Single Slit Diffraction
- Author:
- Timo Budarz
![[url=https://upload.wikimedia.org/wikipedia/commons/4/42/Laser_Interference.JPG]"Circular Diffraction"[/url] by Wisky is in the [url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]](https://www.geogebra.org/resource/mfRu9TjN/Is6MvvSsoVk5EUiP/material-mfRu9TjN.png)
The Single Slit
When we looked at slits, we first began by considering two slits with Young's double slit experiment. While that seems like a better place to start discussions of wave interference than a single slit, where seemingly nothing is there to interfere, it turns out that the story is more complex than that.
In the case of the double slit the idea was that light was divided and forced to travel along two different paths to a common destination. If the two paths were unequal in length it led to a phase shift and interference of waves. It would seem that a single slit provides only one path for the light, but in fact it depends on how small the single slit is. By the way, when you hear people use words like "small" or "large" or "fast" in scientific circles, you should get in the habit of asking the question "Small (or large or fast) in comparison to what?" After all, the range of sizes and speeds of things in nature is immense.
So, what is it about the light beam that we should compare with the single slit's size? The answer is the wavelength. If the wavelength of light is very small as compared to the opening or slit, as would be true of a doorway, nothing striking happens. But when the slit size becomes comparable to the wavelength - or within maybe a few orders of magnitude - interesting things start happening. An example is seen above. The "slit" in this case is a small circular opening.
At that point we get parts of the beam of light interfering with other parts of the same beam. When this happens, it is called diffraction. The technical details of diffraction are what I'd like to discuss with you in this chapter.
A Rectangular Single Slit
When we considered the double slit in the last chapter, we supposed that there were only two paths along which light could travel and reach the screen. The reality is a bit more complex than that. After all, each slit has a width to it. Can't light pass through along slightly different paths when in one case it passes through the left edge of a single slit and in another case the right edge or the center? The answer is yes, and we must account for such path length variation to find the resulting intensity of light projected onto a screen after passing a single slit.
The difference in the math is just that instead of two phasors to add, now we have a near infinite number, each corresponding to one of the multitude of different paths possible through the single slit opening. Together, if added tip to tail as we often do vectors, they look like an arc segment. We once again will assume that the size of the opening is much smaller than the projection distance to the screen.