Chasing Rainbows

“C’mon, Sy, Newton gets three cheers for tying numbers to the rainbow’s colors and all that, but what’s it got to do with that three speeds of light thing which is where we started this discussion?”

“Vinnie, they weren’t just numbers, they were angles. The puzzle was why each color was bent to a different degree when entering or leaving the prism. That was an inconvenient truth for Newton.”

“Inconvenient? There’s a loaded word.”

“Indeed. A little context — Newton was in a big brouhaha about whether light was particles or waves. Newton was a particle guy all the way, battling wave theory proponents like Euler and Descartes and their followers on the Continent. Even Hooke in London had a wave theory. Newton’s problem was that his beam deflections happened right at the prism’s air‑glass interfaces.”

“What difference does that … wait, you mean that there’s no bending inside the prism? Light inside still goes straight but in a different direction?”

“That’s it, exactly. The deflection angles are the same, whether the beam hits the prism near the short‑path tip or the long‑path base. No evidence of further deviation inside the prism unless it has bubbles — Newton had to discard or mask off some bad prisms. Explaining the no‑curvature behavior is difficult in a particle framework, easy in a wave framework.”

“Really? I don’t see why.”

Left: faster medium, right: slower medium
Credit: Ulflund, under Creative Commons 1.0

“Suppose light is particles, which by definition are local things affected only by local forces. The medium’s effects on a particle would happen in the bulk material rather than at the interface. The effect would accumulate as the particles travel further through the medium. The bend should be a curve. Unfortunately for Newton, that’s not what his observations showed.”

“OK, scratch particles. Why not scratch waves, too?”

“Waves have no problem with abrupt variation at an interface, They flip immediately to a new stable mode. For example. here’s an animation showing an abrupt speed change at the interface between a fast‑travel medium like air and a slow‑travel medium like glass or water. See how one end of each bar gets slowed down while the other end is still moving at speed? By the time the whole bar is inside, its path has slewed to the refraction angle.”

“Like a car sliding on ice when a rear wheel sticks for an moment, eh Sy?”

“That was not a fun ride, Vinnie.”

“I enjoyed it. Whatever, I get how going air‑to‑glass or vice‑versa can change a beam’s direction. But if everything’s going through the same angle, how do rainbows happen?”

“Everything doesn’t go through the same angle. Frequencies make a difference. Go back to the video and keep your eye on one bar as it sweeps up the interface. See how the sweep’s speed controls the deflection angle?”

“Yeah, if the sweep went slower the beam would get a chance to bend further. Faster sweeps would bend it less. But what could change the sweep speed?

“Two things. One, change the medium to one with a different transmission speed. Two, change the wave itself so it has a different speed. According to Snell’s Law, the important parameter for a pair of media is their ratio of fast‑speed divided by slow‑speed. If the fast medium is a vacuum that ratio is the slow medium’s index of refraction. The greater the index, the greater the bend.”

“Changing the medium doesn’t apply. I got one prism, it’s got one index, but I still get a whole rainbow.”

“Right, rainbows are about how one prism treats a bunch of waves with different time and space frequencies.”

“Space frequency?”

“If you measure a wave in meters it’s cycles per meter.”

“Wavelength upside down. Got it.”

“Whether you figure in frequencies or intervals, the wave speed works out the same.”

“Speed of light, finally.”

“Point is, when a wave goes through any medium, its time frequency doesn’t change but its space frequency does. Interaction with local charge shortens the wavelength. Short‑wavelength blue waves are held back more than long‑wavelength red ones. The different angles make your rainbow. The hold‑back is why refraction indices are usually greater than one.”

“Usually?”

~~ Rich Olcott

Through A Prism Brightly

Familiar footsteps outside my office. “C’mon in, Vinnie, the door’s open.”

“Hi, Sy, gotta minute?”

“Sure, Vinnie, business is slow. What’s up?”

“Business is slow for me, too. I was looking over some of your old posts—”

“That slow, eh?”

“You know it. Anyway, I’m hung up on that video where light’s got two different speeds.”

“Three, really.”

“That’s even worse. What’s the story?”

“Well, first thing, it depends on where the light is. If you’re out in the vacuum, far away from atoms, they’re all the same, c. Simple.”

“Matter messes things up, then.”

“Of course. Our familiar kind of matter, anyway, made of charges like quarks and electrons. Light’s whole job is to interact with charges. When it does, things happen.”

“Sure — photon bangs into a rock, it stops.”

“It’s not that simple. Remember the wave-particle craziness? Light’s a particle at either end of its trip but in between it’s a wave. The wave could reflect off the rock or diffract around it. Interstellar infra-red astronomy depends upon IR scooting around dust particles so we can see the stars behind the dust clouds. What gets interesting is when the light encounters a mostly transparent medium.”

“I get suspicious when you emphasize ‘mostly.’ Mostly how?”

“Transparent means no absorption. The only thing that’s completely transparent is empty space. Anything made of normal matter can’t be completely transparent, because every kind of atom absorbs certain frequencies.”

“Glass is transparent.”

“To visible light, but even that depends on the glass. Ever notice how cheap drinking glasses have a greenish tint when you look down at the rim? Some light absorption, just not very much. Even pure silica glass is opaque beyond the near ultraviolet. … Okay, bear with me on this. Why do you suppose Newton made such a fuss about prisms?”

“Because he saw it made a rainbow in sunlight and thought that was pretty?”

“Nothing so mild. We’re talking Newton here. No, it had to do with one of his famous ‘I’m right and everyone else is wrong‘ battles. Aristotle said that sunlight is pure white‑color, and that objects emit various kinds of darkness to overcome the white and produce colors for us. That was academic gospel for 2000 years until Newton decided it was wrong. He went to war with Aristotle using prisms as his primary weapons.”

