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| Introduction to Lenses | Convex Lenses |

Introduction to Lenses

In the section on reflection and refraction, we looked at the reflection of light from flat and curved surfaces, and the refraction of light at a plane boundary between media of different densities. Now we ask the question, "What happens if the refractive boundary between media is curved rather than being a plane surface?" We'll examine the possibilities in this series of pages.

Cross section of a common double-convex lens.

To the right is a cross section of a shaped piece of glass. Everyone has seen this sort of thing many times. It's a circular piece of glass that's thick in the middle and thin around the edge.

Ideally, the curve of the lens cross section is parabolic. However, it is difficult and expensive to grind lenses to that precise shape, so many lenses are ground with a circular cross section instead. This works acceptably for many applications, since the "nose" of a parabola almost exactly coincides with a portion of a circle. However, such lenses do not operate perfectly, and do introduce some distortion. In our discussion of lens optics, we will assume ideal lenses for our calculations and descriptions, unless otherwise noted.

Cross section of a double-concave lens.

It's not necessary for a lens to be thicker in the middle than at the edges. Just the opposite is shown in the cross section to the right. This type of lens also has its uses, and has a number of practical applications.

It is not necessary for the two sides of a lense to be the same. Often one side is simply flat. We can also have a lens with a concave side and a convex side. In the latter case, the lens does not have to be the same thickness at all points.

In this set of pages, we will look at various lenses to see how they behave and how they can be used in practical situations.

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