# Why does a prism spread its "output" out over space, not time?

I'm having fun learning about the physics of optical networks at a new job. It's fun connecting elementary physics learned so many years ago with how they're leveraged today in practical application.

My question is about the concept of chromatic dispersion. I've read chromatic dispersion defined thus:

[T]he differential delay - or time spreading - in picoseconds of a wavelength generated by a laser that has a spectral width of 1 nanomater per kilometer of optical fiber.

In other words, different wavelengths of light at different speeds down optical fiber. Elsewhere:

Chromatic dispersion is commonplace, as it is actually what causes rainbows - sunlight is dispersed by droplets of water in the air.
https://www.m2optics.com/blog/bid/61431/chromatic-dispersion-in-optical-fibers

I'm having trouble reconciling the description of chromatic dispersion as a displacement in time of wavelengths traveling through a medium versus the observed reality of the different colors/wavelengths of rainbows projected through a prism as being displaced in space. I.e. the time-related description of chromatic dispersion makes me think that the output through a prism should be a time-shifted cycle of colors from blue to red.

Can someone please help reconcile the time-related definition of chromatic dispersion with observed reality of prisms' output being dispersed in space, not time?

• Commented Sep 4, 2020 at 2:35

A "time dispersed" signal is what the radar (sonar) engineer calls "chirp" or linear frequency modulation. It can be created by externally varying the frequency of an oscillator or by a medium whose propagation delay is a linear function of frequency. The former technique is employed by bats the latter is what a prism does. To see the effects of time dispersion you need time markers when you start and stop, say a short pulse, and a reconstruction mechanism of the dispersed pulse that results in a another pulse where you observe the ensuing delay. The bat's ear does the reconstruction for the reflected sonar chirp. For a dispersing prism a complementary "prism" that would reconstruct the original pulse you would need another optical gadget that would delay the various frequencies in the opposite way to that of the first dispersing prism so that the combination of the two would result in only a simple overall composite delay of the pulse; unfortunately there is no such gadget can be made of a simple glass having chromatic dispersion.

There is a famous technique to use pulse stretching-pulse compression for high power optical (laser) output generation, see https://en.wikipedia.org/wiki/Chirped_pulse_amplification

Huh. I never thought about that.

You just aren't fast enough to perceive the transitory time between when the first colour starts to leave the prism and the last colour hits the target. It is a beam after all and is identical everywhere in the middle so you can't distinguish any midbeam point from any other so so once the beam is bridging both ends it all looks the same. But you can observe the ends being different as long as they exist.

What you're asking for is a way for it to make sense. So you probably don't just want the equations that describe what happens.

Prisms work because they change the direction of light, and they change the direction more for blue light than red light.

Why do they change the direction? Maybe because they change the speed.

Imagine you're driving a car and you hit a patch of loose sand just on one side. It will make the car veer, won't it? The tires on one side are pulling you ahead more than the tires on the other side.

If you were just coasting along slowly and you hit a patch of sticky tar on one side, wouldn't that make you veer too?

So if light is like cars or bullets, particles that have a finite width, then going into materials that change the speed would change its angle if it doesn't go straight in.

And if light is like a wave, ditto. Imagine a wave like an ocean wave, with a crest. The direction the wave travels is the direction the crest travels. Imagine the crest going at an angle into a material that slows it down. The part that goes into the new material first gets slowed down first. The part that goes fast in the old material longest, goes farther. So the direction the crest moves through the new material will be different (and slower). The bigger the speed difference, the bigger the turn.

• Thank you, and, yes, I was looking for an amateur-targeted analogy, and not the describing equations. If I understand you correctly (and cross-referencing with the Wikipedia article that Adrian Howard referenced), the chromatic dispersion that happens in the medium (glass) is both time and space - true? Obviously the human eye/brain couldn't comprehend the time difference in the "output", but it can perceive the space difference -- is that a fair understanding? Commented Sep 4, 2020 at 15:54
• And to use your analogy: the time dispersion is, in a sense, because of the space dispersion. I.e. the light "hits a patch of loose sand or tar" and changes direction thereby "slowing down" its travel and eventual exit from the medium -- is that a correct understanding of your analogy? It sounds like the dispersion is a result of some combination of intrinsic and extrinsic absorption by the medium - i.e. the intrinsic properties of silica as well as impurities are kind of like "resistance/friction" from the road and patches of tar/sand in your analogy -- is that fair to say? Commented Sep 4, 2020 at 16:23
• The way I see it, it's the slowing down that causes the change in direction, because it slows one side sooner than the other. A change in speed is kind of a change in both time and space. If light goes straight in from air to glass you can't see that it takes longer to get through the glass, and you can't see that it travels slower through the glass either one. But you can tell the difference in direction. Commented Sep 4, 2020 at 23:31