# If light propagates like waves, why can't I see around corners?

I know two different descriptions of how light propagates in space; (1) like particles traveling and reflecting in straight lines. And (2) like waves spreading and interfering in space. And that both these descriptions are true.

It seems to me that scenario (1) is how I perceive the world. I can see things from which the light is reflected into my eyes in a straight line, but I cannot see behind opaque objects, around corners etc.

But if scenario (2) is an equally or more correct description of how light behaves, spreading like waves, filling space, interfering etc.: how come the light hitting my eyes is not equally likely to have travelled from behind objects and around corners? I.e. if this is the true description, all I would expect see is a bright blur, with no way of telling from where the light hitting my eyes have originated.

Any enlightening (zing!) answers much appreciated.

Edit: maybe a clearer way to phrase my question is: can light change direction in empty space by interacting with itself?

• Why would you expect to be able to "see around corners"? Waves don't magically ignore obstacles, they diffract around them. Jan 29, 2022 at 12:17
• Light waves in free space do interfere, but do not interact. Once the light waves have passed through one another, you cannot measure a change due to the other wave. (The situation is different in non-linear media, but most media require very high light intensities to be notably non-linear). Jan 29, 2022 at 12:55
• Much of hearing around corners is reflection as well. You can experiment on this yourself. Stand just around a corner from the source of a quiet sound (a phone alarm turned down low would do the trick). Hold up a book or other flat surface near your ear at a 45 degree angle to both the source and your ear. You will note a significant increase in the loudness of the sound. Being flat it should be reflecting only, not focusing sound.
– g s
Jan 29, 2022 at 20:35
• @erikm, hi, your doubts are understandable, but light does not interact with itself, photons cannot couple to each other by QED rules. Diffraction is not light interacting with itself, but rather the possible pathways light can take interacting with each other, a beautiful feature of quantum field theory. See my answer below.
– Arc
Jan 31, 2022 at 13:42
• You can see around corners. Go watch a sunset.
– J...
Jan 31, 2022 at 19:44

The bending of waves around corners is known as “diffraction,” and its natural length scale is the wavelength of the diffracted wave. So if you want to block the sound from a speaker playing a middle C, with a wavelength in air of about a meter, then you need an obstacle which is many meters across. (A building is a good size.) But to block visible light, with sub-micron wavelength, a millimeter-scale object is a sufficiently enormous obstacle.

• Thank you for your answer. In my mind I see these light waves spreading and interacting with each other in space, ending up with a jumble of light waves bouncing off each other and filling space. Maybe this was the mistake in my thinking. Jan 29, 2022 at 12:39
• Sir by your answer you mean the bending is negligible when the length ratio appears to be greater than critical limit after that bending is very insignificant right ? By length ratio i mean ( length of object/wavelength ) Jan 29, 2022 at 14:24
• @Orion_Pax Yes. You can use the formulae for single-slit diffraction to see this, as simulated e.g. here
– rob
Jan 29, 2022 at 15:25
• @erikm light waves don’t bounce off of each other. They pass through each other. If certain conditions are met interference can happen. Jan 29, 2022 at 15:32
• @Orion_Pax No, the interference happens everywhere in space. If you put a detector (like a screen) at a location where interference is constructive, the detector will sense a lot of light; however if you put your detector where the interference is destructive, your detector will stay dark.
– rob
Feb 1, 2022 at 22:43

Light traveling in straight lines is an approximation that works very well most of the time. The most common case where it fails is when light travels through a pinhole or slit. Then it bends a little. This is called diffraction.

You can see an example of light bending when you hold your finger and thumb close together as you look between them at your computer monitor. When they are separated, light goes straight from the monitor to your eye. As they nearly touch, a dark bump seems to grow from your fingers to fill the gap. What is really happening is light that was headed toward your eye is bent away.

It happens all the time, but most of the time, the effect is too small to notice. It sometimes matters when people want to be very precise about where light goes.

One place this matters is in camera lenses. They are designed to bring all light that comes from one point of an object to one point on the sensor. If they don't come to a perfect point, the image is blurry.

