Lens equation

1f=1x+1y\dfrac{1}{f}=\dfrac{1}{x}+\dfrac{1}{y}

Result unit: 1/m (inverse of length)

What it describes

Relates the focal length of a lens to the object distance and the image distance.

Symbols

ff
focal length
[m]
xx
object distance
[m]
yy
image distance
[m]

Where it comes from

Relates the focal length of a lens to the object and image distances. The signs of the quantities depend on the type of lens and on whether the image is real or virtual.

When to use it

Image construction in lenses; camera, eye, magnifying glass.

Example

A lens with a focal length of 0.2 m, an object at a distance of 0.5 m. Calculate the image distance.
Substitution1y=10.2−10.5=5−2=3\dfrac{1}{y}=\dfrac{1}{0.2}-\dfrac{1}{0.5}=5-2=3.
Resulty=13≈0.33y=\dfrac{1}{3}\approx0.33 m.

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