How Can Changing Variables in a Laser Experiment Alter the Interference Pattern?

[student07]

Homework Statement

a) Imagine that you are conducting an activity with a laser to create an interference pattern. Use the appropriate equations to predict two ways (other than the way described in the following example) to change the interference pattern in order to have closer fringes. Explain your predictions.
The example they give is : Δx = Lλ/d
the distance between the fringes (Δx) is proportional to the wavelength (since they are both numerators). This means that increasing one will increase the other. Therefore, decreasing the wavelength will decrease the distance between the fringes. (Hint: You can use the "Thomas Young's Double-slit Experiment" simulation to verify predictions).
b) If you were using a hands-on activity to verify your predictions and use measurements to determine the wavelength of the laser being used, describe any safety precautions you would take and sources of error that you might encounter. Be sure to explain how you might reduce the effects of the sources of error.
2. The attempt at a solution
a) One way is using:
mλ = d sinθm for maxima or (n-1/2)λ = d sinθn for minima
d would represent the separation between fringes, where the distance of the fringes can be found for a nodal or antinodal line at a given angle.

Another way is:
mλ = d Xm / L for maxima or (n-1/2)λ = dXn / L for minima
the distance of the fringes is proportional to the distance of the slit to the screen (L); thus, decreasing the distance between the screen to where the laser is being projected on, decreases the distance between the fringes.

b) Wearing the correct safety goggles will diminish chances of damaging the retina; thus pointing laser at a person's face is not recommended. If using a laser beam do not leave uncovered after use.
A source of error could be the dot of the laser, since the experiment is not done in a vacuum, the light is spread out making it difficult to get an accurate measurement. If measured with a ruler then the reflection of the laser might be deceiving since the user might not read the exact wavelength or the ruler might not make an accurate horizontal with the surface the laser is reflected on. This could be solved by taking all the appropriate distances measurements from the reflection point to the fringe location and solve for the points where the laser is reflected on. Any suggestions are appreciated thank you

 

[BvU]

Your a1): no, the separation between fringes is Δx. Check what d stands for - and how it influences the distance between fringes.
Your a2): good.

Your safety precautions under b):

Never ever point a laser in a direction where the light can enter someone's pupil ! "Not recommended" is far too weak. You get an extra blind spot before you know it -- and if you move or your eye moves it'll be a blind area. This isn't only true for the beam itself, but also for reflections from glossy surfaces.
So a precaution is also to avoid reflecting surfaces in and around the working area.
And reducing the size of the pupil by working in a well-lit area as much as possible (from time to time you'll need darkness for accurate measurements for wide-angle diffraction)
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Your error reduction measures under b):

As you said, the fringe distances are affected by the distance from the slits to the screen, so make sure the screen is precisely perpendicular to the axis.

Most diffraction patterns are symmetrical, so you can make twice as many measurements using both sides
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[student07]

d is the distance between sources(waves)

 

[student07]

Then is just number 2 one for maxima and one for minima because I didn't learn other equations

 

[BvU]

Do you have a drawing or a link to a drawing to show what you mean ? In the text I read "d would represent the separation between fringes"

 

[student07]

yeah I had that wrong it's the distance between sources here is an example https://www.physicsforums.com/threads/please-help-simple-wave-interference-problem.767541/

 

[BvU]

yeah I had that wrong it's the distance between sources here is an example https://www.physicsforums.com/threads/please-help-simple-wave-interference-problem.767541/

That is the kind of thing you are going to do with a laser, but laser light has a lot smaller wavelength so you get very small angles. Better look around in hyperphysics single slit and here