Image from Pass My Exams

A lens is a giant pinhole. A big pinhole causes less bending than a small pinhole. But for a really good lens, diffraction is the biggest reason the focus isn't perfect.

Another place it can matter is in a laser beam. People may want a perfectly cylindrical laser beam that never spreads out. Most beams are pretty close, but they do spread over distance. The rays follow a nearly straight hyperbolic path. This kind of beam is called Gaussian. Here you see a sketch of the curved wave fronts. The rays show the direction the wave fronts travel. The rays are always perpendicular to the wave fronts. The spread is usually a fraction of a degree.

Image from the RP Photonics article on Gaussian Beams

Edit - Responding to comments

The blurring in the out-of-focus planes of a camera is not due to diffraction and is equally well described by the particle model of light.

Good point. The picture does not illustrate diffraction. Perhaps this is confusing. It illustrates that if rays from one point on an object do not hit the same point on the sensor, the image will be blurry. Film or sensor at the wrong distance is one way for this to happen. Lens aberrations are another way of getting rays that do not focus at a point.

Even if these are not present, diffraction will prevent a perfect focus.

A lens causes bending primarily by refraction, and again a particle model describes this exactly.

Refraction is typically derived from the wave model.

Lens design is usually based on ray tracing and refraction, and typically ignores diffraction. Ray tracing is calculated from the surface radii and indices of refraction of the lenses. The effect of diffraction is usually separately calculated from lens diameters. Diffraction is typically treated as a constraint. There is no point to designing a lens where the aberrations are smaller than the diffraction blur circle.

Diffraction can be calculated from the particle model using the uncertainty principle. This is more easily described with a slit. If a particle of light passes through a slit, the uncertainty of the x component of its position the width of the slit. This creates an uncertainty in the x component of its momentum. This means the particle cannot be precisely aimed that the point predicted from ray tracing. Diffraction through a circular aperture is similar, but the calculations is 2-D.

The changing size of a focused beam of light as it propagates is owing to the curved wavefronts, and this is mostly not diffraction. Diffraction is the fact that wavefronts of finite width cannot avoid some spreading even when they are collimated as much as possible.

There is more to a Gaussian beam than the curved wavefronts. The beam cross section has a Gaussian intensity profile. It is brightest in the center, fading away without reaching $$0$$. This is not exactly like passing through a pinhole, but the non-uniformity is the cause of the curved wavefronts. This is properly described as diffraction.

The picture illustrates what happens when a beam is focused with a lens. Given a good lens, diffraction determines the spot size, and therefore how much that spot is heated. But exactly the same thing determines the angle at which a collimated beam spreads. The picture would be the same except for a larger beam waist and shallower divergance angle. Either way, the rays are hyperbolic.

As an aside, there is an intensity profile with a Bessel function distribution that is perfectly collimated. This can approximately be achieved by passing a Gaussian beam through an axicon lens. This has applications in drilling operations.

• "What is really happening is light that was headed toward your eye is bent away." - Is this proven? I remember reading that it was an artifact of the human visual system reading brightness on a logarithmic scale Jan 29, 2022 at 23:28
• @user253751 - If you do it carefully, you can see a series of bright and dark stripes, where light constructively and destructively interferes. It isn't just dark. Jan 30, 2022 at 0:07
• There are several problems with this answer. 1. The blurring in the out-of-focus planes of a camera is not due to diffraction and is equally well described by the particle model of light. 2. A lens causes bending primarily by refraction, and again a particle model describes this exactly. 3. The changing size of a focused beam of light as it propagates is owing to the curved wavefronts, and this is mostly not diffraction. Diffraction is the fact that wavefronts of finite width cannot avoid some spreading even when they are collimated as much as possible. Feb 1, 2022 at 10:26
• Umm I think this answer is conflating refraction and diffraction which are two different phenomena Feb 1, 2022 at 14:48
• @AndrewSteane - I responded to your comments. Feb 2, 2022 at 8:19

TL;DR: Visible light - no, but radio waves - yes.

