What is a rainbow?

This video explores the physics of rainbows by considering how light is refracted as it passes through water droplets. The formation of both primary and secondary rainbows (double rainbows) is explained, as well as the formation of the dark band known as 'Alexander's band'.

In his poem of 1820 entitled Lamia, John Keats complained that cold science had destroyed the magic of nature, conquering all mysteries by rule and line, and that Newton, through his work on optics, had un-weaved the rainbow. In this video I would like to show that Keats was misguided, and that by understanding the physics of rainbows, using only the basic tools of geometry and imagination, the experience of seeing a rainbow is enhanced, not diminished, and that the pursuit of scientific knowledge only ever adds to the magic and mystery of reality. It never subtracts.

References:
The Feynman Lectures - Richard Feynman
For the Love of Physics - Walter Lewin

[michaelmello]

After watching this stunning presentation, I am reminded of Richard Feynman's comments regarding a scientist's perception of beauty in nature. "An artist friend holds up a flower and says, 'Look how beautiful it is, ' and I agree. Then he says, 'I as an artist can see how
beautiful this is but you as a scientist will take this all apart and it becomes a dull thing'... Although I may not be quite as
refined aesthetically as he is... I see much more about the flower than he sees... beauty at smaller dimensions, the inner
structure, also the processes... It only adds. I don't understand how it subtracts."
(Richard Feynman)

[DoganErbahar]

I love the level of details you dig in your videos. Being an associate professor of physics myself I have listened, read and taught this many times. But the "enhanced intensity of rays" around max. angle nuance has always escaped my attention. Thank you for the quality work and keep it up! Best regards from Turkey...

[markbehets]

Best physics channel I’ve ever seen. Lots of channels avoid any maths fearing to lose viewers ; others do not refer to the history explaining how theories were developed. And just these elements are necessary for understanding. And understanding increases the mind and brings joy. Thanks.

[talhashahid]

Found this channel just now. Feeling lucky.

[FranFerioli]

The obligatory quote: "...the science knowledge only adds to the excitement, the mystery and the awe... It only adds. I don't understand how it subtracts.” 

― Richard P. Feynman,

[santhoshwagle]

Nobody has ever explained it this way... Amazing.. If only i could give thousand likes... Bravo

[annadasilvachen]

I appreciate that you take time to explain the subject in a deeper manner but still targeted for laymen like myself. There's not that many channels like yours in youtube

[hughmungous]

Starting a degree in physics soon (October) I must say I love your well made, articulated and presented videos. Especially how you show the maths, equations and thought processes for proofs; certainly helps me stay sharp in my physical intuition.

[Paul-fnwb]

Thanks for great videos!

I don't know if it matters to you... but when someone asked you to drop ads, you agreed for some reason and left only one slot. I believe you deserve more following and a bit more ads is the least we can do to support your work. Those who don't want to watch ads can always buy youtube subscription and enjoy the ads-free experience.

[wyrmhero]

Another insanely good video :)
Keep up your amazing work!

[arnolddowney]

We had intense rainbow here yesterday and as a scientist I was asked to explain it. I did my best and got maybe 3/4ths of this explanation, but this video explained the whole thing really well and helps me understand the details I was missing. Really well done, congrats.

[jeffjo]

Thank you for this accurate description. Far too often, when rainbows are explained for non-physicists, it goes beyond being just inaccurate. It actually teaches some of the underlying concepts incorrectly. The most egregious might be that the bright bands occur due to Total Internal Reflection occurring at just one angle. With no reflection occurring at other angles. The truth is that, at every encounter with the water/air boundary, a small fraction of the light is reflected while the rest transmits.

Here is the non-physics explanation that I like to use (all numbers are approximate):

1) Rainbows are created by all of the light hitting a raindrop, not just light at one spot. So any explanation that draw just one ray of incoming sunlight is already inaccurate.
2) The drop reflects this light back toward the sun in a ~40° wide (from the center) beam, much like the mirror in a car's headlight or a flashlight/torch.
3) But there are two significant differences:
3A) The width of the beam varies with the color of light, extending out to 42° for red.
3B) Each color is much, much brighter in the outer 0.5° of its range.
4) This places the bright-red part of the beam between 41.5° and 42°, with (essentially) no other colors of light in that range. So we see a bright red band of color there.
5A) The bright orange band is between 41.25° and 41.75°. Half of it overlaps the red band, but there is some red under all of it.
5B) The bright yellow band is between 41° and 41.5°. Some overlaps the orange band, but there is red and yellow light under all of it.
5C) This continues, making each color toward the end of ROYGBIV appear paler that the same color in a spectrum, until we reach white light inside the violet band.

For double rainbows:
7) Because there are two reflections, the beam is reflects _away_ from the sun, and is ~130° wide.
8) The red band is still on the "outside" of this beam, and the overlapping occurs the same way. But because the width is more then 90°, the beam wraps around the top of the sky and is seen - _upside_ _down, _ not reversed - about 10° above the primary rainbow.

[Scrogan]

I think some cases of physics remove the beauty of perceived reality. Like when Steve Mould and the laser guy were looking at a laser interacting with a soap bubble, and it occasionally showered the room with hundreds of little dots. After some careful examination, they deduced that it was caused by the disco ball on the ceiling.

Jokes aside, nice explanation! I think I’d be interested in seeing a graph or at least equation that predicted the spectral radiant intensity at a given angle, to see how much each colour dominated. Because technically the Sun’s light is dominated by green light, but our eyes see it as white because it’s a broad peak. Though it’s probably just got an f(solar black body) multiplied in front of the equation in the first place.

[markushansen]

Thank you the great explanation. I had an entire section of an assignment based around this topic. I have yet to find in depth explanations like yours, and i really hope you will keep making these videos!

[algorithminc.]

A truly enjoyable channel on YouTube ... I point these lectures out to my son ... hoping enough is understood, that he would study more out of interest. Thank you ...

[omarjea]

It was at 10:38 when I had a eureka moment. So awesome! Thank you for sharing.

[ThePhysicist]

A very good balance bwtween the necessary mathemaical complexity and the simplicity of physica of rainbow formation. This video not only sufficiently explains the process of rainbow formation for a highschool grader but also provides clues for deeper studies into this topic. Great job!!!

[thexyouman]

Damn i was hoping to binge another channel
Whatever ill sub and wait
Good stuff man

[nassimhadjbenali]

Great content! Your explanations are perfect and filled with interesting details. You're doing some good to humanity !

[santiospina]

This channel should have more recognition!