picture of magnifying glass

picture of diverging lens

How are images formed by lenses?

Basic Definitions 

convex lens A convex lens is widest at its center and narrower at the ends.
concave lens A concave lens is widest at its edges and narrower in the center.
A real image is formed when light rays intersect.  A real image can be viewed on a screen.

A virtual image is formed at the position where diverging light rays appear to come from.  Virtual images cannot be viewed on a screen, but can be seen by cameras, our eyes and other optical instruments.

The principle axis is a horizontal line drawn through the center of the lens.

Three Principal Rays for a Convex (converging) Lens

Note:  When we draw ray diagrams, we will show the refraction (bending) occurring at the center of the lens (a vertical line drawn through the center).  This is an approximation.
The focal point of a convex lens is the point that parallel light rays are converged to.
convex focus
Principle Ray #1 for the Convex Lens
convex ray 1
A ray that enters the lens parallel to the principle axis will be refracted through the focal point.

Principle Ray #2 for the Convex Lens
convex ray 2
A ray that enters the lens coming from the focal point will be refracted parallel to the principle axis.

Principle Ray #3 for the Convex Lens
convex ray 3
A ray that passes through the center of the lens will not bend.

Three Principle Rays for a Concave (diverging) Lens

The focal point of a concave lens is the point that parallel light rays entering the lens are refracted away from.
concave focus
Principle Ray #1 for the Concave Lens
concave ray 1
A ray that enters the lens parallel to the principle axis will be refracted away from the focal point.

Principle Ray #2 for the Convex Lens
concave ray 2
A ray that enters the lens as if it is going to the focal point will be refracted parallel to the principle axis.

Principle Ray #3 for the Convex Lens
concave ray 3
A ray that passes through the center of the lens will not bend.

Ray Tracing Diagrams
Made 17 May 2008
by Lori Andersen.