Measuring the Speed of Light.

CARA Yerkes Summer Institute, August 1994

*
This is meant to be given to the students.*

For example, it takes 0.12 second for light (or microwaves, or
any other kind of *electromagnetic radiation*) to travel from the Earth
to a communications satellite in a geosynchronous orbit. The round
trip - from Earth and back - for a microwave transmission would be
twice this, or 2 x 0.12 second = 0.24 second, which explains why
there is a slight delay in some long-distance telephone calls. We can
think of this as a distance of 0.24 *light-seconds*.

Light takes 1.28 seconds to travel from the Moon to Earth, and
500 seconds or 8.3 minutes to travel from the Sun to Earth. Since
Jupiter is 5.2 times as far from the Sun as the Earth, it takes 5.2 x 8.3
min = 43 min for light to travel from the Sun to Jupiter, and we can
say that Jupiter is 43 *light-minutes* from the Sun.
Pluto is 39.5 times
farther from the Sun than is the Earth; this works out to a distance of
5.5 *light hours*.

These examples give you another way of thinking about the
size of the Solar System. (As still another example, stars are
typically *light years* apart, not light hours.)

Astronomers thus use time to measure distances, and the scale is based on the speed of light. This is possible because of an important rule:

The other important rule is:

distance traveled speed = -------------------------------. time to travel that distanceWe'll first practice using this equation by calculating the speed of a ball thrown by one student to another. We need to measure the distance between the students, and we need to measure the time-of- flight. If the distance between the students is measured in

To understand why this last statement is true, we need to understand a bit about how a TV set works. A beam of electrons hits a phosphor inside the TV tube, creating a glowing dot. The electron beam is scanned rapidly sideways and down the screen, such that in just 1/30th of a second, the whole screen has been "painted" by 525 scans of the glowing dot, from top to bottom. The scanning is too fast for the eye to see. In the next 1/30th of a second, another picture is painted, and so on, to create something the eye + brain interprets as a moving image.

Since there are 525 scans (also called "lines" or "scan lines"), each one must take only

1 1 -------- = -------- 30 x 525 15,750of a second to travel from the left-hand side of the screen to the right-hand side of the screen.

That means that if a reflected image is offset to the right by one-tenth of the width of the screen, the difference in time between the main image and the ghost must be 157,500th of a second; if the offset is only 1% of the width of the screen, then the difference in time is 1,575,000th of a second, and so on. The point is that a measurement of the offset of the ghost, as a fraction of the width of the screen, gives us a way to measure very small intervals of time.

Our antenna, the large dome, and Rockford, Illinois are approximately in a line. That means that if we tune to stations in Rockford, the difference in distance traveled between the main signal and the reflected signal will be simple to calculate - it is just twice the distance from our antenna to the main building. The Rockford stations are:

- channel 13 WREX ABC
- channel 17 WTVO NBC
- channel 23 WIFR CBS
- channel 39 WQRF Fox

__________ offset distance between main image and ghost image

Measure the width of the TV screen in millimeters, and write down that number in the space below.

__________ width of the TV screen

Now, what fraction of the width of the screen is the offset of the ghost image?

offset distance ------------------- = ----------------- = width of TV screenThis is equal to the fraction of the width of the screen

Now, finally, what is the delay time for the ghost? That is, by what amount of time did the ghost signal arrive after the main signal?

__________ seconds delay.

__________ distance between the antenna and the main building

Now write down the

__________ difference in distance traveled from Rockford to the antenna between the main signal and the reflected signal

_____________ speed of light.

How can you check whether this number is right?

[Hint: the number you wrote down above is probably in feet per second or in meters per second. The number for the speed of light you will find in a textbook is probably in miles per second or in kilometers per second. That means that you will need to do a bit more math in order to compare the two values.]