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

In summary, the problem involves 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, with another screen at a distance d >> a,b from the first. The periodicity of fringes on the screen can be found by finding the phase difference between each pair of slits and adding them together. This will give the final phase difference and help determine the intensity of the fringes.
  • #1
radonballoon
21
0

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


[tex]\Delta \phi = \frac{2\pi}{\lambda}(x_1-x_2)[/tex]

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.
 
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  • #2
radonballoon said:

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


[tex]\Delta \phi = \frac{2\pi}{\lambda}(x_1-x_2)[/tex]


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.
 
  • #3
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?
 
  • #4
radonballoon said:
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 :)
 

1. What is "Triple Slit interference"?

Triple slit interference is a phenomenon in which light waves passing through three parallel slits produce an interference pattern on a screen. This pattern is a result of the waves overlapping and interfering with each other.

2. How does triple slit interference differ from double slit interference?

In triple slit interference, there are three slits instead of two, which results in a more complex interference pattern. The intensity of the pattern is also different, with more peaks and valleys compared to the simpler double slit pattern.

3. What factors affect the interference pattern in triple slit interference?

The interference pattern in triple slit interference is affected by the distance between the slits, the wavelength of the light, and the relative phase of the waves passing through the slits. These factors determine the spacing and intensity of the fringes in the pattern.

4. Can any type of light produce a triple slit interference pattern?

Yes, any type of light can produce a triple slit interference pattern as long as it is coherent and has a constant wavelength. This includes both monochromatic light, such as from a laser, and white light that has been filtered to a specific wavelength.

5. What are the practical applications of studying triple slit interference?

Studying triple slit interference can help scientists understand the nature of light and its wave-like behavior. It also has practical applications in fields such as optics and engineering, where precise control and manipulation of light waves are necessary. Triple slit interference is also used in experiments to test the validity of quantum physics theories.

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