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We can use the principles of reflection and refraction that we covered earlier to make graphic images with a computer. But what happens in the real world? Let's consider the reflection of a small object in front of flat mirror. Incoming or incident light waves hit the mirror and reflect off the mirror according to the law of reflection. Recall that the law of reflection states that the angle of reflection is equal to the angle of incidence. If we extend the paths of the reflected rays through the back the mirror and beyond, the lines meet at a single point behind the mirror. This point is called the mirror's image. This image, known as a virtual image, is what you see when you look at yourself in an ordinary mirror. The image is called virtual because the image appears to be behind the mirror, even though no light actually reaches behind the mirror. Though the image is called virtual, this term does not mean that we cannot see the image. When we look at an object in a mirror, our eyes intercept only the rays reflected from it. Our brains interpret them as an image of the object behind the mirror. Notice that, for a flat mirror, the distance between the image and the mirror - known as the image distance, s sub i - is the same as the distance between the object being reflected and the mirror - known as the object distance, s sub o. The situation gets both more complicated and more interesting when the mirror reflecting an object is curved. With curved mirrors, the reflected images may be different in size, position, or orientation - or all of these - than the object being reflected. When curved mirrors are involved, using the law of reflection directly to trace the rays becomes very difficult. We need another method to achieve this. Consider the mirror illustrated. Because the light hits it on the side that curves inward it is called a concave mirror. You can remember this by imagining that the mirror forms a small cave. If the reflecting mirror is parabolic, when incident, or incoming, light rays that are parallel to the axis of the mirror are reflected by the mirror, the reflected rays meet at a single point. This point is called the focal point. The distance between the focal point and the mirror is called the focal length and is denoted by lower case f. Because the light converges, concave mirrors are also called converging mirrors. Conversely, light that approaches the mirror through the focal point is reflected parallel to the axis of the mirror. In practice, parabolic mirrors are hard to make, so we use spherical mirrors instead. As long as we use only a small portion of the sphere, the mirror is very nearly parabolic, and the focal length is simply half the mirror's radius of curvature. Which of these mirrors has the shortest focal length? ... The mirror with the smallest radius - and thus the most curvature - has the shortest focal length. ... Now we'll begin to trace rays to find the position of images formed by the mirror. In reality, light leaves the object in all directions and reflects off all parts of the mirror. However, we will trace just a few special rays that are easy to show, and then use them to find the location of the image. It is convenient to use an upward pointing arrow as our object. The image, then, will be shown as either an upward or downward pointing arrow. The tip of the arrow indicates where the rays cross and the base of the arrow lies on the axis of the mirror. First we consider a single ray of light that leaves the object parallel to the axis of the mirror. Because this ray approaches the mirror are parallel to the mirror's axis, when it is reflected, it must pass through the focal point. Next we consider the ray that leaves the object and passes through the focal point of the mirror. When it reflects off the mirror it must be parallel to the axis. Generally the two rays we have considered are sufficient to determine the location and orientation of the reflected object's image. But there are two other sorts of rays can be used check our answer involving two other sorts of rays. The first check is to draw the ray that hits the center of the mirror, and then, using the law of reflection, draw the reflected ray. The second way to check is to draw the ray that passes through the center of curvature. This ray will be perpendicular to the mirror, and thus will reflect directly back along its original path. This ray, while simple and helpful, is often the least accurate of the principle rays. Let's review what we've covered here. There are four principle rays. The first ray is parallel to the axis as it approaches the mirror and is reflected back through the focus. The second passes through the focus as it approaches the mirror and is reflected back parallel to the axis. The third ray strikes the center of the mirror, and is reflected back in accordance with the law of reflection. The fourth passes through the center of curvature and is reflected directly back out, following its ingoing path. If we put a screen, such as a thin piece of paper, at the point where the rays cross, an image forms on the screen. Because the rays actually cross at that position, the image is called a real image. Notice that the image is upside down or inverted. This is a general property of real images formed by a single optical element. The image is also closer to the mirror than the object being reflected is, and it is smaller than the object. Thus, such an image is described as real, inverted, and smaller. Accordingly, we describe an image from a flat mirror as virtual, upright, and the same size. Suppose we have a mirror shaped like the outside of our last mirror, reflecting light off the outside surface. Such a mirror is known as a convex mirror. Parallel light that approaches the mirror cannot converge to the mirror's focus, because the focus is on the far side of the mirror. Instead, the light reflects as if it has come from the focus, and diverges outward. Notice that if we extend the paths of the reflected rays backward through the mirror, the lines meet at the focal point. Because the rays reflected by this kind of mirror diverge, convex mirrors are also called diverging mirrors. As you might expect from our earlier discussion, rays moving towards the mirror that are heading towards the focal point are parallel to the mirror's axis when they are reflected back by the mirror. Here again, though these rays are directed towards the focus as they approach the mirror, they are reflected before actually reaching the focus. Convex mirrors have four principal rays of interest. The first ray approaches the mirror parallel to the mirror's axis and its reflection moves from the mirror as if it had been reflected from the focal point of the mirror. The second ray approaches the mirror in alignment with the focus and reflects along the line through the point of reflection and parallel to the mirror's axis. The third ray approaches the mirror and reflects from its center such that angle of approach equals the angle out, relative to the axis of the mirror. The fourth ray approaches the mirror along a line perpendicular to the mirror's center of curvature and reflects straight back, retracing its incoming path. Notice that the reflected rays do not cross. However, if we extend the lines back behind the mirror from their points of reflection, they do cross. Thus this is a virtual image, because the rays leave as if they had crossed at a point, even though none of them actually reached that point. The image created is virtual, upright, and smaller than the object. In general, images from a concave or diverging mirror will be virtual, upright, and smaller than the original object.
Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education