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AT THE BLACKBOARD II Ihe illnazinU Hl'aholoid Double reflection and redistribution of energy by M. l. Feingold HE "PHYSICAL" DEFINITION of the optical properties of aparabola can be based on the following property: a beam oi light that strikes a parabola parallel to its axis of symmetry Passes through its focus after reflection. From the principle of reversibility of light it follows that abeam coming from the focus of a parabola will travel parallel to its symmetry axis after reflection. In this article we'Il look at some purely "physical" features of light reflection from a paraboloid-that is, the surface formed by revolving a parabola about its axis of symmetry. The paraboloidal mirror is a paraboloid with a reflective interior surface. I{ light falls on such a mirror parallel to the axis of symmetry of the paraboloid, after reflection all the beams pass through its focus as if they were being collected there. On the other hand, rays ema- Figure 1 nating from a point source at the focus wili propagate as a parallel beam after reflection on the mirror surface. I should point out that both of these effects are the result of only one reflection of the rays from the paraboloidal surface. If a paraboloid is rather deep, most of the entering rays willbe reflected twice (fig. 1). AIter the first reflection each beam, having passed through the focus, will again be re{lected from the opposite side of the paraboloid. In other words, the focus becomes a kind of point source of light.l But the rays of such a source leave the paraboloid as a parallelbeam. Thus, we come to the conclusion that the paraboloid converts the incoming beam, which is parallel to its symmetry axis, into an outgoing beam that is also parallel to this axis. The incident and reflected beams do differ, however, with regard to their energies. To understand this, let's look at figure 2. It shows the results of a very simple experiment. Photographic film is placed pe{penficular to the mirror's qrmmetry axis, with the photosensitive layer facing the reflective surface. The mirror is illuminated by a Light beam parallel to the symmetry axis with homogelln reality the designation "point source" is appropriate only to a certain extent/ in the sense that the dimensions are small. Later we'II see how this source differs from the point source. neous energy distribution over the cross section-that is, an equal amount of energy passes Per unit time through a unit area placed at any location perpendicular to the beam. The incoming light would strike the film homogeneously. However, in our experiment the film is struck bY reflected light, which produces the result shown in figure 2. ',",i Figure2 (a) Intensity distribution over the cross section of the outgoing beam; (b) plot of the intensity as a function of distance from the beam's axis. o E Y .= E o -o 40 JUtY/[lJ0UST lSg4
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