How to Derive the Thin Lens Equation

(1/d_o)+(1/d_i)=(1/f)

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A thin lens is defined as a lens with a thickness that is approximately ignorable compared with the radii of curvature of the lens. If a lens is thicker than that measure, the thin lens equation cannot be used.

Due to the geometrical symmetry, the thin lens equation can be used for a convex and concave mirrors.

Please note the following so you can understand how the thin len equation can be derived:

This derivation is not fundamental, but it is more intuitive.

If you identify two equal angles in two different triangles as shown, the two triangles are similar. Namely, each correspondent side has the same ratio.

Jump to other Animations or Main Hiro's Physics Main Multimeter Tutorial Vector Addition Caliper Tutorial Derivation of the Thin Lens Eq. Normal Force Changed with Angles The Free-Body Diagram with an Inclined Plane Projectile vertically upward on the Moon

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Here is an additional information. The object and image distances have to be taken from the center of the lens as shown below. Then, you can prove the thin lens equation works.

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