Formation of rainbows (& how far are they) | Physics | Khan Academy

Rainbows are formed by the dispersion of light & reflection (not total internal reflection) from drops of water. The rainbow color sequence can be analyzed by drawing a ray diagram of the refraction of sunlight inside water drops. Get more practice on the rainbow formation here

More free lessons & practice

Khan Academy is a nonprofit organization with the mission of providing free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Created by Mahesh Shenoy

[jeffjo]

You do get kudos for explaining that (although you didn't explain why) total internal reflection does not occur. But (1) dispersion is not synonymous with separation of colors, and (2) separation does not explain why we see bright, colored bands. If it did, we would see a rainbow in the light that exits without reflecting (this light is visible, and is called the zero-order glow).

Part (2) first. If you would draw a ray of sunlight that hits the drop a little higher or lower than the one you used, its reflected blue ray can exit the drop at the same angle your red ray did. And the same goes for every color in between. Over most of the reflection, an observer sees all colors combined, making white. Just like in the zero-order glow. This is why the sky inside the rainbow is brighter than outside.

An incoming sun ray that hits the drop in the center is reflected straight back toward the sun. As it moves up on the drop, the angle between the incoming and reflected ray increases, but only up to about 40 degrees. There, it stops increasing and begins to decrease. This change causes many rays to "bunch up" right around 40 degrees, making the reflection brighter there. This effect, called an optical caustic, is quite often seen at the bottom of a mostly-still swimming pool or clear pond on a sunny day. Bright bands of sunlight are seen to almost be dancing around the bottom of the pool, mimicing the waves on the surface.

The caustic in a rainbow is seen at about 40 degrees. But "dispersion" means that all of the colors, which were treated the same way before hitting the drop, must be treated differently after. If there were only one ray (or many that all retract the same way), then separation of colors occurs. But when they refract differently, the effect is know as color aberration. It is commonly seen, when lenses are used to project images on a screen, as a blurring of colors around the edges of objects.

So rainbows are caused by the combination of optical caustic and color aberration. Red appears on the outside because its caustic is at 42 degrees, not because it refracts less

[AlokKumar-ooyt]

My main problem was the reflection of colours inside rain drops. Now it is clear. Thank you sir.

[parneetthind]

Now I can easily explain this concept to anyone

[parneetthind]

Thank you so much sir, it was really too simple and I understood the concept of rainbow. I often think that how are the rainbows formed and try to search for it online, but get confused because none explains it too deeply as you and no other expert tells any logic for the concept 👍👍👍

[ashwin]

Thank you so much sir! It was too simple :)

[hongchai]

I get the reflection and refraction in the raindrop part from other online materials. You are best in explaining why a rainbow goes from red on top to violet at bottom, and why it appears circle or arch shaped. Thank you so very much.

[ashleyjain]

i find this video better than all the video i ave so far seen!! U really helped sir...thanku for explaining in so detail..

[AdityaSingh-etlb]

best ever video, i've ever found on any topic..just lit!!!

[loriandcrew]

Amazing; thank you so much for this explanation.

[ft-parthapratimbaishya]

Sir, you told us that the a part of light refracts before reflecting internally after dispersing in the raindrop. So even if we face the sun why can't we see the rainbow? The colours which refracted should be reaching our eyes isn't it?

[VG__]

It's the best lecture on rainbow I hv seen till now on utube..u don't need to switch to another video bcz believe me, it's best explanation till now🌟

[gajendrajitkakati]

God bless you. Rainbows have puzzled me so much. Learnt a lot. Thank you.👍👍👍👍🧠

[benYaakov]

At 7 : 34, the reason that why light reflects in even transparent media is that the angle of incidence made by incident monochromatic light inside raindrop is greater than critical angle and light reflects .
Critical angle is the angle of incidence at which the angle of refraction becomes 90 ° when light passes through the denser medium ( water drop ) to rarer medium ( air ) . Hence, when the incident angle exceeds critical angle, the light refracts but in the direction outside the interface or say axis which results in total internal reflection .

[MukeshKumar-fekw]

Thanks sir I love your voice nice explanation

[emeraldaisle]

Well said. Nice, clear presentation. Thanks.

[meetgulrajani]

thank u soo much tommorow is presentation of rainbow formation and my tuation teacher is absent i was really tensed about it

[xboxgamer]

It was super duper I can't explain what i was finding that "is there not mess of rainbows" but sir you explained it so perfect unbelievably nicely that I just can't words fit into your effort...Hats off 🤠🤠❤️❤️👍👍👍🙏🙏🙏

[a.k]

Sir I have a doubt, as you said that so many rain drops in a line makes a specific colour visible d but do'nt the rain drops reflect the light which is coming from forward rain drops

[kaustubhchakrabarti]

Thank you so much Sir. My concept is much clearer now

[shivbholeshivbhole]

Yes to me also rakesh sir has recommended the video