# Why exactly does diffraction occur?

Why do waves that were traveling in a straight direction change direction when passing through an opening?

I thought that the waves (red arrow) when colliding with the wall bounce in the opposite direction (green arrow).

And the waves that pass through the aperture follow its path normally as shown in the image on the right.

The waves that go in a straight direction should follow traveling straight line like a car that goes under a bridge the car is straight on the road. But this is not so.

Why does the direction of the waves change?

How is the direction of the waves calculated?

• I think OP wants to know why the diffraction occurs and why the waves don't just continue like they pointed out in the diagram. Maybe an answer with wavelets and Huygens' Principle. I don't understand the principle well enough to write a good answer though. – Tausif Hossain Dec 3 '18 at 17:08
• @TausifHossain Yeah that is why I posted a comment :) It seems like the OP doesn't know what it is called, or else they would have said "How does diffraction work" or something like that. Just thought the reference would be helpful just in case. – Aaron Stevens Dec 3 '18 at 17:11
• Possible duplicate of How does the Huygens–Fresnel principle apply to diffraction? – Aaron Stevens Dec 3 '18 at 17:13
• I see, you're right. Though I found it hard to find a good intuitive explanation of the Huygens Principle online. – Tausif Hossain Dec 3 '18 at 17:16
• @TausifHossain I used your comment for an answer – HolgerFiedler Dec 3 '18 at 20:12

For the full math, you can look up 'diffraction' and 'Huygens Principle' but here I will just post a quick observation that is enough to get a good physical intuition.

Suppose we are considering water waves, and imagine yourself sitting behind the barrier in the 'harbour' (at the lower part of your diagram), watching the waves approaching from 'out at sea' (i.e. the top of your diagram). As the waves reach the 'harbour mouth' (i.e. the small opening in your diagram) the water there is caused to go up and down. So there is this water bobbing up and down in the small opening. Now the surface of the water nearby is going to bob up and down too, isn't it? And the ripples will spread out from there. It doesn't really matter in what direction you consider: the waves will spread out into the 'harbour' because the water at the harbour mouth is moving.

From this way of thinking, you begin to wonder why the waves out at sea are so straight! Ultimately it is because in that case you have oscillating water all along a long line, and so the water all along that long line is caused to move in synchrony.

As I say, this is not a full mathematical answer, just an attempt to give you some intuition about the physics.

• Thanks, the point about why waves generally are straight was good. Every point pushes out a circle, but you have a line of points all doing that at the same time. – JollyJoker Dec 4 '18 at 11:33
• Huygens was the man. – mathreadler Dec 4 '18 at 20:49

The first thing to realize is that waves only appear to travel. But when you look at a fish in the water, it becomes clear that the water only sloshes back and forth. Waves occur because the water movements aren't all in sync, nor could they be - how would all the water molecules know to reverse at the same time? So when you have water molecules traveling on opposite directions >>^<< there's nowhere for them to go but up. That produces the wave crest. And when a bit of water locally reverses direction, the crest moves >^<<<.

Now we know that waves are really a local effect. That means the wave inside the slit has no memory where it came from. And that means it also doesn't remember in which direction it would need to travel. All directions are possible.

Now if waves do not have memory, then how do they "know" how to travel in a straight line near the beach? Well, that's not really what happens. Wave crests travel orthogonally to the crest lines. In thin slits, where there's no longer a crest line, this no longer makes sense, and that's why you get the diffraction.

You can see how this makes sense when you look at broader slits. In the middle, there's a well-defined crest line, and you still get the straight pattern. But at both edges, you get the diffraction effects. This frays the edges of the crest lines, progressively making them sorter, until they disappear entirely. After that, you get a complex pattern of isolated peaks.

• The waves travel, but the water doesn't. – Dubu Dec 4 '18 at 13:06

"Why are waves straight?" is the first question.

Let's start with a model of waves where particles don't have much kinetic energy. They just have potential energy.

Each location, if it has less energy than an adjacent spot, steals 1 unit of energy from it.

00000
00000
00900
00000
00000


next tick:

00000
01110
01110
01110
00000


next tick:

0000000
0.111.0
0100010
0101010
0100010
0.111.0
0000000

0.....0
.00000.
.0...0.
.0.0.0.
.0...0.
.00000.
0.....0


where . is a fractional unit of energy.

and we see a really simple model of a "circlular wave" coming from a point.

Now look what happens when we have a wave-front (I'll assume the lines go off "forever" on the left and right, but there is a wall at the top).

0000000000000
9999999999999
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000

3333333333333
3333333333333
3333333333333
0000000000000
0000000000000
0000000000000
0000000000000
0000000000000

3333333333333
3333333333333
0000000000000
3333333333333
0000000000000
0000000000000
0000000000000
0000000000000

3333333333333
0000000000000
5555555555555
0000000000000
1111111111111
0000000000000
0000000000000
0000000000000

0000000000000
4444444444444
0000000000000
4444444444444
0000000000000
1111111111111
0000000000000
0000000000000

3333333333333
0000000000000
2222222222222
0000000000000
3333333333333
0000000000000
1111111111111
0000000000000


hey look, waves. (I did some rounding) with some initial "sloshing" as it bounces off the "wall' at the top.

So suppose you have a bunch of waves causing a hole in a wall to go up and down:

######9######
0000000000000
0000000000000
0000000000000
0000000000000

######0######
0000033300000
0000000000000
0000000000000
0000000000000

######9######
0000100010000
0000111110000
0000000000000
0000000000000

######0######
0001033301000
0001000001000
0001111111000
0000000000000


because there is no intrinsic direction to the wave, just up and down, it induces a circular wave at the point of departure.

