Topic 23. Thin Lenses, part 2. Ray tracing rules.

The ray-tracing rules described in this section can be used to find the position and size of an image given the focal length of the lens and the position of the object. The rules depend on the same approximations as for mirrors: the rules are valid only when the rays strike the lens in the paraxial region (i.e., close to the central axis of symmetry). In addition, the lens must be “thin,” which means that its thickness must be small compared to its focal length. Many real-world lenses (such as those in cameras) do not satisfy this condition exactly, but the general principles of this section are still applicable.

Ray-tracing rules for a converging (positive) lens:

1. A ray that strikes the lens parallel to the axis is refracted through the lens and passes through the focal point on the far side of the lens. (This is often called the second focal point). See the top ray in the figure above.

2. A ray that passes through the center of the lens emerges traveling in the same direction with no change. See the middle ray in the figure above.

3. A ray which passes through the first focal point (on the object side of the lens) is refracted so that it emerges on the other side parallel to the axis of the lens. See the bottom ray in the figure above.

Ray tracing rules for a diverging (negative) lens:

1. A ray that strikes the lens parallel to the axis is refracted through the lens so that it appears to come from the focal point on the object side of the lens. See the top ray in the figure above.

2. A ray that strikes the lens heading for the focal point on the image side of the lens is refracted through the lens so that it emerges parallel to the axis on the other side. See the middle ray in the figure above.

3. A ray that strikes the lens in the center emerges traveling in the same direction on the image side. See the bottom ray in the figure above.

In general, only two of the three rules are needed to locate the image, and the most convenient pair of rules can be chosen in any situation.

The fundamental assumption of these rules is that all of the rays from any point on the object will reach the same point of the image: the rays that are chosen are only examples that are easier to draw.