What is the approach for finding fringes on a screen with three slits?

[radonballoon]

Homework Statement

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?

Homework Equations

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

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.

 

[nathan12343]

Homework Statement

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?

Homework Equations

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

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.

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.

 

[radonballoon]

So then would I be on the right track if I found the phase difference between each pair and then added them to get the final phase difference?

 

[nathan12343]

So then would I be on the right track if I found the phase difference between each pair and then added them to get the final phase difference?

Sounds right to me :)