The thin lens equation
allows us to find the distance
of an image from a lens given an object distance
and the focal length of the lens
The diagram below shows an example of a lens forming an image.
The image is formed by three diagnostic rays of light.
One ray travels from the object O straight through the centre of the lens and Is unrefracted.
One ray travels from the object O, parallel to the axis, and one reaching the lens, is refracted to pass through the focal point F.
One ray travels from the object O, passes through the focal point F to the lens, and is refracted by the lens to pass parallel to the axis.
The the rays of light meet at a single point where the three rays of light meet.
From the diagram above
and
From the first equation
and from the second,
Equating these two gives
or
Dividing throughout bygives us
Adding
to both sides then gives