Being more mathematical, a linear wave is just a bunch of circular waves. Take 5 copies of this:

00000
00000
00900
00000
00000


offset by one horizontally and you get:

000000000
000000000
009999900
000000000
000000000

000000000
013333310
030000030
013333310
000000000

012333210
100000001
102000201
100000001
012333210


because the "hump" of 9s adjacent to each 9 slows inflow.

A real physical wave is more complex than this simple discrete time cell model. But the basic idea; that "humps" push water away and "gulfs" pull it in, and that there is enough momentum to cause overshoot -- result in a similar effect. Linear waves are the result of linear adjacent "humps" and "gulfs". When you reach a barrier with a hole, the linear "adjacent humps" go away, and the wave becomes more cicular as it falls both "forward" and "sideways", instead of being supported on the sides by other "humps" of water.

Your aperture only allows a very short segment of the incoming plane wave to pass through. As the aperture becomes smaller, the segment looks more and more like a point source. A point source emits spherical waves like you show in your lower right figure. (this is almost intuitively obvious because of symmetry--what other shape of wave would a point emit?).

This is usually explained more formally via diffraction:

https://isaacphysics.org/concepts/cp_diffraction

"Diffraction is the spreading out of waves as they pass through an aperture or around objects. ... In an aperture with width smaller than the wavelength, the wave transmitted through the aperture spreads all the way round and behaves like a point source of waves (they spread out below)"

A quick answer would be that they are not changing direction. Each point in the plane is the source of a single wave. Single waves expand in circles, but as you put many single waves together you sum them and get a plane wave. The aperture if small enough simply blocks the other waves allowing only one to pass and thus it re-takes circular shape.

This is a simplification of diffraction and huygens' principle but it might help you get an idea.

• @Will, What do you mean about the pinhole camera? In every explanation I've ever heard about how a typical pinhole camera forms an image, the discussion is limited to geometric optics. Everybody who's ever made a pinhole camera knows that a smaller pinhole lets less light through, but it also gives you a sharper image. But that's only true up to a point. If you go beyond what's typical, and you make a really tiny pinhole that only lets a really tiny amount of light through, you hit a limit to how sharp the image can be. Is that what you're talking about? – Solomon Slow Dec 4 '18 at 16:41
• @SolomonSlow Yes below a certain pinhole size the diffraction effects become significant and distort the captured image. – bradgonesurfing Dec 5 '18 at 8:18

Tausif commented:

I think OP wants to know why the diffraction occurs and why the waves don't just continue like they pointed out in the diagram.

In any elastic medium, a pressure effect not only leads to material displacement in this direction, but also to lateral displacement. (In an inelastic medium the material gets simply punched out.) So the awaited longitudinal wave is accompanied always by a transversal wave.

This transversal wave spread out in isotropic media as a spherical wave. The obstacle with the slit limiting the isotropy and instead of a spherical wave on get only have of a spherecal wave.

• "So the awaited longitudinal wave is accompanied always by a transversal wave." I think you have mis-understood these terms: I presume you mean to re-state Huygens' principle, but this is not a correct statement. In particular pressure waves in a fluid diffract while remaining purely longitudinal. You can also see this in a geophysical context: the P-and S- waves travel and different speeds and don't transform into one another when diffracting resulting is well separated arrival times. – dmckee --- ex-moderator kitten Dec 6 '18 at 15:26
• @dmckee The pressure of a falling stone does not only go into the depth, but is distributed laterally in every elastic medium. Even punching out a hole in a thick sheet often leads to a thickening of the material at the edge. – HolgerFiedler Dec 6 '18 at 18:50
• Again: you misunderstand the terms you are using. The fact that pressure is omnidirectional does not make the wave transverse. In any small element the the Poynting vector for a sound wave is in the direction of displacement meaning that the wave is longitudinal. Certainly the Poynting vector is non-constant in space, but that is not what those words characterize. Nor does thinking about plastic deformation change the situation as it tells you about the dissipative behavior rather than the wave-propagation. – dmckee --- ex-moderator kitten Dec 6 '18 at 19:26
• @dmckee If you position an underwater buoy next to the impact point, the buoy will also periodically move away from and back to the impact point. This corresponds to a transverse wave. I could not see why I could not name it this way. – HolgerFiedler Dec 6 '18 at 19:36
• You seem to be imagining that there is some global "direction of the wave everywhere" to which you compare. This is incorrect. You always compare the local displacement to the local direction of the wave (as identified by the local Poynting vector). – dmckee --- ex-moderator kitten Dec 6 '18 at 19:58

Your initial picture is incomplete in describing a more in-depth version of the waves. The waves are actually not a bunch of parallel beams traveling in straight lines down the page as you show. What there is is a superposition of point sources of energy and a single point source of energy will produce a circular wave. Your wavefront is made up of a nearly infinite number of these point sources and it is the superposition of the waves from these point sources that combine to create a uniform wavefront. So, when the wave comes upon an aperture it then acts like the point source that it is and the result is just like a point source of energy would act, i.e. a circular wave.

• I'd just like to point out that your answer is good but it's best not to call the diagram wrong but rather incomplete as the diagram is correct from a certain simplified perspective. – Tausif Hossain Dec 5 '18 at 17:40

In the aperture the wave us no longer plane : it us the product of a rect function, which is unity in the aperture and zero outside it, and a plane wave. You can inspect which wave vectors are present by Fourier transforming this product. The result is a convolution of the transform of the rect, the so called sinc function, and the plane wave. The message is that the result is a sum of plane waves of varying direction. For a point aperture all plane waves are present with equal amplitude and phase, that is, a spherical wave. Alas this requires some elementary math to understand.