Diffraction with a large array of slits

In summary, in order to observe diffraction with a system of slits, the slit width must be smaller than the distance between slits, and the distance between slits must be larger than the wavelength of the incident light. The smallest possible value for the distance between slits is the wavelength of the light, and for the slit width, it is half the distance between slits.
  • #1
Flucky
95
1
Hi all, exams soon and I'm stressing out over this small question. If anyone could guide me through, explaining why you're doing what you're doing that'd be beyond great. I posted this in the introductory thread but with no replies thought I should move it here (unsure of how to delete the other one).

Homework Statement


Light of wavelength λ is incident normally on a screen with a large array of slits having
equal widths b, and periodically displaced by a distance a.

(i) Find the maximum diffraction order which can be observed using this system of slits.

(ii) Find the minimum period a for which diffraction can be observed for light with
wavelength λ = 10µm.


Homework Equations


AFAIK the only equation relevant is asinθ = mλ

One that has cropped up is sinθ[itex]\pm1[/itex] = [itex]\pm\frac{λ}{b}[/itex] , although there is no explanation next to this one so I'm not sure what it means.


The Attempt at a Solution


Initial thoughts are to set θ = 90° as it's asking for a maximum. Past this I don't know where to go :frown:
 
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  • #2
For part (i): you are right, because the maximum angle is 90 degrees.

Part (ii): What happens when width of slit approaches the distance between slits?
 
  • #3
From the second equation it looks like as the slit width increases the angle between maxima will decrease. Am I able to set the two equations equal to each other? If so as slit width approaches slit separation the diffraction order will go to 1.

Thanks for the reply btw.
 
  • #4
I don't think the second equation makes any sense. All you need is the first one.
 
  • #5
Flucky said:
From the second equation it looks like as the slit width increases the angle between maxima will decrease. Am I able to set the two equations equal to each other? If so as slit width approaches slit separation the diffraction order will go to 1.

Thanks for the reply btw.

When the separation of slits approaches the slit width, the two slits become one - meaning it is a single slit diffraction. We can't let that happen, ##a## has to be bigger than the width of a slit, ##b##.

Conversely, when the width of the slit approaches the separation, the two slits become one - meaning it is a single slit diffraction. We can't let that happen, so ##b## has to be smaller than slit separation of slits, ##a##.

Thus, to answer your question - what is the smallest possible value of ##a##, in order for multiple slit diffraction to occur?
 
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Related to Diffraction with a large array of slits

1. What is diffraction with a large array of slits?

Diffraction with a large array of slits is a phenomenon that occurs when light passes through a series of closely-spaced parallel slits. This causes the light to diffract, or spread out, creating a pattern of bright and dark fringes.

2. How does the number of slits affect the diffraction pattern?

The number of slits in the array directly affects the spacing and intensity of the fringes in the diffraction pattern. As the number of slits increases, the fringes become closer together and the central bright fringe becomes brighter.

3. What is the relationship between slit width and diffraction pattern?

The slit width also plays a role in the diffraction pattern. A narrower slit will result in a wider diffraction pattern, while a wider slit will result in a narrower pattern. This is because the narrower the slit, the more diffraction occurs.

4. Can diffraction with a large array of slits be observed with other types of waves besides light?

Yes, diffraction can occur with any type of wave, including sound waves and water waves. In fact, the concept of diffraction was first observed with water waves in the early 19th century.

5. How is the diffraction pattern affected by the distance between the slits in the array?

The distance between the slits, also known as the slit spacing, affects the spacing of the fringes in the diffraction pattern. As the slit spacing increases, the fringes become closer together, resulting in a wider diffraction pattern. Similarly, as the slit spacing decreases, the fringes become further apart, resulting in a narrower pattern.

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