Single-slit diffraction intensity

In summary, single-slit diffraction is a phenomenon where light passing through a narrow slit creates a pattern of light and dark fringes. The intensity of the light is given by the equation I = I0*(sinc(B))^2, where B is determined by the wavenumber, slit width, and angle of observation. This equation does not take into account the distance from the slit, but this factor can be accounted for by measuring the beam width at different distances. The intensity decreases as the distance from the slit increases, and the diffraction pattern becomes wider. Overall, the formula for intensity in single-slit diffraction simplifies the relationship between angle and intensity in order to focus on the more interesting physics of the transverse distribution
  • #1
uzy5o
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I have looked through my optics textbook and many websites about single-slit diffraction. They all end up deriving an equation that looks something like this: I = I0*(sinc(B))2, where B = (1/2)*k*b*sin(theta), k = wavenumber, b = slit width. I don't know if there's something I'm not understanding, but I have a hard time believing that the intensity only depends on the angle. Shouldn't intensity decrease as distance from the slit increases?
Thanks.
 
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  • #2
You are correct that the intensity does also vary with distance - the diffraction pattern is wider at greater distances so must be fainter. In the formula you quoted, I0 is the on-axis intensity (i.e. I(θ=0)=I0), and this is where the distance dependence has been "hidden". Generally, you don't care about distance dependence in far-field diffraction because the transverse distribution is where the interesting physics is, so your text has hidden the boring bits in the interests of clarity. Well spotted.

If you wanted to insert a distance term, the formula above tells you the way the pattern spreads perpendicular to the slit and you could measure laser beam width at different distances to get the spread parallel to the slit. The product of the two is the overall dependence of I0 on distance from the slit.

Does that make sense?
 
  • #3
Here is an animation of single slit diffraction for different widths of slits:
http://youtu.be/uPQMI2q_vPQ
 

1. What is single-slit diffraction intensity?

Single-slit diffraction intensity refers to the pattern of light or sound waves that are diffracted through a single slit aperture. It is a phenomenon that occurs when waves pass through a narrow opening and spread out, creating a characteristic diffraction pattern.

2. How is single-slit diffraction intensity calculated?

Single-slit diffraction intensity can be calculated using the equation I = (A sinθ/θ)^2, where I is the intensity of the diffracted wave, A is the amplitude of the incident wave, and θ is the angle of diffraction. This equation is known as the diffraction formula.

3. What factors can affect single-slit diffraction intensity?

The intensity of single-slit diffraction can be affected by several factors, including the wavelength of the incident wave, the width of the slit, and the distance between the slit and the screen where the diffraction pattern is observed. The intensity also depends on the angle at which the diffraction pattern is observed.

4. What is the purpose of studying single-slit diffraction intensity?

Studying single-slit diffraction intensity can provide valuable insights into the properties of waves and how they behave when they encounter obstacles. It is also a useful tool for understanding the nature of light and sound and their interactions with matter. Additionally, understanding diffraction can have practical applications in fields such as optics, acoustics, and signal processing.

5. How is single-slit diffraction intensity related to the concept of interference?

Single-slit diffraction is closely related to the concept of interference, as both phenomena involve the interaction of waves. In single-slit diffraction, the waves passing through the slit interfere with each other, resulting in a characteristic diffraction pattern. Similarly, in interference, two or more waves overlap and interact, leading to a pattern of constructive and destructive interference.

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