Image formation by lenses

by Dominic Ford

Lens 1

Lens 2

Lens 3

Lens 4



The simulation above shows the formation of images by convex and concave lenses. Click and drag the lenses or the source image from side to side to move their relative positions.

To simulate the optics of a telescope or pair of binoculars, where the image is in the far distance, change the "Source image" control to "Image at infinity". The red and blue rays then represent parallel rays of light coming from two directions in the far distance.

The focal lengths of the lenses are expressed as a number of the small squares in the background of the demo. The focal power is expressed in diopters, assuming a conversion of ten small squares to the meter.

Equations

The location of the images formed by each lens is given by the thin lens equation:

\[ \frac{1}{u} + \frac{1}{v} = \frac{1}{f} \]

where

u is the distance of the source object to the left of the lens,
v is the distance of the image produced to the right of the lens,
f is the focal length of the lens.

Here, the Cartesian sign convention is used, with u measured leftwards from the lens, and v measured rightwards from the lens. u is negative if the object is to the right of the lens, and v is negative if an image if formed to the left of the lens.