Mirrors

You are in the middle of two mirrors set at an angle of 50° and your eyes are 1 meter from the vertex.  You can see 6 images of yourself.  Here’s the problem:

 (a) Plot, for each image, the path of the light ray as it travels from your nose back to your eye.

(b) Calculate, for each image, its apparent distance from you.

In our view, this problem is a “must” for grade 10. It’s challenging—there’s no doubt about that––but it is experiential with a capital E. This is a beautiful inter-section of triangle trig with the law of re-flection––too good to miss.

And at the end, as you will see, there’s an extraordinarily simple formula that de-rives from an elegant argument.

We bought these mirrors in JYSK for $12 each, used duct tape to put them together, and set them up in the classroom. It was worth it—the kids kept going back to look and think.

Curriculum Expectations

  • Use of Mathematical Processes

  • Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;

  • Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;

  • Solve problems involving acute triangles, using the sine law and the cosine law