Diffraction: how to know the amount of slits from a diffraction pattern?

In summary, determining the number of slits in a diffraction grating can be done by counting the number of main maximums in the case of no middle minimums, or by counting the number of middle minimums in the case of N-2 middle minimums. However, for more complex cases, other methods such as plotting intensity graphs or comparing with a known sample may be necessary to determine the number of slits.
  • #1
Paavo T
1
0

Homework Statement



There are at least two different situations. If you have N-2 middle minimums, the amount of slits is N. Please, see the bottom left http://scienceworld.wolfram.com/physics/DiffractionGrating.html" [Broken]. The case with no such thing is the question about. How can I determine the amount of slits with the other cases? Please, see the other pictures in the link.

Homework Equations



[tex]a sin(\theta) = n \lambda[/tex]

where a is the width of the separtion of two side-by-side slits.

Intensityhttp://mathbin.net/47038" [Broken]
[tex]I = I_{0} \left[ \frac{sin \left( \pi b sin \left( \frac{\theta}{\lambda} \right) \right) }{\pi b sin \left( \frac{\theta}{\lambda}} \right) \right]^{2} \left[\frac{sin\left(N \pi a sin\left(\frac{\theta}{\lambda}\right)\right)}{sin \left( \pi a sin\left( \frac{\theta}{\lambda}}\right) \right) \right]^{2}[/tex]

The Attempt at a Solution



If you have 2 slits, then you have 5 main maximums. My proposal that the amount of maximums is 2N+1, where N is the amount of slits was rejected, by my teacher. You can see that it is not the case from the Wolfram link above. Then I tried to delve into the wave function but I am really lost with it. Cannot see how it helps in finding the the number of slits.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2

Thank you for your question. I would like to offer some insights into determining the number of slits in different scenarios.

Firstly, in the case where there are no middle minimums, the number of slits can be easily determined by counting the number of main maximums. This is because each main maximum corresponds to a slit, and there are no middle minimums to confuse the count. Therefore, in this case, the number of slits is equal to the number of main maximums.

Secondly, in the case where there are N-2 middle minimums, the number of slits is indeed N. This is because each main maximum corresponds to a slit, and the middle minimums are caused by the interference between the light waves passing through adjacent slits. Therefore, by counting the number of middle minimums, we can determine the number of slits.

In the case where there are more than 2 middle minimums, it becomes more complicated. In this case, the number of slits cannot be determined by simply counting the number of main maximums or middle minimums. This is because the interference patterns can become quite complex and may not follow a simple pattern.

To determine the number of slits in this case, one approach could be to use the intensity equation provided in the forum post. By measuring the intensity at different angles, we can plot a graph and look for patterns. The number of slits can then be determined by fitting the experimental data to the theoretical intensity equation and finding the value of N that best fits the data.

Another approach could be to use a diffraction grating with a known number of slits and compare the interference patterns with the unknown sample. By adjusting the angle and measuring the intensity, we can determine the number of slits in the unknown sample by comparing it to the known sample.

I hope this helps in your understanding of determining the number of slits in a diffraction grating. Please feel free to ask any further questions or clarifications.Scientist
 

1. How does diffraction occur?

Diffraction is a phenomenon that occurs when a wave, such as light or sound, encounters an obstacle or opening that is comparable in size to its wavelength. The wave bends or spreads around the obstacle, creating a pattern of interference.

2. What is a diffraction pattern?

A diffraction pattern is a series of bright and dark lines or spots that are observed when a wave passes through a narrow slit or is diffracted by a grating. The pattern is a result of the interference between the diffracted waves.

3. How do you determine the number of slits from a diffraction pattern?

The number of slits can be determined by counting the number of bright spots in a diffraction pattern. Each bright spot corresponds to a slit in the grating or a slit in the obstacle through which the wave passed.

4. What is the relationship between the number of slits and the spacing of the diffraction pattern?

The spacing between the bright spots in a diffraction pattern is directly related to the number of slits. As the number of slits increases, the spacing between the bright spots decreases, resulting in a narrower pattern.

5. How does the distance between the source and the diffraction grating affect the diffraction pattern?

The distance between the source and the diffraction grating does not affect the number of slits in a diffraction pattern. However, it does affect the spacing between the bright spots. As the distance increases, the spacing between the bright spots decreases, resulting in a narrower pattern.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
549
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
34
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
776
  • Introductory Physics Homework Help
Replies
28
Views
261
Back
Top