# Diffraction (Physics): Definition, Examples & Patterns

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Diffraction is the bending of waves around obstacles or corners. All waves do this, including light waves, sound waves and water waves. (Even subatomic particles like neutrons and electrons, which quantum mechanics says also behave like waves, experience diffraction.) It's typically seen when a wave passes through an aperture.

The amount of bending depends on the relative size of the wavelength to the size of the aperture; the closer the size of the aperture is relative to the wavelength, the more bending will occur.

When light waves are diffracted around an opening or obstacle, it can cause the light to interfere with itself. This creates a diffraction pattern.

## Sound Waves and Water Waves

While placing obstacles between a person and a source of sound can reduce the intensity of sound the person hears, the person can still hear it. This is because sound is a wave, and therefore diffracts, or bends, around corners and obstacles.

If Fred is in one room, and Dianne in another, when Dianne shouts something to Fred he will hear it as if she were shouting from the doorway, regardless of where she is in the other room. That's because the doorway acts as a secondary source of the sound waves. Likewise, if a member of the audience at an orchestra performance sits behind a pillar, they can still hear the orchestra just fine; the sound has a long enough wavelength to bend around the pillar (assuming it's of a reasonable size).

Ocean waves also diffract around features like jetties, or the corners of coves. Small surface waves will also bend around obstacles like boats, and turn into circular wave fronts when passing through a small opening.

## Huygens-Fresnel Principle

Every point of a wave front can be thought of as the source of a wave on its own, with the speed equal to the wave front's speed. You can think of the edge of a wave as a line of point sources of circular wavelets. These circular wavelets mutually interfere in the direction parallel to the wave front; a line tangent to every one of those circular wavelets (which, again, are all traveling at the same speed) is a new wave front, free from the interference of the other circular wavelets. Thinking of it this way, it makes it clear how and why waves bend around obstacles or openings.

Christiaan Huygens, a Dutch scientist, proposed this idea in the 1600s, but it didn't quite explain how waves bent around obstacles and through apertures. French scientist Augustin-Jean Fresnel later corrected his theory in the 1800s in a way that allowed for diffraction. This principle then became named the Huygens-Fresnel Principle. It works for all wave types, and it can even be used to explain reflection and refraction.

## Interference Patterns of Electromagnetic Waves

Just like with other waves, light waves can interfere with each other and can diffract, or bend, around a barrier or opening. A wave diffracts more when the width of the slit or opening is closer in size to the wavelength of the light. This diffraction causes an interference pattern – regions where the waves add together and regions where the waves cancel each other out. Interference patterns change with the wavelength of light, the size of the opening and the number of openings.

When a light wave encounters an opening, each wave front emerges on the other side of the opening as a circular wave front. If a wall is placed opposite to the opening, the diffraction pattern will be seen on the other side.

The diffraction pattern is a pattern of constructive and destructive interference. Because the light has to travel different distances to get to different points on the opposite wall, there will be phase differences, leading to spots of bright light and spots of no light.

## Single-Slit Diffraction Pattern

If you imagine a straight line from the center of the slit to the wall, where that line hits the wall should be a bright spot of constructive interference.

We can model the light from a light source passing through the slit as a line of multiple point sources via Huygens' principle, emitting wavelets. Two particular point sources, the one at the left edge of the slit and the other at the right edge, will have traveled the same distance to get to the center spot on the wall, and so will be in phase and constructively interfere, creating a central maximum. The next point in on the left and the next point in on the right will also constructively interfere in that spot, and so on, creating a bright maximum in the center.

The first spot where destructive interference will occur (also called the first minimum) can be determined as follows: Imagine the light coming from the point at the left end of the slit (point A) and a point coming from the middle (point B). If the path difference from each of those sources to the wall differs by λ/2, 3λ/2 and so on, then they will destructively interfere, forming dark bands.

If we take the next point in on the left and the next point to the right of the middle, the path length difference between these two source points and the first two would be approximately the same, so they would also destructively interfere.

