A First Course in Physics · Ch. XIX, §§ 495–501 · Chapter 19: Nature and Propagation of Light
58. The speed of light, straight-line travel and shadows
Goal: Your student can describe how Roemer and Michelson measured the speed of light, explain how light's straight-line travel makes shadows, and tell umbra from penumbra.
You'll need
- The book, open to these pages
- A flashlight and a small LED or a candle (with an adult)
- A ball or orange (a small earth or moon) and a larger ball
- A white wall or sheet of paper
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Galileo's lantern experiment; Roemer's measurement from the eclipses of Jupiter's moon (1675); Michelson's and Perrotin's modern values (about 300,000 km per second); seeing the stars as they were long ago; light slower in water; light travels in straight lines; umbra and penumbra and eclipses. Six problems follow.
The lesson, step by step
Hook question
SayWhen you look at a star, are you seeing it as it is tonight?
Read together
Read §§ 495–501. The modern value:
For most purposes it is sufficiently accurate to take the velocity of light in round numbers as 300,000 km. per second, which is equivalent to about 186,000 miles per second.
Explain Roemer's idea
Using Fig. 407, explain: when the earth is on the far side of its orbit, light from Jupiter's moon has farther to travel, so its eclipses come late. The delay (the book's 996 seconds) is the time for light to cross the earth's orbit (§ 496).
What we know now: light actually takes about 1000 seconds (about 16½ minutes) to cross the orbit. The speed of light is now exactly 299,792,458 m per second, because since 1983 the meter has been defined by it. Jupiter has dozens of known moons, not the seven the book mentions.
Try it: umbra and penumbra
In a dark room, shine a small LED (a near-point source) past a ball onto the wall: the shadow is sharp. Use a broad light (a lamp shade or several LEDs) instead: a dark center (umbra) and a fuzzy edge (penumbra) appear (§ 501). Move the ball toward the light and watch the penumbra grow.
Try it: model an eclipse
Hold a small ball (moon) between the flashlight (sun) and a larger ball (earth). Where on the earth is the moon's umbra? The penumbra? Then put the moon behind the earth for an eclipse of the moon (Fig. 410).
Say it back
Your student explains why the shadow of a tree in sunlight is sharp near its base but fuzzy near the top.
Problems
Work problems 1–6 on book page 392. For the umbra problems, use similar triangles: the cone narrows from the size of the sun to a point.
Afterwards
Look at shadows outdoors at different times of day, and at a streetlight's shadow versus the sun's.
Tip
A tiny LED or a phone flashlight makes a good near-point source; a lamp with a frosted shade or a bright window makes a broad one.
Answers to the book's problems
1. About 320,000,000,000,000 miles (54.5 years × 186,000 miles a second). 2. About 873,000 miles (8000 × 93,000,000 ÷ 852,000). 3. About 217,000 miles. 4. No; the moon's umbra is a narrow cone that only just reaches the earth. 5. About 37 miles (the umbra's width 4000 miles from its tip). 6. About 102 years.
Worked out for this site from the scan. If a number in your copy differs, trust the book.