Note, however, that in showing the focal length of the lens above, we used light rays that were all parallel as they came to the lens. This isn't always the case: we can have light rays incident at different angles.

We use lenses and mirrors everyday but sometimes don't really understand how and why they do what they do. In this section of the Readings, we'll learn a little more about how light interacts with such things as lenses and how this interaction can help us.

Negative focal lengthreal or virtual

In the diagram above, I chose "special" rays to locate the image: the ray (1) passing through the center of the lens will always travel in a straight line without refracting; the ray (2) coming straight in from the candle top (parallel to the optical axis) is bent so it passes through the focal point on the other side of the lens; and the ray (3) passing through the focal point on the object (the left) side of the lens will be refracted so the light will exit the lens travelling parallel to the optical axis. A very similar diagram could be drawn for the light rays coming from the bottom of the candle, or from any other point on the candle.

A Fresnel lens replaces a traditional curved lens by adding concentric grooves to the surface of the lens, as seen below left. These grooves act as individual refracting surfaces that turn a light source into parallel rays that can be seen for very long distances, as in the case of the lighthouse. In our demo we take the light in the opposite direction. We face those grooves toward the sun, and its incoming parallel rays, to concentrate the light down to a single point. Fresnel lenses are mostly used for light gathering power not for precision imaging.

The single point to which the light rays are converging is called the focal point. The distance, f, from the lens to the focal point is the focal length. Each lens and mirror has its own focal length, which is its defining characteristic.

Negative focal lengthmirror

So what kind of image does a convex lens make? The drawing below shows us that a convex (positive) lens forms images on the side of the lens opposite the source.

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Focal length

Most real images are seen inverted (upside-down) while virtual images are seen upright. Look in both faces of a well-polished spoon. One surface is a convex mirror, the other is a concave mirror: on which side is your image inverted?

If we know the focal length of each of the lenses and/or mirrors, our 3 rays will show us where the image of a point from the source (or object) will be located.

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We've seen how we can find the focal length of various types of lenses, and what the difference is between a real and a virtual image. Now we need to bring these concepts together so we can use them to our advantage.

Overview: A Fresnel lens can be looked at as many layers of lenses cut and stacked on top of each other. Creating a lens in this manner provides great collecting or great dispersion power. Lighthouses use Fresnel lenses to project light miles out into the ocean. In this demo, we turn that same lens around to collect and focus sun light into a spot that is so powerful that it will melt rocks. While Fresnel lenses can collect a lot of light in a compact lightweight package, they do not have very good resolution

Negative focal lengthdiverging lens

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So when we discuss the "focal length" of a certain lens or mirror, we are usually referring to the focal length you get when a distant object's light rays (parallel light) are incident on the lens or mirror.

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Image

FOV tofocal length

In the case above, the focal point is farther from the lens, because the incident rays were diverging as they came to the lens.

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What does it mean for a lens to have a negative or positive focal length? A positive focal length means that the focal point of the lens is on the other side of the lens from where the object is placed. On the other hand, a negative focal length means that the focal point is on the same side of the lens as where the object is placed. This terminology is just a useful convention that allow physicists and engineers to characterize lenses and mirrors; it has no real physical meaning.

Lenses that correct dispersion for two wavelengths are called achromatic lenses. Lenses with three corrected wavelengths are called apochromatic lenses. Ideal ...

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This kind of image on the same side as the source is called a virtual image . It's an image that isn't really there; the focal point in the drawing above is just the point where the rays would converge if they could. We can't focus the beams onto a piece of paper, for instance like you tried earlier. The strange thing about a virtual image, however, is that we can see it!

Focal lengthof convex mirror is positive ornegative

Since there are an uncountable number of light rays (shaded area above) passing through the lens(es), it would be unreasonable to draw them all. Usually, we need draw only 2 or 3 rays from a point on the light source to represent all the rays coming from that point.

focallength中文

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Only concave mirrors can create real images. When light hits the surface of a concave mirror, an individual light ray is reflected at an acute angle and all the light converges at a point on the object side of the mirror.

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Let's pretend for a moment that we live in a world in which the optometrists or opthamologists won't make our eyeglasses or contact lenses. If you had the raw materials and knew the prescription of your eyes (the eye doctors will at least do that service), how could you find the right lenses to make? We could make some lenses and test them until we found the right ones, but this might make our eyes pretty tired and would take a long time. If we knew the focal length of various lenses, we would be able to use a much more powerful technique to make our glasses.

CAUTION: IT IS EXTREMELY IMPORTANT THAT EVERYONE WEARS SAFETY GOGGLES WITH THIS DEMO. Be sure to have extra people to ensure everyone (including volunteers!) wears safety goggles and does not touch anything that has been melted.

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In an earlier activity, you tried to image (bring to a focus) the room lights with your various lenses. Did you get an image of the lights with your concave lens (Lens C)? Most likely not, since the concave lens, as we have seen, diverges light and can't bring light beams to a focus. The image, if there was one, would have been on the same side of the lens as the source (the light).

Since we can form an image on a piece of paper, we call this kind of image a real image. As you've probably guessed, we can also see real images.

Most optical elements (mirrors, lenses) can be characterized by basically one quantity: their focal length. To understand focal length, we need to know something about the focal point.

Do concave mirrors havenegative focal length

Real and virtual images are not relegated to the domain of just the lenses -- if you want to see another virtual image look in your bathroom mirror. Or in the curved mirror on the passenger side of your car. Virtual images in a mirror form on the image side of a mirror, unlike that of lenses, in which the virtual image forms on the object side of the lens. Again, however, the virtual image is not a true image, in that it cannot be projected onto a screen. This is because the light rays reflecting off a plane mirror never converge, the major criterion for creating a real image. Likewise, light bouncing off a convex mirror never converge, thus these mirrors create virtual images.

In the image above, note how the light rays, after they pass through the lens, converge on a single point. Below is a schematic drawing of the above situation.

What would happen if the rays were already converging as they hit the lens? Where would we find the focal length in that case?

The idea is to draw light rays emanating from the object through the optical system (lenses & mirrors). The diagram below shows how much of the light from the light source (a candle) passes through the lens and is imaged on the other side (notice that the ray that started at the top of the candle ends up below the ray that started at the bottom of the flame: the image is upside down).

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The lenses and mirrors that we are using in this module come in two basic flavors: convex and concave. The lenses A and B in your Optics Kit are called double convex lenses and have positive focal lengths. They have sides that bulge outwards and, as we saw above, converge light to a focal point. Lens C in your Kit is called a double concave lens and has a negative focal length. The concave lens has sides that bulge inward and diverge light.

Want to try activities highlighting these principles? Click on the name of this activity to find an easy, hands-on experiment:

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With this technique of tracing various rays from a light source, we can tell where an image will form and how it will be oriented: inverted or upright.

Objectives: Learn more about a type of lens structure that can be lightweight, for its size, yet very powerful at the same time for the way it collects light.

Ray tracing allows us to "see" how light is going to behave when we have lenses and mirrors in the path of the light. If we know where the focal point of each lens and mirror is, we can figure out where the image of a certain object will be formed. This will tell us where the image will fall on our retina so we can see it.