“So that’s why he invented them?”

“No, no, they’d been around for millennia, ever since humans discovered that prismatic quartz crystals in a beam of sunlight throw rainbows. Newton’s innovation was to use multiple prisms arrayed with lenses and mirrors. His most direct attack on Aristotle used two prisms. He aimed the beam coming out of the first prism onto a reversed second prism. Except for some red and violet fringes at the edges, the light coming out of the second prism matched the original sunlight beam. That proved colors are in the light, not in Aristotle’s darknesses.”

“Newton won. End of story.”

“Not by a long shot. Aristotle had the strength of tradition behind him. A lot of Continental academics and churchmen had built their careers around his works. Newton’s earlier battles had won him many enemies and some grudging respect but few effective allies. Worse, Newton published his experiments and observations in a treatise which he wrote in English instead of the conventional scholarly Latin. Typical Newtonian belligerence, probably. The French academicians reacted by simply rejecting his claims out of hand. It took a generational turnover before his thinking was widely accepted.”

“Where do speeds come into this?”

“Through another experiment in Newton’s Optics treatise. If he used a card with a hole in it to isolate, say, green light in the space between the two prisms, the light beam coming from the second prism was the matching green. No evidence of any other colors. That was an important observation on its own, but Newton’s real genius move was to measure the diffraction angles. Every color had its own angle. No matter the conditions, any particular light color was always bent by the same number of degrees. Newton had put numbers to colors. That laid the groundwork for all of spectroscopic science.”

“And that ties to speed how?”

~~ Rich Olcott

The Sight And Sound of Snow

<ring> “Moire here.”

“Uncle Sy! Uncle Sy! It’s snowing! It’s snowing!”

“Yes, Teena, it started last night after you went to bed. But it’s real early now and I haven’t had breakfast yet. I’ll be over there in a little while and we can do snow stuff.”

“Yaaay! I’ll have breakfast, too. Mommie, can we have oatmeal with raisins?” <click>


<knock, knock> “Uncle Sy! You’re here! I wanna go sledding! Get my sled out, please?”

“G’morning, Sis. G’morning, Teena. Get your snowsuit and boots on, Sweetie. Want to come along, Sis? It’s a cold, dry snow, not much wind.”

“No, I’ll just stay warm and get the hot chocolate ready.”

“Bless you for that, Sis. OK, young’un, ready to go?”

“Ready! Pull me on the sled to the sledding hill, Uncle Sy!”


“Ooo, it’s so quiet. Why’s it always quiet when snow’s falling, Uncle Sy? Is the world holding its breath? And why is snow white? When I hold snow in my hand it melts and then it’s no-color.”

“Always the good questions. Actually, these two are related and they both have to do with the shape of snowflakes. Here, hold out your arm and let’s see if you can catch a few. No, don’t try to chase them, the breeze from your arm will blow them away. Just let them fall onto your arm. That’s right. Now look at them real close.”

“They’re all spiky, not flat and pretty like the ones in my picture book!”

“That’s because they grew fast in a really cold cloud and didn’t have time to develop evenly. You have to work slow to make something that’s really pretty.”

“But if they’re spiky like this they can’t lay down flat together and be cozy!”

“Ah, that’s the key. Fresh spiky snowflakes make fluffy snow, which is why skiers love it. See how the flakes puff into the air when I scuff my boot? Those tiny spikes break off easily and make it easy for a ski to glide over the surface. Your sled, too — you’ve grown so big I’d be hard-put to pull you over wet snow. That fluffiness is why <hushed voice> it’s so quiet now.”

“Shhh … <whispered> yeah … <back to full voice> Wait, how does fluffy make quiet?”

“Because sound waves … Have we talked about sound waves? I guess we haven’t. OK, clap your hands once.”

<CLAP!>

“Good. When your hands came together they pushed away the air molecules that were between them. Those molecules pushed on the next molecules and those pushed on the next ones on and on until they got to your ear and you heard the sound. Make sense?”

“Ye-aa-uh. Is the push-push-push the wave?”

“Exactly. OK, now imagine that a wave hits a wall or some packed-down icy snow. What will happen?”

“It’ll bounce off like my paddle-ball toy!”

“Smart girl. Now imagine that a wave hits fluffy snow.”

“Um … it’ll get all lost bouncing between all the spikes, right?”

“Perfect. That’s exactly what happens. Some of the wave is scattered by falling snowflakes and much of what’s left spreads into the snow on the ground. That doesn’t leave much sound energy for us to hear.”

“You said that snow’s white because of what snow does to sound, but look, it’s so bright I have to squint my eyes!”

“That’s not exactly what I said, I said they’re related. Hmm… ah! You know that ornament your Mommie has hanging in the kitchen window?”

“The fairy holding the glass jewel? Yeah, when the sunlight hits it there’s rainbows all over the room! I love that!”

A beam or white light passing through two prisms.  The first produces a spectrum and the second remixes the colors to white.

“I do, too. White light like sunlight has all colors in it and that jewel splits the colors apart so you can see them. Well, suppose that jewel is surrounded by other jewels that can put the colors together again. Here’s a picture on my cellphone for a clue.”

“White goes to rainbow and back to white again … I’ll bet the snowflakes act like little jewels and bounce all the colors around but the light doesn’t get trapped and it comes out and we see the WHITE again! Right?”

“So right that we’re going home for hot chocolate.”

“Yaaay!”

~~ Rich Olcott

PS – A Deeper Look.