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Where Do R a i n b o w s Come From?

Where Do R a i n b o w s Come From?. A Tour of Differential Calculus. Where would you rather be?. Supernumerary Rainbows. Rainbows in Mythology. Greek: Path to heaven made by Iris. Chinese: Goddess Nuwa uses 5 stones of different colors to patch a slit in the sky

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Where Do R a i n b o w s Come From?

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  1. Where Do Rainbows Come From? A Tour of Differential Calculus

  2. Where would you rather be?

  3. Supernumerary Rainbows

  4. Rainbows in Mythology • Greek: Path to heaven made by Iris. • Chinese: Goddess Nuwa uses 5 stones of different colors to patch a slit in the sky • Indian: Bow of Indra, God of thunder • Irish: Leprechauns hide their pot of gold at the end of rainbow • Persian: Reflection of light off of holy sites

  5. Rainbows in Bible • The Deluge (Genesis 9.13-15): • I have set my bow in the clouds, and it shall be a sign of the covenant between me and the earth. When I bring clouds over the earth and the bow is seen in the clouds, I will remember my covenant that is between me and you and every living creature of all flesh; and the waters shall never again become a flood to destroy all flesh.

  6. Rainbows in Religion

  7. Where do rainbows come from?Attempts by the scientists • IbnSahl, Al-Biruni ~ 990 • Al-Hacen, Al-Shirazi, Al-Farisi ~ 1280 • Freiberg ~ 1300 • Snell, Descartes, Huygens, Newton, Fermat ~ 1650 • Young, Airy ~ 1830 • Mie ~ 1910 • You ~ 2020

  8. Unweaving the Rainbow Do not all charms fly At the mere touch of cold philosophy? There was an awful rainbow once in heaven: We know her woof, her texture; she is given In the dull catalogue of common things. Philosophy will clip an Angel's wings, Conquer all mysteries by rule and line, Empty the haunted air, and gnomed mine - Unweave a rainbow … Keats, 1820 Lamia

  9. Where Do Rainbows Come From? Basics: Reflection and Refraction

  10. Let Us Unweave the Rainbow • Q- How does light choose a path to go from point A to point B? • A- Light is like an intelligent prescient being. Light chooses a path that takes the least time to go from A to B! • This is Fermat’s Principle. • Depending on your point of view it unweaves or camouflages some of the mysteries of rainbows. • Let’s see how it explains reflection and refraction.

  11. How does light reflect? • Suppose you are to run from A to B and touch the wall L on the way. What path is the shortest?

  12. Geometry to the rescue! Angle of Incidence=Angle of Reflection

  13. So we understand the reflection part.How about refraction?

  14. Refraction: Shallow deep pools, broken straight lines

  15. How Does Light Refract?

  16. Calculus to the Rescue!

  17. Draw a Picture

  18. Time Minimization

  19. Enter the Dragon

  20. But where do rainbows come from? • Different colors of light travel at different speeds in water, so they refract differently. This gives the spectrum of colors. • Intensity is highest when deflection is stationary. So we need to find angle of deflection and differentiate it. • Now Enters the Real Dragon.

  21. Which ray causes the rainbow?

  22. Angle of Deviation

  23. Where do rainbows come from?

  24. 42 degrees above sun’s line

  25. References • James Stewart, Calculus • Richard Dawkins, Unweaving the Rainbow • Wikipedia (for pictures)

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