

[eczeno]

first off, you are right, the dark bands will get closer together; and you are right not to know what your TA is getting at, because i don't either.

now, we still need to show that the bands will get closer together. your formula is correct, but you should isolate y, because that is what we need to work with. so, the distance between dark bands, call it dy, will be the difference in the value of y for consecutive values of m. what you need to do is find an expression for dy, and see how it depends on d.

cheers.