Measure the Angular Displacement of the Sun and/or Moon!
As an introduction to angular quantities, one of the demos/activities I do is to have the kids actually measure the angular displacement of the sun - if it's actually out, that is. Here's what you need:
- Pair of large polarized sheets or large sun filter for telescope.
- Meter stick.
- The Sun - or Moon on a clear day!
Here's what to do:
- Show the kids the basics of angular displacement by using a window / woods analogy. By looking thru a window that may only be 2 feet wide, you can still see 200 feet of woods across the parking lot - or any other such distant structure(s). By diagraming on the board, a pair of similar isosceles triangles are made. One that terminates at the window and one that terminates at the woods. See picture.
- Introduce quickly the basic workings of the polarized sheets and demonstrate how they block most light when placed at right angles.
- Go outside and have kids look thru the filters at arms length at the sun while partners measure the distance from his/her eyes to the filter - the radius R - and the apparent height of the sun as seen ON the filter by the holder - the arc length L. Do the same for the Moon if it's out.
- C'mon back in and do some quick calculations making sure the kids understand the definition of a radian.
By the results I get, it's a success. The average angular displacement of the sun from here is 0.009 rad. The kids, just yesterday 02/11/03, got 0.012 rad and 0.016 rad respectively in my two classes. Pretty good for eyeballing measurements! Once in the classroom, they are asked to determine WITHOUT MEASEUREMENTS the "true" angular displacement of the sun. All they have to do is look in the front cover of their text OR look on my wall of knowledge for the radius of the sun and the distance between us and it... Use definition of Ang Dis = L/R and they be done!
If you ONLY measure the sun while outside, after all the analysis with the sun, ask them for the Ang Disp of the Moon! It's amazing to see these bright Juniors and Seniors COPY my math procedure and look in the book or on my wall for the numbers and start calculating... sigh... After about 10 or 15 seconds, I yell loudly for them to stop and think! NO CALCULATIONS! All of a sudden, someone makes the conection that the Moon has the same apparent size as the Sun! Answer? 0.009 rad! Then we discuss that for a minute or two...
This could also, and usually does, lead into a description of "Cheap Sunglasses". Not the pop song by ZZ Top! But, how cheap sunglasses actually cause eye damage by preventing you from squinting and NOT blocking the UV which will then have a license to kick your retina's buttocks!
