Finding Maximum Number of Interference Maxima?

In summary: So, the central maximum and the two first orders can be observed. So, the answer is 3In summary, the maximum number of interference maxima that could be observed when light of wavelength λ = 535 nm shines through two narrow slits 670 μm apart is 3, including the central maximum and the two first orders. This is based on the equation m = d/λ, where m is the integer number of maxima, d is the slit distance, and λ is the wavelength. The maximum angle allowed is 90°, which corresponds to a value of m = 1.26, but since m must be an integer, the answer is rounded down to 1. Therefore, the maximum number of
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Homework Statement


Light of wavelength λ = 535 nm shines through two narrow slits which are 670 μm apart. What is the maximum number of interference maxima which could conceivably be observed (assuming that diffraction minima do not extinguish them and the screen is arbitrarily large)?Your answer should be an integer. There is no sig-fig requirement for your answer

  1. Hint: What is the maximum angle allowed? Did you remember to count the maxima below the center?

Homework Equations


When I tried to answer the first time, the question gave me the a hint to look for the max angle allowed, so I think I'll need to use
dsinθ = mλ, where d=slit distance = 670 μm = 6.7 x 10-7m and λ=535nm = 5.35 x 10-7m
I also think I'll need y=mdL/λ, where y=distance between maxima, m= maxima integer, d=slit distance, L=distance between slits and screen (not given) and λ= wavelength, so maybe not this equation (because L isn't given?)
I thought about using wsinθ=mλ (where w=slit width), but because the question states to assume diffraction minima do not extinguish the maxima, I didn't think it was necessary to factor this in as well.

The Attempt at a Solution


Honestly I'm not even sure where to begin with this. I tried solving for the maximum angle as the question gave me feedback, and I got 52.98°. But I don't know if this is even relevant or what. For an earlier question I did m= d/λ and got the correct answer, but for some reason this does not work here.

Thanks in advance for any help!
 
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  • #2
What can be the diffraction angle maximum ? Can it exceed 90°?
 
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If it's 90°, wouldn't the equation be dsin(90°) = mλ? And sin(90°) = 1
Rearranging for m: m=d/λ= (6.7 x 10-7m)/(5.35 x 10-7m) = 1.26. Is this the number of maxima produced? Or just for one side of the central maxima?
So I multiplied by 2 (for either side) and got 2, but that's wrong. So I'm getting confused somewhere.
 
  • #4
hrf2 said:
If it's 90°, wouldn't the equation be dsin(90°) = mλ? And sin(90°) = 1
Rearranging for m: m=d/λ= (6.7 x 10-7m)/(5.35 x 10-7m) = 1.26. Is this the number of maxima produced? Or just for one side of the central maxima?
So I multiplied by 2 (for either side) and got 2, but that's wrong. So I'm getting confused somewhere.
Yes, m would be 1,26, but it must be integer. You need to tale the integer part. It is 1, so the orders of ±1 are observed, one maximum at both sides of the central maximum. The question was What is the maximum number of interference maxima which could conceivably be observed? . You observe the central maximum, too.
 
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1. What is the concept of "Finding Maximum Number of Interference Maxima"?

The concept of "Finding Maximum Number of Interference Maxima" involves studying the interference pattern formed by two or more waves, and determining the maximum number of bright and dark spots (maxima and minima) that can be observed. This is important in understanding the behavior of waves and the principles of interference.

2. How is the maximum number of interference maxima calculated?

The maximum number of interference maxima is calculated using the formula N = (d*sinθ)/λ, where N is the number of maxima, d is the distance between the sources, θ is the angle of observation, and λ is the wavelength of the waves. This formula applies to both double-slit and single-slit interference experiments.

3. What factors affect the maximum number of interference maxima?

The maximum number of interference maxima is affected by factors such as the distance between the sources, the angle of observation, and the wavelength of the waves. Additionally, the width and spacing of the slits in a double-slit experiment can also affect the number of maxima that are observed.

4. Why is it important to find the maximum number of interference maxima?

Finding the maximum number of interference maxima allows us to understand the behavior of waves and the principles of interference. It also helps in determining the properties of the sources, such as their distance and wavelength, and can be used to study the effects of changing these parameters on the interference pattern.

5. Can the maximum number of interference maxima be greater than the number of sources?

No, the maximum number of interference maxima cannot be greater than the number of sources. This is because each source can only produce one bright spot (maxima) at a given angle of observation. However, the number of maxima can be increased by using multiple sources or changing the parameters mentioned in question 3.

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