Multiple-Slit Interference (Again)

[robera1]

Homework Statement

Consider the original double slit pattern from problem 1. Suppose that a third slit with the same width were added halfway between the original two slits. So that d goes from being 1 to being 0.5 for both.
Would point Z be a principal maximum, minimum, or neither?

Homework Equations

I don't need any questions, I just need to know what happens to the pattern once a slit is added in between the two. I know that the minimums will change, so that there is a brighter spot in the middle of each line, and I think that the width of each will double (since you are halving the distance between them)
But I am not sure?

The Attempt at a Solution

 

[jbsteele]

Point Z will be a principal maximum. When a third slit is added halfway between the two slits, the distance d between the slits goes from 1 to 0.5. This means that the width of each line will double, resulting in a brighter spot in the middle of each line. The bright spot in the middle of each line will be a principal maximum.

 

[nlightner]

Adding a third slit in between the original two will result in a change in the interference pattern. This is because the addition of another slit will introduce more wave sources, leading to more interference. This will result in a more complex pattern with additional bright and dark fringes.

In terms of point Z, it will no longer be a principal maximum or minimum. Instead, it will be a secondary maximum or minimum, meaning that it will not be as bright or dark as the principal ones. The width of each fringe will also change, becoming narrower due to the increased number of slits.

To fully understand the changes in the interference pattern, it would be helpful to use the equation for multiple-slit interference, which is given by d sinθ = mλ, where d is the distance between the slits, θ is the angle of diffraction, m is the order of the maximum or minimum, and λ is the wavelength of the light. By plugging in the new values for d and solving for θ, we can see how the pattern has changed.

In conclusion, adding a third slit in between the original two will result in a more complex interference pattern with narrower fringes and additional bright and dark spots. Point Z will no longer be a principal maximum or minimum, but rather a secondary one. This is just one example of how small changes can greatly impact the behavior of waves and the resulting interference patterns.