# Can an electromagnetic wave travel less than the speed of light and yet perceived by the eye as a light?

When an electromagnetic field passes through different mediums, it is known that it will refract. And during refraction - since its frequency is kept constant - the only parameter that changes is its wavelength which intern will change its speed. With this keeping in mind lets look at this prism that disperses light.

When the white light comes to the prism it has a speed of $$c$$. But after it is refracted by the prism, hadn't its speed change? And if that happens, wouldn't it contradict with the fact that all electromagnetic waves have the same speed?

The second question is, could two electromagnetic waves of different speed and wavelength have similar color?

The following is my reason for this question. It is thought that light is composed of the other seven colors (by the way what does composed of mean in this sense?) Right? During the dispersion by a prism, each component will refract by different angles, having new wave lengths and new speeds, which means they had a different wave length and speed before refraction. Which intern means the red we see after refraction isn't the red that made up the white light unless electromagnetic waves of different wavelength and speed can be perceived as similar by the eye?

• Consider that when you see light it is travelling through the material of your eye, which is not vacuum. – The Photon Apr 26 at 15:00

In vauum, all the electromagnetic waves have the same speed $$c$$. When the wave passes through a material, such as the glass of a prism, the speed is decreased, but only during the passage, inside the material. When the wave exits from the prism, its speed comes back to the speed $$c$$ (or slightly less, if the wave is propagating in air instead of vacuum).

When the wave enters into the prism, it keeps its frequency (how many periods per second). But, since it is slowed down, its wave length becomes shorter: in a period, it travels a shorter path. But, also in this case, when the wave exits, it takes back its wave length, the same it had when it entered.

Coming to the second question. It is useful to think that the color of the light is associated to the frequency, which never changes in refraction, reflection and diffraction processes. Frequency is important because the "sensors" in our eye are sensitive to the photon energy, which depends on the frequency. On the other hand, the speed of light in our eye depends on the material of the eye itself, so there is also a well defined and fixed relation between wave length and frequency!

So said, a beam with a given color, after passing through a glass prism or a lens, will still have the same color. Of course, its wave length will change along its path, but our eye will never know it.

Finally, what does it mean that a beam is the superposition of various wave lengths? This would deserve a separate question, but this can help to understand the principles:

https://demonstrations.wolfram.com/SuperpositionOfWaves/

• "When the wave exits from the prism, its speed comes back to the speed c (or slightly less, if the wave is propagating in air instead of vacuum)." does this mean it refracts again. " Of course, its wave length will change along its path, but our eye will never know it." An what does this mean – Hilea Apr 26 at 13:36
• First question. Yes, the light is refracted one time when it enters in the prism and a second time when it goes out. But it is better to say that it always has the same speed in the same material. Light is not something that you can "accelerate"... its speed depends on the material only, not on what happened to it before your observation (at variance with, e.g., a bullet). – Doriano Brogioli Apr 26 at 14:34
• Second question. What is fixed along the path is the frequency. The wave length changes along the path, depending on the materials in which it is travelling. However, when it reaches the eye, its is simply a wave with a given frequency. Its speed (in the eye) is determined only by the composition in the eye, and also its wave length. So, inside the eye, the light does not have any information on the path it made. Of course, we are only speaking of wave length and color: refraction takes place. – Doriano Brogioli Apr 26 at 14:38

The speed of light depends on the properties of the medium it trravels through. Only in the vacuum it's equal to $$c$$, in other mediums like air, water or glass it's lower than $$c$$ and it's speed depends on its frequency/color. Different colors of light have different speeds inside the prism, and that causes refraction, but outside the prism their speed returns to the original.

It's simplification that white light consist of only seven colors. White light consists of light of many different frequencies, and each frequency can technically be called a different color. However, human eye cannot distinguish light of similar frequencies well. It's customary to divide the rainbow into seven colors but the boundaries between them are blurry; there's no sharp boundaries between one and the next, but they change one into another fluently.

Moreover, the way that human brain perceives colors causes that some mixtures of colors may look like a different color. For example mixture of green and red light can look like yellow light (effect used in LCD screens), and mixture of red and blue (i.e. purple) looks very similar to violet (which corresponds to a different frequency than blue or red).

It is also worth noting that the eye doesn't really care about the wavelength of the light, but about the energy of a single photon of this light, which is related to the frequency. And the frequency of light usually doesn't change when it pasess from one medium to another (some excepions include for example non-linear crystals). Therefore you can transmit monochromatic light through a complicated optical system, and it's color won't change. Color of not-monochromatic light may change, as some of the frequencies are absorbed or refracted stronger than others, which means they are no longer present in the output (that's how most of the things in the world get their colors).

