1 / 30

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

aelan
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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)

More Related