We started today with the six cases of curved mirrors—five for concave mirrors and one for convex mirrors. We learned about the principal rays of light to find where the image will form. Of course, any time I draw mirror diagrams, I have to pull out the concave and convex mirrors. They make weird images!
For the first time of my teaching career, I did a geometric proof of the mirror equation. It looked familiar, but I don't think I saw it since the 1990s. Why did I never do it before? It's so cool. The students who loved geometry loved that proof.
As you can tell, it was a lot of me in the front of the room. I felt it. It was needed and useful, but I remembered why I don't like lecturing.