Optical images can also be created through refraction by lenses. A lens is simply a piece of glass, plastic, or other clear material that is curved on one or both faces; the curves cause light rays passing through the lens to bend. The bending of light by a thin lens can be described by fairly simple equations. The bending by very thick lenses, however, is very complicated. We will consider thin lenses in this section. A thin lens is called thin because its thickness or width w is very small compared to its diameter d. Light rays passing through a thin lens behave in a specific fashion with regards to the focal points of the lens. One kind of thin lens is a converging thin lens. When light rays that are parallel to the axis of a converging thin lens strike the lens' surface, they are bent in such a way that they converge at the focal point on the other side of the lens. Light rays that pass through a focal point before striking the converging lens are deflected by the lens to a path parallel to the lens axis. In a diverging thin lens the roles of the two focal points are reversed: when light rays that are parallel to the lens' axis pass through the lens, they are deflected to diverge as if the light came directly from the first focus. Light rays that initially are directed towards the far focus are turned outward by the lens and move on parallel to the lens axis. Converging lenses are often convex on both sides. That is, they curve outward on both sides. However, one side can be flat - or even concave - as long as the lenses are thicker in the middle than at the edges. This central thickness ensures that the convex side dominates the deflection of light rays. Diverging lenses are often concave on both sides, giving them an hour-glass shape. However, one side can be flat - or even convex - as long as the lenses are thinner in the middle than at the edges. If we have a thin lens, the effect of one or both of the concave sides insures that the light waves will diverge or move away from one another. Now that we know what features make up a converging or a diverging lens, let's see what determines the value of the focal length, f. What do you suppose will happen to the focal length of this lens if we increase the curvature of the lens? ... Try sketching a lens with a larger curvature on a separate piece of paper. ... As the curvature increases and the lens gets thicker, the focal length decreases. This is because the light hits the lens at a greater angle and therefore refracts more. This is true for both converging and diverging lenses Now let's study image formation by a lens. As we did for mirrors we will locate the image by tracing certain principle rays that are easy to find as they move from a single point on the object. Remember, however, that though we consider only a few principal rays here, light rays from this point strike all parts of the lens, and all of them contribute to the image. Let's examine the first principal ray. The incident ray is parallel to the lens' axis and the reflected ray goes through the focus. With a converging lens, the light ray travels through the focus on the far side of the lens. A diverging lens bends the parallel ray, and the ray then leaves the far side as if it came from the focus on the near side. Now let's look at the second principal ray. The incident ray is aligned with the lens's focal point, and the reflected ray is parallel to the lens axis when leaves the backside of the lens. In the case of a converging lens, the incident ray passes through the focus on the near side of the lens. In the case of a diverging lens, the reflected ray passes through the focus on the near side of the lens. In general these two rays are enough to locate the image. However, if the two focal points are the same distance from the lens, a third principal ray can be drawn. This ray extends from the object and passes through the center of the lens where it meets the lens axis. Because the ray goes through the center of the lens, where the two lens surfaces are parallel, it does not bend. The image produced by the converging lens is now obvious. In this case it is a real, inverted image that is bigger than the object. For the diverging lens, the image is slightly more difficult to find. Because it is a virtual image, we must trace the outgoing rays backward until they cross. This reveals a virtual, upright image that is smaller than the object. Keep in mind that we considered only two simple examples of image production by lenses. In this case the image from the converging lens was real, but sometimes images from converging lenses are virtual. Finding them will necessitate tracing outgoing rays backward.

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