A First Course in Physics · Ch. XXI, §§ 575–579 · Chapter 21: Color Phenomena
67. Dispersion and the rainbow
Goal: Your student can explain why a prism spreads colors (each travels at its own speed in glass), why lenses show colored fringes, and how raindrops make the primary and secondary rainbows.
You'll need
- The book, open to these pages
- A garden hose with a fine spray nozzle (on a sunny day), or a clear round glass bowl or jar of water
- A magnifying glass and a white card
- A notebook and pencil
What's in the book
Violet bends most because it travels slowest in glass; chromatic aberration of lenses; achromatic lenses of crown and flint glass; the rainbow made by refraction and reflection in drops (red at 42°, violet at 40°); the secondary bow with its colors reversed. Four questions follow.
The lesson, step by step
Hook question
SayWhy is a rainbow always a circle around the point directly opposite the sun?
Read together
Read §§ 575–579. Why colors separate:
Since, therefore, the blue light was bent more than the red, it follows that the speed of blue light in glass must be less than that of red light.
Try it: make a rainbow
On a sunny morning or late afternoon, stand with your back to the sun and spray a fine mist from the hose: a rainbow appears in the spray. Notice red is on the outside, violet inside (§ 578). Look for a fainter second bow outside it, with colors reversed (§ 579). (Indoors: shine a flashlight through a round glass of water onto a wall.)
Try it: colored fringes
Use the magnifying glass to throw an image of a bright window onto a card. Move the card a little closer and then a little farther: the edges of the image show red and blue fringes (chromatic aberration, § 576).
Explain the idea
In glass or water, violet slows more than red, so it bends more. In a raindrop, light is bent going in, reflected inside, and bent coming out; red leaves at about 42° from the line to the sun, violet at about 40°. So all the drops that send you red lie on a circle 42° around the point opposite the sun. Good lenses pair crown and flint glass to cancel the color fringes (§ 577).
Say it back
Your student explains why you never see a rainbow at noon in summer (question 3).
Questions
Work questions 1–4 on book page 454.
Afterwards
Watch for rainbows in sprinklers, waterfalls and the spray of waves, and check that the sun is always behind you.
Tip
Never look straight at the Sun while hunting for rainbows.
Answers to the book's problems
1. In the west, opposite the morning sun. 2. Lower at 4 o'clock, since the sun is higher then and the bow is always directly opposite it. 3. When the sun is more than 42° above the horizon the whole bow lies below the horizon. 4. In the middle the overlapping colored images of neighboring parts of the paper mix back to white; only at the edges is one color left uncovered.
Worked out for this site from the scan. If a number in your copy differs, trust the book.