Diffraction Patterns: Does Distance Affect Diffraction?

In summary, there are no two sources in single slit diffraction, but the opening can be divided into multiple sources that interfere constructively at certain angles. The resulting intensity pattern is given by ##{\sin^2 x \over x^2}\ ##, with the important function ##{\rm sinc}\ x## being used to describe the intensity at a given point on the screen.
  • #1
haha1234
109
0

Homework Statement



Is it necessary that a single slit diffraction occur with the two source having the distance of [itex]\frac{a}{2}[/itex]?Are there any diffractions occur when the point source having the distance of [itex]\frac{a}{3}[/itex],[itex]\frac{a}{4}[/itex] and so on?
And I would like to know whether are there only destructive interference occur?

Homework Equations





The Attempt at a Solution

 

Attachments

  • 1393493114853[1].jpg
    1393493114853[1].jpg
    19.3 KB · Views: 377
Physics news on Phys.org
  • #2
Hi Ha,
There are no two sources in the drawing; there is only the one slit opening that is imagined to be subdivided into two "sources" that are deemed a/2 apart. As you correctly suspect, it is equally well possible to subdivide into 3, 4, 5, etc. sources (with successively smaller extension / width) that interfere constructively at greater and greater angles. In the resulting intensity pattern the angles in between have destructive interference.

The intensity at a given point on the screen is in fact an integral over the slit opening. See e.g. Fraunhofer diffraction or Single slit diffraction.

The resulting intensity pattern is ##{\sin^2 x \over x^2}\ ##; ##\ \ \ {\sin x \over x}## has been found to be important enough to get its own name: ##{\rm sinc}\ x##
 
  • Like
Likes 1 person

Related to Diffraction Patterns: Does Distance Affect Diffraction?

1. How does distance affect the diffraction pattern?

As the distance between the light source and the diffracting object increases, the diffraction pattern becomes wider and more spread out. This is because the light waves have more space to interact with the edges of the object, causing the interference pattern to become more complex.

2. Can diffraction patterns be observed at any distance?

Yes, diffraction patterns can be observed at any distance. However, the intensity and clarity of the pattern may vary depending on the distance between the light source and the diffracting object.

3. How does the size of the diffracting object affect the diffraction pattern?

The size of the diffracting object affects the size and complexity of the diffraction pattern. Larger objects will produce wider and more intricate patterns, while smaller objects will produce narrower and simpler patterns.

4. Is there a limit to how far the diffraction pattern can be observed?

There is no specific limit to how far the diffraction pattern can be observed, but as the distance increases, the pattern becomes increasingly faint and difficult to detect. This is due to the spreading out and weakening of the light waves as they travel a greater distance.

5. How does the wavelength of the light affect the diffraction pattern at different distances?

The wavelength of the light can also have an impact on the diffraction pattern at different distances. Longer wavelengths tend to produce wider and more spread out patterns, while shorter wavelengths produce narrower and more concentrated patterns.

Similar threads

  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
34
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
6K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
761
  • Introductory Physics Homework Help
Replies
8
Views
2K
Back
Top