# Fresnel Lenses

A Fresnel lens is an extension of what we've already learned about prisms and refraction. As shown in the diagram below, if we have prisms of varying angle or thickness, we get refraction of varying amounts. The extreme, of course, is a "prism" with parallel sides where there is no cumulative bending of the light.

### CONVERGING LIGHT

What we are going to do next is try to converge parallel light rays to a point using a series of prisms.

As shown on the right, if we stack a series of prisms of varying angles up, we can get the top one to bend light more, the next one to bend it less, and so on until we get to the bottom where there is no bending at all.

If the prisms were graduated just right, the emerging light rays could be collected into a small area, which we might call a focal area or focal point.

To complete a "lens" we would want light coming in below our stack of prisms to be bent upwards towards the focal area. Thus we finish our lens with a second stack of prisms, only pointed downwards instead of up.

But most of the lenses that I've seen are round. What is shown here is anything but round. I need an explanation!

What we see on the right is a cross-section of a lens. If we were to rotate it around the axis (running through the center), it would look like the diagram below, a series of concentric circles.

Looking at both the cross-section and the side view, we can see how one is related to the other. In a Fresnel lens, there are really a series of concentric circular prisms which have the combined effect that we desire.

But what is the relation between the cross-section that I see here and a smoothly curved real lens?

The sequence below shows how a prismatic cross section can be "fleshed out" to become a smoothly curved convex lens.

I understand that development, but I have seen Fresnel lenses, and they only seemed to have ridges on one side. How can this be?

If we make the back side of the prism "flat" we reduce its ability to deflect light, but this can be compensated for by increasing the angle on the other side. The result is a lens which is flat and smooth on one side, with concentric ridges on the other.

One of the advantages of such a lens is our ability to stamp it out of a clear piece of plastic, much like making a record (disc). A mold in the shape of the prism surfaces is pressed into the plastic, leaving us with a flat lens which works the much the same as the thicker, heavier lens.

### DIVERGING LIGHT

I know that there are lenses which don't converge light to a point, but which cause it to diverge. Can we make a Fresnel lens that does that?

It seems that we should be able to do this in much the same way that we made the converging lens. Examine the series of prisms to the right to predict what will happen when parallel light passes through them.

As you can clearly see, the light rays that pass through these prisms are deflected apart from one another, creating a diverging beam of light. This is the same effect we get from a concave lens.

Thus, we should be able to make a diverging Fresnel lens using the same technology that we used for the converging lenses, and we do.

### WHERE ARE FRESNEL LENSES FOUND?

We find Fresnel lenses being sold for use in buses and campers. By putting them on the rear window, it gives the driver a wider-angle view of what's behind the vehicle.

Fresnel lenses are used in the page magnifiers that are advertised in many magazines. They are also handy pocket magnifiers.

Fresnel lenses are used in overhead projectors under the glass where we place the transparency.

A common lighting device in theaters is called a "Fresnel." This allows the crew to focus light to either a broad beam or to zoom in to a close spot.

Fresnel lenses are used in traffic lights, directing the light into only the lane for which the signal is intended. This helps prevent driver confusion and accidents.

Finally, a type of Fresnel lens is used in automobile headlights. In this application, the "lens" is actually a series of prisms which widens the beam and sends it down to the road, rather than into the eyes of the oncoming cars!