When light goes from a vacuum into some material, it slows down. The speed of light in a vacuum is c = 3x108m/s. When is enters window glass it slows to a v = 2x108m/s. The ratio of c to v is called the index of refraction for that material and is given the symbol n.
n = c/v
The interesting thing about n is that it also describes another important property of light. When light moving in a vacuum strikes a piece of glass, the direction of its motion may also change. If it strikes a piece of flat glass perpendicular (i.e. normal) to the surface, the direction does not change. However, if it strikes at another angle, the direction will change. The larger the index of refraction, the more the bending.
In the figure above on the right, it bends when it enters the glass and when it leaves the glass. Since glass has a higher index than a vacuum (or air) it bends one way when it goes from vacuum or air to glass and the other way when it goes back to the vacuum or air. (The line perpendicular to the face of the glass is called the normal.) When it enters the glass it bends toward the normal and when it leaves the glass it bends away from the normal. If the two glass faces are parallel, the final beam will be parallel to the original one. {When a light beam enters a medium of higher index of refraction from a medium of lower index, it bends toward the normal and when a light beam enters a medium of lower index of refraction from a medium of higher index, it bends away from the normal)
| An interesting effect occurs if the faces are not parallel. Then the
incoming and final beams or rays are not parallel as shown below. If the angle
between the light ray and the normal is larger, the ray will be bent more
when it emerges on the other side. If I have different triangles the
rays will emerge at different angles.
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One can put two of these triangles together and make the beams or rays from the top one intersect the ones from the bottom one as shown below.
| This acts a little like a lens. A convex lens is really a piece of glass that is shaped like part of a sphere. I have shown a convex lens with one flat side at the right. The light strikes the curved surface a different angles because the normal to the surface keeps changing direction. As a result the beams farther from the center are bent more, because they strike it at a greater angle. In this case the incoming rays are all parallel and |  |
they all cross at a single place on the lens' axis. The distance from the lens to this point is the focal length and this point is called a focus or focal point of the lens. (This is the place where parallel incoming rays cross the axis through the center of the lens.) The focal length is usually measured in meters or centimeters. This type of lens is called a converging lens because it bends parallel rays so that they all converge on a single point. Of course they diverge again after that as they continue on. This is what you are doing when you use a magnifying glass to focus the sun's light down to a small spot to start a fire.
When light comes from an object, the rays are not parallel, but the light spreads out in all directions. Everyone in a room can see the light from a candle flame as it spreads out. The same is true for diffuse reflection from something like an arrow or can of soda. Reflected light from the tip of an arrow, representing a candle, will spread as shown at the right. If I put a lens to the right of the arrow, some of the light from the tip will strike the lens. If the lens is convex (I've shown a lens that is convex on both sides, or a double convex lens) the lens bend the light beams or rays. If the arrow is farther from the lens than one focal length, all the rays from the tip that strike the lens will be bent so that they pass though a single point on the right side of the lens. This is shown in the figure below. The black dots in the image are one focal lenght to the left and right of the lens. Each of these is called a focus |
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or focal point of the lens and is labeled f. This type of construction can be made on graph paper if you know the focal length of the lens and the distance from the object (i.e. the arrow or candle) to the lens. (The symbol for focal length is f and the symbol for the object distance is do.) In this case the light rays from another point on the
| arrow or candle will also be brought to a single point, but not same point as the tip. This process will produce an image of the original object somewhere on the right side of the lens. The distance from the lens to this image is called the image distance or di. If I put a piece of paper, or film, where this image forms, it will show up on the paper or film. One can find the position and size of the image using graph paper. The dashed line through the center of the lens is called the optical axis. The ray that goes from the tip of the arrow and travels parallel to the axis (labeled 1) is bent by the lens so that it goes through the focal point on the right side of the lens. Ray 2 goes from the tip to the center of the lens and it is not bent. Ray 3 goes from the tip of the arrow through the focal point on the object side of the lens and when it strikes the lens, it is bent so that it now goes parallel to the optical axis. The image of the tip of the arrow forms where these three cross. (The rays will continue through this point and diverge from it unless something is put there to stop them, e.g. some film.) |  |
There is a mathematical relation between the
