# Labs from YSI 94 : Measuring the Speed of Light.

Dr. Rich Kron
CARA Yerkes Summer Institute, August 1994

This is meant to be given to the students.

## Part I. Importance of the Speed of Light

Light travels so quickly that it seems to be instantaneous - we are normally not aware that is has a speed at all. Yet, astronomical distances are so enormous that light may take a long time to go from one object - a planet or a star - to another.

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:

### light always travels at exactly the same speed.

(This is strictly true in a vacuum. When light travels through a medium such as air, water, or glass, it goes a bit slower. For all practical purposes, we can ignore this when measuring large distances.)

The other important rule is:

## Part II. The General Technique

The speed of something - a car, or a baseball, or a satellite - can be measured if you know the distance traveled and the time to travel that distance. The formula is:

```                distance traveled
speed  = -------------------------------.
time to travel that distance
```
We'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 feet, and the time-of-flight is measured in seconds, then we will measure the speed in feet per second.

## Part III. A Ghost Story

Most people who use a TV antenna (as opposed to cable) have noticed that on some stations you see two pictures - the main picture, and another, fainter one that is offset a bit to the right. The fainter one is called a ghost. What's happening is this: the antenna is picking up not only the direct signal from the station, but also another signal that has bounced off of a building, mountain, or some other object that can reflect TV signals. The reflected signal will be weaker, but more importantly, it will arrive a bit later, because it had to travel farther. Since it arrives later in time, it appears to be offset on the TV set.

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       15,750
```
of 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.

## Part IV. The Ghost from the Yerkes Large Dome

It is often difficult to tell exactly what is causing the reflected signal, since the TV transmission can bounce around a lot before it gets to your antenna. But, if we set up an antenna in the back building and aim it at the large dome, it is reasonable to assume there is only one object that can reflect the transmission, namely the large dome itself. If the antenna also receives a bit of the signal directly from the station, then we will have a main image plus an offset ghost image.

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

### Step 1

Turn on the equipment, rotate the dome of the 10-inch telescope to face the main building, and point the antenna towards the large dome. Select any of the different stations listed above and note which gives the best images. Try moving the antenna around to get a good ghost image.

### Step 2

With a millimeter scale, measure the offset between the main image and the ghost image, and write that number in the space below.

__________ 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 screen
```
This 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.

### Part 3

Measure the distance from the antenna to the large dome, and write the value in the space below.

__________ 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

### Part 4

Good! You have now measured the two quantities needed to determine the speed of light: the distance traveled, and the time to travel that distance. Use the first formula given to calculate the speed of light.

_____________ 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.]

Important Disclaimers and Caveats: