The passage of light through simple concave and convex lenses is governed by the principles of refraction, and can be understood with the aid of a few simple rules about the geometry involved in tracing light rays through the lens. The focal length of a lens is dependent upon lens curvature radius and the refractive index. The Thin Lens equations are very straight forward but are only valid when the thickness of the lens is negligible compared to the focal length of the lens. Lenses whose thickness is not negligible are sometimes called thick lenses to emphasize that their thickness is not being neglected. This tutorial is going to discuss solely lenses with a thickness that is negligible compared to its focal length.

There are two basic kinds of thin lenses: convex lenses and concave lenses.

Rules for Convex Lenses

There are three simple rules that govern how light passes through a thin convex lens. 1. Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens. 2. Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. 3. An incident ray which passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens.

Ray Diagrams for Convex Lenses

Now that we understand these basic rules governing lenses we can create what are called ray diagrams in order to predict the position, orientation, and size of the image generated by the lens. 1. Draw two incident rays traveling towards the lens from the top of the object. Draw one ray so that it passes exactly through the focal point on the way to the lens. Draw the second ray such that it travels exactly parallel to the principal axis. 2. Once these incident rays strike the lens, refract them according to the rules of refraction discussed earlier. 3. The image point of the top of the object is the point where the two refracted rays intersect. Note that if the two refracted rays intersect on the same side of the lens as the object the image formed in called a virtual image.

Rules for Concave Lenses

There are also three simple rules that govern how light passes through a thin concave lens. 1. Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point). 2. Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. 3. An incident ray which passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens.

Ray Diagrams for Concave Lenses

Now that we understand these basic rules governing lenses we can create what are called ray diagrams in order to predict the position, orientation, and size of the image generated by the lens. 1. Draw two incident rays traveling towards the lens from the top of the object. Draw one ray so that it travels towards the focal point on the opposite side of the lens (this ray will strike the lens before reaching the focal point). Draw the second ray such that it travels exactly parallel to the principal axis. 2. Once these incident rays strike the lens, refract them according to the rules of refraction discussed earlier. 3. The image point of the top of the object is the point where the two refracted rays intersect. Since the refracted rays are diverging, they must be extended behind the lens in order to intersect. When the image is formed on the same side of the lens as the object it is know as a virtual image.