1. Introduction: One Line That Does All the Work
In the last lessons you drew ray diagrams. You stood the object up, sent two rays, and read off where the image landed. That works, but it is slow, and your hand can lie — a slightly crooked ray and the image jumps to the wrong place.
Here is the idea. There is one short equation that gives you the image position straight from numbers, with no drawing at all:
And a second one tells you how big the image is and which way up:
Tell it where the object is, and it tells you exactly where the image is, how tall, and whether it is upright or upside down. No protractor, no shaky lines.
Stop scrolling. Try it in your head before reading on: in the ray diagram, what two things did you always have to find — where the image is, and what else about it?
This lesson does two jobs. First, we build that mirror formula from a ray diagram, so you trust it instead of just memorising it. Then we learn to use it and its partner, the magnification formula, the way a careful person uses a tool — checking the sign every single time.