# Using Phasors to Graph Intensity vs Angle (4 slits)

• Casebur
In summary, use phasors to sketch the intensity vs. angle for a 4-slit interference pattern, taking into account the identical width and separation of d=5 microns and wavelength =0.5 microns. Then, on the same angular scale, draw the intensity pattern if the top two slits are covered. The intensity pattern if the bottom 2 slits are covered is the same as the one with the top two slits covered, as they can be considered as two sources with an angularly dependent radiation pattern interfering with each other. For the next step, draw the intensity pattern for interference of two uniform slit sources separated by 2d, and then multiply this by the pattern in the previous step to get the pattern
Casebur
3.a) Use phasors to sketch the intensity vs. angle for a 4-slit interference pattern (identical
width and separation d=5 microns, wavelength =0.5 microns.)

b) On the same angular scale, draw the intensity pattern if the top two slits are covered.

c) The intensity pattern if the bottom 2 slits are covered is the same as (b), of course. So
you can consider the top and bottom pairs of slits as two sources that have an angularly
dependent radiation pattern. These two sources interfere with each other, and they are
separated by 2d (center to center.) Draw, on the same angular scale, the intensity pattern
for interference of two uniform slit sources separated by 2d. If you multiply this by your
pattern in (b), you should get your pattern in (a).

d) Now consider the interference pattern from just the top and bottom slits, which have a
separation of 3d. (Cover the two middle slits.) Sketch, on the same angular scale, this
pattern. Are the zeros of intensity at the same angles as in (a)? Discuss why or why not.

Hey, I have been working on this problem for a while now and am not sure where to start,

so far I have dsin(θ)=mλ and i calculated the angle to be θ=asin(.5μ/5μ) which gave me a value of 5.74 degrees. am i on the right track?

Any help on how to move forward will help a lot!
Thanks

!Yes, you are on the right track. The next step is to use phasors to sketch the intensity vs angle for a 4-slit interference pattern. You can do this by using the same equation you used to calculate the angle: dsin(θ)=mλ. The m value is the order of interference, which ranges from -2 to 2. For each value of m, you need to calculate the angle and then draw a phasor of the corresponding intensity at that angle. Once you have all 4 phasors drawn, you should be able to get the entire interference pattern.

## What is the purpose of using phasors to graph intensity vs angle in the 4 slits experiment?

The purpose of using phasors in this experiment is to represent the complex amplitudes of the wave at different angles and to visualize the interference pattern created by the four slits. This allows us to better understand the behavior of waves and the relationship between intensity and angle.

## How do phasors help in understanding the interference pattern produced by the four slits?

Phasors help in understanding the interference pattern by representing the amplitude and phase of the wave at different angles. This allows us to see the constructive and destructive interference at different points in the pattern, as well as the overall shape of the pattern.

## What factors can affect the intensity vs angle graph in the four slits experiment?

The intensity vs angle graph can be affected by the number and spacing of the slits, the wavelength of the wave, and the distance between the slits and the screen. These factors can change the interference pattern and alter the overall shape and intensity of the graph.

## How can phasors be used to find the distance between the slits and the screen in the four slits experiment?

Phasors can be used to find the distance between the slits and the screen by measuring the distance between consecutive bright spots on the graph. This distance is directly related to the wavelength of the wave and can be used to calculate the distance between the slits and the screen.

## What other applications can phasors have in the study of waves and interference?

Phasors have many applications in the study of waves and interference, including in the fields of optics, acoustics, and signal processing. They can be used to analyze the behavior of waves in various systems and to design systems that utilize interference to produce desired effects.

• Introductory Physics Homework Help
Replies
4
Views
4K
• Introductory Physics Homework Help
Replies
3
Views
4K
• Introductory Physics Homework Help
Replies
14
Views
4K
• Introductory Physics Homework Help
Replies
3
Views
4K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
6K
• Introductory Physics Homework Help
Replies
23
Views
2K