# Triple Slit interference

1. Mar 23, 2009

1. The problem statement, all variables and given/known data
There are three slits in a screen, with one aligned with the source at z=0, one a distance a above 0, and one a distance b below 0. Another screen is at a distance d >> a,b from the first. What is the periodicity of fringes on the screen?

2. Relevant equations
$$\Delta \phi = \frac{2\pi}{\lambda}(x_1-x_2)$$

3. The attempt at a solution
I know for two slits that you subtract the distances from the slits to the screen and multiply by the wave vector to get the difference in their phases, and when that difference is a multiple of pi that the intensity is minimum. My question is what do you do for three slits? Subtract two and then subtract the third from that? I'm confused as to how to approach this problem. Any help would be appreciated.

2. Mar 23, 2009

### nathan12343

Well, you know what the pattern from TWO slits looks like, so you're most of the way there. Three slits is the same thing as three pairs of slits, three double-slit patterns superposed on each other. The rest is just some moderately complicated algebra.

3. Mar 23, 2009