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Multiple-slit Diffraction: Interference Pattern & Equations

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  • 0:05 Multiple Slits
  • 1:04 Uses of Diffraction Gratings
  • 1:56 Equation
  • 3:15 Calculation EXample
  • 4:18 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you will be able to describe the diffraction pattern produced by multiple slits, as well as how it differs from single-slits and double-slits. You will also be able to list examples of diffraction gratings in real life and solve problems to figure out the position of the maxima and minima produced when light in shined through a diffraction grating. A short quiz will follow.

Multiple Slits

If you understand double-slit diffraction, multiple slits is easy. In the real world, we don't tend to use Young's double-slit experiment any more. Why? Well, it produces a relatively faint pattern unless you get it just right. But multiple slits, on the other hand, produces a pattern that is super sharp and easy to see.

A diffraction grating is a grid of slits and gaps that is made by scratching crisscrossed lines into glass. This is what we usually use for our multiple slits, and it's super easy to manufacture.

The pattern we get from a diffraction grating is pretty similar to the pattern we get for double-slits. Take a look at this single-slit diffraction pattern (top pattern below):

Single-slit (top) and double-slit (bottom) diffraction patterns
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Now take a look at the double-slit diffraction pattern (bottom pattern above). Notice how the maxima from the single-slit pattern now has stripes down it. If we go to a diffraction grating (multiple slits), those stripes will have their own stripes. But they'll be so small that our eyes often can't even register them. However, one thing our eyes can register is how this makes the central maximum thinner and sharper.

Uses of Diffraction Gratings

Diffraction gratings, aside from producing clearer images than double-slits, are also eminently more useful. Whereas double-slits don't really have any obvious uses outside of research, diffraction gratings certainly do.

Diffraction gratings are used in medical imaging of biological samples, where a grating is chosen specifically to look at light of a particular wavelength. Certain diseased cells in a biopsy sample emit light of particular wavelengths, so they can be detected in this way. Diffraction gratings are also used in fiber optics to select for the optimal wavelength of light, improving the quality of the signal.

Even nature contains diffraction gratings. A stone called the Australian opal contains diffraction grating-like crystals that diffract light differently depending on its color, producing iridescent rainbow effects. And many butterflies have reflectors that act like gratings, reflecting different colors at different angles.

Equation

The equation for the position of the maxima for a diffraction grating is actually exactly the same as the equation for double-slits because it's derived in exactly the same way, using exactly the same geometry. So that's pretty convenient for us. Or at least for anyone who's already watched the lesson on double-slit diffraction.

Here are the double-slit equations, which also apply to a diffraction grating:

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One helps you figure out the positions of the maxima and the other the positions of the minima. In these equations, d is the average distance between each slit measured in meters; lambda is the wavelength of the light traveling through the slits, also measured in meters; and m is the 'order' of the minima or maxima. That's just a number that determines whether you're talking about the 1st minima, 2nd minima, 3rd minima, and so-on. But you start counting at zero. So for the first maxima, you plug in m = 0, for the second you plug in m = 1, and so-forth.

Last of all, the angle theta is the position of the minima or maxima on the screen, the angle above or below the center line. Straightforward is zero degrees, so if theta for the first maxima is, say, 27 degrees, that means that the first maxima appears at 27 degrees above the center of the diffraction grating (and also 27 degrees below). You can then use that information to figure out where it'll appear on the screen.

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