Electromagnetic waves do bend around the corners, if their wavelength is comparable to the size of the object (such as building, for example). Visible light with a typical wave length of a few hundred nanometers is obviously not a good candidate, but for radio waves, which may have wave lengths ranging from centimeters to many kilometers, this is a normal state of affairs. This is why we can use a radio transmitter inside a room. Exceptionally long wave lengths are even known to travel around the Earth (see Extremely low frequency and Longwave).

You do see light around corners. Turn on a light and walk around the corner, do you see light? Of course you do, because the light reflects off of surfaces. Chances are that you can't resolve the source of the light well, if at all, due to interference from the light reflecting off of the myriad of imperfections in surfaces of the wall you're looking at. But if you smooth those out and make a nice mirror, you'll notice that you can resolve quite a lot of detail from around the corner.

• True, but also not what the questioner asked about. Feb 21, 2022 at 4:49

If light propagates like waves, why can't I see around corners?

You can. Moreover, you can see the light diffract exactly as a sound wave. The difference is in scale.

Try the following experiment. Take a clean knife, put a small bright LED (e.g. a phone camera flashlight in torch mode) behind this knife. Turn off room light to watch the edge of the knife in the darkness (disturbed only by the LED). You'll see that the edge glows. As you slowly move the LED closer to the edge, you'll see the edge glow brighter until at some point you can see the LED itself.

What you've seen in this experiment is the light from the LED diffracting on the edge of the knife. It appears as if the edge itself emits this light. Similarly you would hear someone shout from behind a lone building: as if the sound is emitted from the edge of the building, not from behind it.

Other answers already mention that visible light has a very short wavelength, so we don't normally see around corners just like we hear sounds around corners. And that's a good thing, else we would see a pretty messy world around us!

But we can actually see around corners, and look inside objects, if we use femto-photography, a technique that can "create slow-motion videos of light in motion". I recommend everyone watch this most amazing TED talk: Imaging at a trillion frames per second. They managed to publish a Nature Communications, Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging, and Nature even produced a cool animation, How to see around corners. The technique is so amazing that some images present diffraction ripples in the wrong direction due to time warp.

Another, very, very cool - but yet mostly theoretical - way to see around objects is the phase-conjugation mirror (see also this and this articles on Scientific American), a technique that relies on the strange effects of non-linear optics to produce a conjugate wave that auto-compensates phase distortion and focus, but as far as I know, only very tiny and frequency-limited mirrors have been built so far.

Light does not interact with itself, from quantum electrodynamics we know that photons cannot couple to each other as they are massless bosons. What happens in a double-slit diffraction experiment is that the photon interacts with itself - or better, the possible pathways throught the slits interfere with each other - as proven by experiments in which the light source is so faint that just a single particle crosses the slits at a time, and still the diffraction pattern persists (see here and here).

• Thank you for your answer. So when I see images of the dark and light regions registered at the end of a double slit experiment: would it be correct to say that the photons hitting the light regions are not photons initially heading for the dark regions but deflected to the light regions by the waveforms crossing each other, but rather the waves cancelling each other out so the light heading for the dark regions are never registered by an observer at the far-end of the experiment? Feb 2, 2022 at 17:10
• @erikm, well, quite. There are lots of people saying that light waves behave just like water waves on a pool (like the Open University video provided above). In a simplified way they do, and so your understanding is not quite incorrect. But quantum mechanics is ultimately weird, perhaps the strangest theory of all. It's not the waves that cancel each other, it's the possible wavepaths that cancel each other. The interference happens even when the electromagnetic field is empty!
– Arc
Feb 2, 2022 at 17:51
• The links I provided show experiments where the beam is so weak that only a single particle crosses the double slit at a time. The particle - a photon, an electron, or even larger molecules - will fill all the possible pathways there are, because quantum mechanics state that, unless you measure which path it goes through, then the paths must be indistinguishable, and the particle acts as if it goes through both slits. Whenever you try to determine the slit through which the particle passes, you destroy the interference pattern!
– Arc
Feb 2, 2022 at 17:59
• And so we say that the "photon interacts with itself", but in fact the photon at the same time goes through one slit, and also goes through the other, filling all possible pathways. It's own wave has a phase passing through a slit, and a slightly different phase passing through the other slit, the resulting phase is the sum of these phases, which happens to cancel (subtract) each other at the dark fringes of the apparatus.
– Arc
Feb 2, 2022 at 18:08
• I really recommend you read Richard Feyman's QED: The Strange Theory of Light and Matter, in which he explains very well these phenomena of particles' phases (clocks) in many different experiments.
– Arc
Feb 2, 2022 at 18:11

All light will bend (diffract) around corners and obstacles.

