Rainbows don't work the way you think they work

A visual explanation of the mathematics at the end of the rainbow.

#SoME1

[MatsVermeeren]

FAQs

* How does a double rainbow form?


* Doesn't some of the light exit at the back instead of reflecting?

Yes it does. In the animation I've only drawn those rays that contribute to the primary rainbow. Which fraction of the light is reflected depends on the angle of incidence. The animation does not take into account this dependence. This is one of several reasons why my animated rainbow is only an approximation of the real thing.

* Does total internal reflection take place?

[martensamulowitz]

this was a ridiculously good explanation! and beautifully animated as well!

[GregorShapiro]

I often see double rainbows (most often the outer one is much weaker than the inner one). 50 years ago I saw a triple rainbow, all of which were very bright. It took me 48 years to understand how that could have happened. The answer is that one (probably the innermost) was due to the Sun's reflection from the smooth surface of a lake behind me; so there were in effect two Suns making the three rainbows!

[AJMansfield]

There's other effects also happening here, particularly to do with the internal reflection off the back of the droplet. Until the angle is shallower than a critical angle, most of the energy will be transmitted out the back rather than reflected. Likewise, if that exit refraction is sufficiently shallow, you instead get a second internal reflection, giving a double -- or with even more reflections, a triple -- rainbow.

[franciskisner]

Rays hitting the drop near center (small angles) are likely to hit the back of the inside of the drop at higher than the critical angle and pass through the drop without reflecting. The "critical angle" is where any light completely reflects off the inside surface. This can be demonstrated by filling a glass with water and looking somewhat upward at the surface of the water. At some angle, the surface suddenly looks silvery and reflects what is on the other side of the glass. At this angle and all shallower angles, all the light hitting the bottom of the surface is reflected. At higher angles, we look through the surface of the water and little light is being reflected. If this is considered, the left end of the graph would be missing.

[PeterNerlich]

OMG thank you! Man, I wondered multiple times already whether I was just seeing psychological or other phenomenons at the rainbow, but it turns out the default explanation is just off. Thank you for highlighting something that makes much more sense and models the actual observations way more accurately!

[JWentu]

one of the best explanations of rainbows I ever saw. waiting for the second part, with the 2nd rainbow, the dark part between the two and the additional (quantum?) effects!

[Boxland_]

A title like that makes me think that the video will first present a simple and naive explanation that I know to be inaccurate. But the initial explanation was the most intuitive and comprehensive explanation I've ever heard, bar the rest of the video.

[bensay]

Never had such a ”Eureka!” moment watching a YouTube video before. Brilliant video.

[michaelwinter]

This is the best and clearest explanation of rainbows I’ve ever seen. Thank you.

[nathanaelvetters]

Something to note is that in this 2D representation you give all entry locations equal weight, while in 3D you have expanding circles rather than just a moving point. This means the graph should start quite flat and curve upwards, reaching a more pronounced maximum at ~42°, which strengthens the effect, and is why you usually only see a little white glow just inside the main rim of the rainbow. Of course, our vision working on a log scale complicates things even further.

[andykay]

I've never before a good explanation of why the inside of a rainbow is brighter than the outside. Thanks!

[Rationalific]

Fascinating! I hope you get a lot more views! (I found you on 3Blue1Brown's playlist.)

[math-phys]

The best explanation on rainbows I have seen. You sir really know how to satisfy curiosity.

[bensbotanicalbedroom]

Yes, the brightness of the area inside the rainbow is often dramatic compared to the darkness around it. This was a very good explanation for why that is.

[ntign]

The brightness difference between inside and outside of the rainbow is something I'd been wondering about for a couple years. I am really glad I just randomly stumbled upon your video Mats. Thank you for the clear explanation :)

[justins]

Fantastic - Always fun to take something you think you know and go to the next level, especially when there are effects you haven’t noticed that are only explained by that deeper knowledge.

[andrewsemenenko]

I was always wondering why it's brighter, and now I now!
Thank you, really awesome🌟

[NXaiUL]

Wow. One of the best explanation videos I've ever seen! The best part is that I actually understood it! Well kind-off...

But I'm hooked, to say the least. Thank you so much.

[ttsuyaguy]

That is the best explanation of rainbows I have ever seen. Thank you.