This pattern repeats for all remaining pairs of points: The distance between the point and the wall will determine that wave's phase when it hits the wall. If the difference in wall distance for two point sources is a multiple of λ/2, those wavelets will be exactly out of phase when they hit the wall, leading to a spot of darkness.

The locations of the intensity minima can also be calculated using the equation

n\lambda = a\sin{\theta}

where ​n​ is a non-zero integer, ​λ​ is the wavelength of the light, ​a​ is the width of the aperture and ​θ​ is the angle between the center of the aperture and the intensity minimum.

## Double Slit and Diffraction Gratings

A slightly different diffraction pattern can also be obtained by passing light through two small slits separated by distance in a double-slit experiment. Here we see constructive interference (bright spots) on the wall anytime the path-length difference between light coming from the two slits is a multiple of the wavelength ​λ​.

The path difference between parallel waves from each slit is ​d​sin​θ​, where ​d​ is the distance between the slits. To arrive in-phase, and constructively interfere, this path difference must be a multiple of the wavelength ​λ​. The equation for the locations of the intensity maximas is therefore nλ = ​d​sin​θ​ , where ​n​ is any integer.

Note the differences between this equation and the corresponding one for single-slit diffraction: This equation is for maxima, rather than minima, and it uses the distance between the slits rather than the width of the slit. In addition, ​n​ can equal zero in this equation, which corresponds to the main maximum in the center of the diffraction pattern.

This experiment is often used to determine the wavelength of the incident light. If the distance between the central maximum and the adjacent maximum in the diffraction pattern is ​x​, and the distance between the slit surface and the wall is ​L​, the small angle approximation can be used:

\sin{\theta}=\frac{x}{L}

Substituting this in the previous equation, with n=1, gives:

\lambda = \frac{dx}{L}

A diffraction grating is something with a regular, repeating structure that can diffract light and create an interference pattern. One example is a card with multiple slits, all the same distance apart. The path difference between adjacent slits is the same as in the double-slit grating, so the equation for finding maxima remains the same, as does the equation for finding the wavelength of the incident light. The number of slits can change the diffraction pattern dramatically.

## Rayleigh Criterion

The Rayleigh criterion is generally accepted to be the limit of image resolution, or the limit of one's ability to distinguish two light sources as being separate. If the Rayleigh criterion is not met, two light sources will look like one.

The equation for the Rayleigh criterion is ​θ​ = 1.22 ​λ/D​ where ​θ​ is the minimum angle of separation between the two light sources (relative to the diffraction aperture), ​λ​ is the wavelength of the light and ​D​ is the width or diameter of the aperture. If the sources are separated by a smaller angle than this, they are not able to be resolved.

This is an issue for any imaging apparatus that uses an aperture, including telescopes and cameras. Notice that increasing ​D​ leads to a decrease in the minimum angle of separation, meaning light sources can be closer together and still be observable as two separate objects. This is why astronomers over the past few centuries have been building bigger and bigger telescopes to see more detailed images of the universe.

On the diffraction pattern, when the light sources are at the minimum angle of separation, the central intensity maximum from one light source is exactly at the first intensity minimum of the second. For smaller angles, the central maxima overlap.

## Diffraction in the Real World

CDs represent an example of a diffraction grating that is not made from apertures. The information on CDs is stored by a series of tiny, reflective pits in the CD surface. The diffraction pattern can be seen by using a CD to reflect light onto a white wall.

X-ray diffraction, or x-ray crystallography, is an imaging process. Crystals have a very regular, periodic structure that has units about the same length as the wavelength of x-rays. In x-ray crystallography, x-rays are emitted at a crystallized sample, and the resultant diffraction pattern is studied. The regular structure of the crystal allows the diffraction pattern to be interpreted, giving insights about the crystal's geometry.

X-ray crystallography has been used to great success determining the molecular structures of biological compounds. The biological compounds are put into a supersaturated solution, which is then crystallized into a structure that contains a great number of molecules of the compound set in a symmetric, regular pattern. Most famously, x-ray crystallography was used by Rosalind Franklin in the 1950s to discover the double-helix structure of DNA.

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