# Ideal Lenses and Nonideal Lenses

In our discussion of lenses, we assumed that the lens was able to focus all parallel rays to a single focus. Such an assumption is called an ideal-lens or thin-lens approximation. Real lenses are not so good. The deviation from ideality is called an aberration.

For one thing, lenses that are very thick cannot focus light to a single point, so the image ends up distorted. If you look through a glass sphere, like a bead or a paperweight, you will notice that the image looks bent out of shape. This is called a spherical aberration.

In Section F we noted that different frequencies of light have slightly different indices of refraction, which can cause different colors to have different focal lengths. This is called a chromatic aberration.

In this chapter we looked at light as an example of waves, looking specifically at reflection, refraction, and lens effects. The properties of waves we have studied in the past three chapters include
1. interference (by superposition),
2. frequencies in standing waves,
3. beats,
4. Doppler shift,
5. reflection and refraction, and
6. dispersion.
All waves exhibit these properties, so the way we have divided them up among chapters titled "Waves", "Sound", and "Light" is somewhat artificial. Refraction is most often observed in light waves, so it is generally studied in the context of light. Likewise, beats are usually observed in sound waves and only extremely rarely in light. You should be aware that sound waves reflect and refract just like light, bending toward the normal of the interface when they pass from a fast medium to a slow one. If you visualize this principle in diagrams such as Figures 13-4 and 13-12 and practice the ray-tracing diagram, then you should do well on problems that this chapter covers.