The Physics of Light -- Images

Images made by a Lens

A converging lens brings parallel beams of light together at one point. The beams might all be coming from a very distant source, like a star, and then the little dot of light made by the lens represents the star -- we will call this a real image of the star (the "real" part means that you can get as close to the image as you like -- you can touch it, if you want). If there are many stars in different directions, there are many images. A photograph of the sky is a record of the images made on the film by the lens of the camera.

A lens is characterized by its focal length, which is determined by the curvature of the surface and the material from which the lens is constructed. The relationship between source and image can be classified as follows:

When the source is very far away (compared to the focal length), the distance between lens and image is nearly equal to the focal length. The image is very small, compared to the size of the source, and is upside down, as shown below.
When the source is several focal lengths from the lens, the image is somewhat more than one focal length from the lens. The image is smaller than the source (and upside down).
When the source is exactly two focal lengths from the lens, the image is also exactly two focal lengths from the lens. The image is the same size as the source.
When the source is closer to the lens than two focal lengths, but more than one focal length from it, the image is several focal lengths away from the lens, and larger than the source.
As the source gets to be exactly one focal length from the lens, the image moves to be very far away and very large.
When the source is closer to the lens than one focal length, there is no longer a real image. The beams of light are deflected by the lens, but it fails to bring them together again. Instead, they are still diverging, as if they came from a source.
Looking back through the lens, it looks like there is a source of a different size, at a different position, which is then called the virtual image (shown in green in the picture below). It is different from a real image, in that it appears to be on the other side of the lens, and you cannot approach the image closely -- you bump into the lens first. The virtual image is right side up, and is larger than the object for this kind of lens. Thus this is an example of a lens used as a magnifier.

Diverging lenses (also called negative lenses) only make virtual images.

Here is an animation that will do all the things described above. You can move the source (the arrow on the left) by clicking on it with your mouse. You can also move the lens, by clicking on it. You will see that you can have real images and virtual images that are big and small.[This applet was written by Fu-Kwun Hwang Copyright 1996 Fu-Kwun Hwang] Here is a similar animation, written by Michael Sheetz (University of Kentucky).

Our eyes are like cameras: they have a lens, and an image is formed on our retina. Sometimes the lens is too weak or too strong, with the result that some people can only focus on nearby objects (lens too strong) or distant objects (lens too weak). Wearing glasses can cure this: a positive (converging) lens will compensate for the eye lens that is too weak, while a negative (diverging) lens will compensate for the eye lens that is too strong. A different way to understand what glasses do is to observe that a negative lens turns a distant object into a nearby virtual image, which a nearsighted person can now focus on.

Curved mirrors combine the properties of a mirror and a lens, and also make images that can be real or virtual, big or small, far or near. The person you see in a flat mirror is an example of a virtual image -- you can bump noses with that person, but you cannot shake hands.
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What have we learned about images?