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OPTICA!, SCIENCE IX CINEMATOGRAPHY 4.r>
the source of light is imaged on a screen, the illumination contributed by the mirror will be in the neighborhood of 5200 times as bright as the illumination contributed directly by the source, since the area of the mirror is approximately 5200 times as large as the source.
An interesting confirmation of the relations between illumination and the size of the image formed by the mirror can be observed in any ordinary mirror spotlight. It is common observation that when such a unit is adjusted to give a flood lighting effect by shifting the lamp closer to the mirror, the margin of the illuminated area shows a bright ring and the center is relatively darker than the margin. If an observer having armed himself with a sufficiently dense filter to protect his eyes or else reduces the illumination by introducing resistance to the point where the source of light is simply red hot, and then
Fig. 3a (Left) Spherical mirror with source in the principal focus showing spherical aberration
of the marginal rays. Fig. 3b — (Right) Parabolic mirror with source in the principal focus producing a parallel beam of light.
walks across the illuminated area looking into the mirror, he will observe that the size of the reflected image, which no longer fills the whole mirror, moves across the face of the mirror and becomes larger as he reaches the edge of the illuminated area and the reflected image moves into the marginal zone of the mirror. Greater brightness is here directly associated with increased size of reflected image establishing a direct connection between the two.
We have in this way attempted to frame an answer to the question why the mirror is used. The answer to the question why a parabolic mirror is used instead of a spherical mirror is very simple. Referring back to Fig. lb, it is seen that all the rays of light reflected on the mirror appear to come from a single point S\ the image of the source S. This represents the true state of affairs without reservations or qualifications. Unfortunately, the plain mirror is the only perfect optical instrument. It is unfortunate for optical designers that its applications are so limited. When we come to a concave spherical mirror, quite different conditions prevail. We fail to find this well-behaved correlation between the reflecting rays, but on the other hand find the conditions such as shown in Fig. 3a. Here the source of light is shown located in the principal focus of the mirror. It is, therefore, imaged at infinity, or in other words, the mirror is supposed to produce a parallel beam of light. Only the very center part of the mirror, however, is capable of performing in this way. As indicated in the picture the deviation of the rays striking the