Derivation of the Thin Lens Equation
On this slide, you see a schematic of a principal ray diagram. By identifying two sets of similar triangles, we will be able to derive the thin lens equation. Let's first define the variables: i is the image distance, and o the object distance; f is the focal length; hi is the height of the image and ho the height of the object. The triangles ABC and ADE are similar, so the ratio of their horizontal sides, i divided by f, is equal to the ratio of their vertical sides, hi +ho divided by ho. This is equation (1). The triangles KGC and DHC are also similar, so hi divided by ho is equal to i divided by o. This is equation (2). This one is easy to remember: hi over ho equals i over o! Take a moment to study the geometry! Use equations (1) and (2) to derive the thin lens equation 1/f = 1/i + 1/o by yourself. On the next slide, you'll see the algebra performed, so you can compare it to your work.