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  • Illustrate image formation in a flat mirror.
  • Explain with ray diagrams the formation of an image using spherical mirrors.
  • Determine focal length and magnification given radius of curvature, distance of object and image.

We only have to look as far as the nearest bathroom to find an example of an image formed by a mirror. Images in flat mirrors are the same size as the object and are located behind the mirror. Like lenses, mirrors can form a variety of images. For example, dental mirrors may produce a magnified image, just as makeup mirrors do. Security mirrors in shops, on the other hand, form images that are smaller than the object. We will use the law of reflection to understand how mirrors form images, and we will find that mirror images are analogous to those formed by lenses.

[link] helps illustrate how a flat mirror forms an image. Two rays are shown emerging from the same point, striking the mirror, and being reflected into the observer’s eye. The rays can diverge slightly, and both still get into the eye. If the rays are extrapolated backward, they seem to originate from a common point behind the mirror, locating the image. (The paths of the reflected rays into the eye are the same as if they had come directly from that point behind the mirror.) Using the law of reflection—the angle of reflection equals the angle of incidence—we can see that the image and object are the same distance from the mirror. This is a virtual image, since it cannot be projected—the rays only appear to originate from a common point behind the mirror. Obviously, if you walk behind the mirror, you cannot see the image, since the rays do not go there. But in front of the mirror, the rays behave exactly as if they had come from behind the mirror, so that is where the image is situated.

A bottle at a distance d sub o from a flat mirror. An observer’s eye looks into the mirror and finds the image at d sub I behind the mirror. The incident rays fall onto the mirror and get reflected to the eye. The dotted lines represent reflected rays extrapolated backward and produce an image of the same size.
Two sets of rays from common points on an object are reflected by a flat mirror into the eye of an observer. The reflected rays seem to originate from behind the mirror, locating the virtual image.

Now let us consider the focal length of a mirror—for example, the concave spherical mirrors in [link] . Rays of light that strike the surface follow the law of reflection. For a mirror that is large compared with its radius of curvature, as in [link] (a), we see that the reflected rays do not cross at the same point, and the mirror does not have a well-defined focal point. If the mirror had the shape of a parabola, the rays would all cross at a single point, and the mirror would have a well-defined focal point. But parabolic mirrors are much more expensive to make than spherical mirrors. The solution is to use a mirror that is small compared with its radius of curvature, as shown in [link] (b). (This is the mirror equivalent of the thin lens approximation.) To a very good approximation, this mirror has a well-defined focal point at F that is the focal distance f size 12{f} {} from the center of the mirror. The focal length f size 12{f} {} of a concave mirror is positive, since it is a converging mirror.

Figure (a) shows a large concave spherical mirror. A beam of parallel rays is incident on the mirror; after reflection it converges at F. Figure (b) shows a concave mirror that is small when compared to its radius of curvature. A beam of parallel rays is incident on the mirror; after reflection it converges at F on the same side. The middle rays of the parallel beam are 1,2, and 3. The distance of F on ray 2 from the center of the mirror is its focal length small f.
(a) Parallel rays reflected from a large spherical mirror do not all cross at a common point. (b) If a spherical mirror is small compared with its radius of curvature, parallel rays are focused to a common point. The distance of the focal point from the center of the mirror is its focal length f size 12{f} {} . Since this mirror is converging, it has a positive focal length.
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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