Commons

infinitesimally from it. In figure s, for instance, light could get fromA to B either by the reflected path AQB or simply by going straightfrom A to B. Although AQB is not the shortest possible path, itcannot be shortened by changing it infinitesimally, e.g., by movingQ a little to the right or left. On the other hand, path APB is physicallyimpossible, because it is possible to improve on it by movingpoint P infinitesimally to the right.It’s not quite right to call this the principle of least time. In figuret, for example, the four physically possible paths by which a raycan return to the center consist of two shortest-time paths and twolongest-time paths. Strictly speaking, we should refer to the principleof least or greatest time, but most physicists omit the niceties,and assume that other physicists understand that both maxima andminima are possible.7.4 Images by ReflectionInfants are always fascinated by the antics of the Baby in the Mirror.Now if you want to know something about mirror images that mostpeople don’t understand, try this. First bring this page closer wandcloser to your eyes, until you can no longer focus on it withoutstraining. Then go in the bathroom and see how close you canget your face to the surface of the mirror before you can no longereasily focus on the image of your own eyes. You will find thatthe shortest comfortable eye-mirror distance is much less than theshortest comfortable eye-paper distance. This demonstrates thatthe image of your face in the mirror acts as if it had depth andexisted in the space behind the mirror. If the image was like a flatpicture in a book, then you wouldn’t be able to focus on it fromsuch a short distance.In this chapter we will study the images formed by flat andcurved mirrors on a qualitative, conceptual basis. Although thistype of image is not as commonly encountered in everyday life asimages formed by lenses, images formed by reflection are simpler tounderstand.t / Light is emitted at the centerof an elliptical mirror. There arefour physically possible paths bywhich a ray can be reflected andreturn to the center.A virtual imageWe can understand a mirror image using a ray diagram. Figureu shows several light rays, 1, that originated by diffuse reflection atthe person’s nose. They bounce off the mirror, producing new rays,2. To anyone whose eye is in the right position to get one of theserays, they appear to have come from a behind the mirror, 3, wherethey would have originated from a single point. This point is wherethe tip of the image-person’s nose appears to be. A similar analysisapplies to every other point on the person’s face, so it looks asthough there was an entire face behind the mirror. The customaryway of describing the situation requires some explanation:u / An image formed by amirror.Section 7.4 Images by Reflection 149