• "but outside the prism their speed returns to the original." How is that possible? – Hilea Apr 26 at 13:29
• As I said, the speed of light depends only on the medium in which it travels. If it started in the air, and ends up in the air, then the speed at the beginning will be the same as at the end. – Adam Latosiński Apr 26 at 15:07

The question has a false assumption, citing as "fact that all electromagnetic waves have the same speed." Electromagnetic waves do not all have the same speed; it depends on their frequency and the medium in which they are traveling. This is a common challenge when designing any medium (like a transmission cable) for electromagnetic signals.

The short answer is yes, and the light we see on a "normal" basis qualifies.

• "The question has a false assumption" off course the speed will change when not talking about vacuum but isn't that how we have the electromagnetic spectrum, electromagnetic waves of similar speed but different frequencies and wavelengths. – Hilea Apr 26 at 13:41
• @Hilea Because we don't live in a vacuum, electromagnetic waves that we perceive are all coming in at less than the "speed of light" [in a vacuum] c, yet we still perceive them as light. The electromagnetic spectrum is a spectrum of different frequencies. These frequencies can all travel at the same speed in a vacuum, but materials slow them down and can affect different frequencies differently. – WBT Apr 26 at 13:44
• ok Thanks, And is there a way we could tell by how much its speed will change passing through a medium by just seeing its frequency(with out an experiment) – Hilea Apr 26 at 13:53

I suggest you have a look at exotic beams such as Airy beams or something like this

https://phys.org/news/2016-03-optical-slower.html

The point is that plane-waves in vacuum move at the speed of light. But Maxwell's equations, in vacuum, admit many weird solutions and those may not move at the speed of light. In fact, you will even struggle to define at what speed do they move.

Consider also this thought experiment. Take two laser beams, place one at (0,1) in xy plane, another one at (0,-1) and get them to cross at (1,0). Now at that point you will have higher light intensity then everywhere else, so you could call it light pulse, but it does not move. You could push this further, add two more lasers at (0,1.1) and (0,-1.1), again cross them at (1,0). Now that point will be 16 times brighter than everywhere else (coherent light). Carry on going adding more lasers. Eventually you will end up with super-bright spot of light and virtually zero light intensity else-where. But it still does not move (the spot that is). You could now start turning the lasers, and the spot would start moving, but you could get it to move at pretty much any speed you want.

There is no funny business with violating SR here. The point is that speed of propagation in electromagnetism may not be defineable unless you have a very simple exictations such as plane wave.

Not only can it be so perceived despite such slower pace of travel, it always is! Right now, all the light you are seeing is light that is traveling slower than $$c$$.

Here's the thing: Your eye has, within the eyeball and filling up the entire space between the lens and retina (the "detector"), a gel-like material called the vitreous humour:

(Adapted from: https://en.wikipedia.org/wiki/Vitreous_body#/media/File:Schematic_diagram_of_the_human_eye_en.svg. Courtesy Rhcastilhos and Jmarchm. cc by-sa 3.0.)

Mostly this is water, but also contains a protein component which makes it thicker and more like a gel. In any case, the refractive index of this medium is strictly larger than 1: according to this source [1], it is about 1.337. That means that light is traveling about 75% as fast as in vacuum (roughly 225 Mm/s instead of 300 Mm/s). Moreover, in all other components of the eye, similar laws apply: the lens, through which light must pass before it gets to the internal fluid, also has a refractive index greater than 1, as it must in order to function as a lens.

Moreover, photons of light are not absorbed at the retinal surface, but instead pass through the surface to reach sensitive molecules in the cell bodies underneath. All this intermediate material also will have positive refractive index.

Hence at virtually no point - from entry to the eyeball to final absorption by a molecule of visual pigment (the stuff that the retinal cells use to register light, effectively a form of photon counter), is the light traveling with the vacuum speed of light ($$c$$). And yet, this light registers all the time, or you would not be able to see!

Regarding your other questions about the physics of speed changes, the answer is that the speed of an electromagnetic wave is set by the medium in which it is traveling right now. It is not set by the past history of the waves, which is what it seems you're referencing with the prism: that when it exits, it will still be going slow, because it was "slowed" therein. Instead, light always travels at $$c$$ in vacuum, and at some speed less than $$c$$ in the prism. When it is approaching the prism, since it is in vacuum (well, on Earth, air, but we'll just use this to make it easy and moreover the same principles still apply), then it will be traveling at speed $$c$$, since that medium is setting the speed to that value. When the waves begin to traverse the prism, that medium sets them to have a speed lower than $$c$$. Finally, when they reach vacuum again, since they are in vacuum now, it resets their speed to $$c$$ again. Then, of course, when they enter your eye, they drop below $$c$$ once more for the final detection.

Yes it can. If you study optics you will learn that a ray of light can change direction while it passes from a medium to another.What also happens is that the speed of this ray is changed.c is refered to speed of light in vacuum.