Frequent contributor Michael Gray sent me a wolfram alpha script this morning on the thin lens equation. Wolfram alpha, if you're not familiar, is a wonderful site that will suck you in with all the crazy things it can do. You can use it as a calculator, equation solver, equation grapher, and more. My students have occasionally used it to check their algebra or calculus on homework problems. All I can say is, I wish this had existed in 1993 when I took my differential equations class. I learned to use integral tables, that's for sure.
(What's an integral table, you ask? Get off my lawn, whippersnapper.)
Anyway. This particular script will solve the thin lens equation for any variable given any input. Great -- so will your calculator. What I love is that the script will include a ray diagram! Your students can not only check their answers to lens questions, but they can see visually if their inputs make sense.
Why is the diagram so useful? Well, any man jack can plug numbers into the thin lens equation. What's tough is getting the signs of the input quantities right, and then interpreting the output. The resulting ray diagram allows a student to interpret physically, not just numerically, whether an answer is reasonable. A diverging lens gave me a real image? Oh, I must have missed a sign.
Let's find another 50 readers, and I'll keep posting. Send in your requests!