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The Lens Equation
We will use some ideas illustrated here to find an expression which will allow us to find the position of the image formed by a lens by calculation (rather than by drawing a scale diagram).

Although the result is usually called the lens equation, it can, in fact, also be used to predict the positions of images formed by curved mirrors.
To derive this equation we will start from a ray diagram showing a converging (convex) lens forming a real image.

On the ray diagram, we see two similar triangles, as shown below.

Therefore, we can write
The ratio H/h is called the linear magnification produced by the lens.

Looking at the ray diagram we also have the following
which, after a bit of messing around gives

This is called the lens equation.
When using this equation, distances to real images and objects are given positive values and distances to virtual images and objects are negative.
This means that the focal length of a diverging lens is represented by a negative figure.

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