The amount it bends, depends on its wavelength (or frequency). Longer wavelengths (=lower frequency) diffracts a lot more, shorter wavelengths (=higher frequency) diffracts a lot less.

So for example, X rays would diffract a lot less around an obstacle than visible light, but they will still diffract - in fact that's one method used to probe the structure of crystals and large molecules - put them in the path of some X-rays and look at the diffraction patterns it creates.

The problem you have is, that visible light is a pretty small band of wavelengths, that are all fairly short compared to everyday object dimensions. So you won't see big amounts of bending, like your question suggests, or a huge blur around every corner.

If you do the same with longer wavelengths, like radio waves, or WiFi, yes, they bend really well round corners. In fact they can bend round the curvature of the earth too.

That's because:

• visible light wavelengths: about 1/1000 of a millimeter (much smaller than everyday objects scale)
• radio wavelengths: about 0.5 m to 10 m (comparable to everyday objects and buildings)

You can see visible light diffract around objects quite easily, even so. There are many experiments and situations where it's plain to the eye. But mostly, their wavelength is small compared to everyday objects and so we usually won't notice the tiny amount of diffraction going on.

Light next to the corner will diffract around the corner. Light a little further from the corner will also diffract, although not quite as much. For a narrow slit, there's only a small amount of light diffracting, but as the slit gets larger and larger, there's more and more places to diffract from. You might think that would mean more light diffracting, but all this diffraction gives rise to destructive interference, so the wider the space next to the corner, the narrower the beam of diffracted light (this is related to the uncertainty principle: if you have a very narrow slit, you have low uncertainty where the light is, so you have high uncertainty what direction it goes).

Whether a slit is "narrow" or not is relative to the wavelength. If you're listening to someone in another room and the door is open, the doorway is "small" compared to the wavelength of sound waves, but it's huge compared to the wavelength of visible light, so the amount of light diffraction is insignificant. Wifi uses EM waves with wavelength much larger than that of visible light, so it can go around corners much better.

how come the light hitting my eyes is not equally likely to have travelled from behind objects and around corners

Generally speaking, the amplitude for direct paths is higher than that for bent paths. There are lots of different bent paths and they can have widely varying phases and so interfere destructively with each other. There's only one direct path and nearby paths will have phases that are close to the same, and so will have constructive interference.

Here's a way to think about it: Only the light really close to the edge gets bent around the edge. And "really close" means "roughly the wavelength of the light", which, as others have pointed out, is tiny. This means two things.

1. The amount of light that gets bent around the corner is just tiny, since it's only the light that was so close to the edge. So you can't really see it because it's just not enough light. (Or maybe you can a little bit in a dark room in the experiment with the knife, but in that case that's why you need the room to be dark.)

2. All the light that gets bent around the corner to you comes from that tiny strip, so you don't get an image of what's behind the wall, just a negligibly brighter edge of the wall. The key thing about seeing an image is that light is entering your eyeball from different directions, and the edge of the wall means that the only directional variation of the diffracted light is up and down. But again, you can't see it anyway because there's too little of it.

• can light change direction in empty space by interacting with itself?

No, just like water waves, light waves they pass though each other, add up on the crossing region ( =interference) and get out as they came in. but light does bend at corners. In a deeper sense, light does interact with itself according to Huygens optics (a wave is a sum of point like oscillators), and that's why it creates waves. And when light cannot interact with it's neighbouring light because there's a corner, then the wave bends (that effect is seen in water waves too).

• how come the light hitting my eyes is not equally likely to have travelled from behind objects and around corners?

Because the effect is small but historically demonstrated with visible light by arago/poisson