Angular Size Lab

Enough was enough. I couldn’t handle going through the chapters in the introductory astronomy course. It was too much material and it was too fast. But I’ve already complained about this in a previous post.

I didn’t have much time to prepare, but I decided to do a lab activity in class. My idea was to have the students build something to measure angular sizes. They could then use this device to measure the size (or distance) of various objects outside. I figured it would be fun to have them actually build things.

So, here is the plan. Step one is to go over the math of angular size. That includes the relationship between the circumference and radius for a circle.

C = 2\pi R

Another important idea is the relationship between the angle in degrees and radians. We need to measure angles in radians, so I also explained this relationship with 360 degrees equal to 2*Pi radians.

The next part was to build an angle measuring device. I’ve done the before in a physics lab, but I wanted something a little simpler. Here’s what I suggested to the students—make some small “flag” that you can hold at arm’s length (so that the distance from eye to flag is constant) and use this to measure angles.

I gave them popsicle sticks and sticky notes and a bunch of other stuff (with the hope that they would come up with their own design). In the end, they had something like this.

This is just a sticky note on a pencil.

The next step is to “calibrate” this instrument. Put your eye a known distance (say 5 meters) from a known length. I had the students use bricks in the wall or put tape on the wall a set distance apart. From this, they can calculate the angular size of the object and make markings on their device. Oh, this diagram might help.

The distance from the eye to the object is R and the length of the object is L. If the object is small compared to the distance, then this length is approximately the same as the arc length of that part of a circle. The value for theta can be determined by dividing L by R.

Now repeat this for another object so that you can turn the angle measuring device into something useful with multiple markings on it. Now we are ready to collect some data.

Here is a large light for the football stadium, you can see it right outside the classroom.

I used Google maps to get the distance to this object (it’s 240 meters) and then had them measure the angular size and calculate the width.

Here are some other questions:

  • What is the angular size of your thumb at arms length?
  • What is the size of a sign on a building across the street?
  • There is a doorway down the hallway. The width of the frame is 0.91 meters. How far is it?
  • What is the angular field of view of your phone’s camera?

Overall, the lab went fairly well. Students have a bunch of trouble with that first step—where they build something. You can tell they don’t feel comfortable without explicit instructions.

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