|How we spend our days is, of course, how we spend our lives. - Anne Dilliard|
Chapter 10 - Lighting:
A very unusual kind of optical illusion is illustrated by the phenomenon of the apparent ending of a search-light beam which has attracted much attention in connection with the powerful searchlights used for locating aeroplanes (Fig. 77). For years the apparent ending has more or less carelessly been attributed to the diminution of the density of atmospheric fog or haze, but recently Karrer [Jour. Amer. Opt. Soc., E. Karrer, 1921.] has suggested what appears to be the correct explanation.
When the beam of light from a powerful searchlight is directed into space, its path is visible owing to the scattering of some of the light by dust and moisture particles and the molecules of the air itself. While obviously the beam itself must go on indefinitely, its luminous path appears to end abruptly at no very great distance from the source. This is true whether the beam is photographed or viewed with the naked eye. The fact that the appearance of the beam is the same when it is directed horizontally as when it is directed vertically disproves the common assumption regarding the ending of the haze or fog.
|Fig. 77. - Apparent ending of a
Furthermore, photometric measurements on the different portions of the beam as seen from a position near the searchlight show that the beam is actually brighter at its outer termination than near its origin. Again, the apparent length of the beam varies with the position of the observer, and bears a direct ratio to his distance from the searchlight.
The fact is, that the luminous path of the beam has no definite ending, and extends to a very great distance - practically to infinity. It appears to be sharply cut off for the same reason that the boundary between earth and sky in a flat landscape is a sharp line. Just as the horizon recedes when the landscape is viewed from an elevation, so the beam appears longer when one's distance from it is increased. The outer portion appears brighter, because here the line of sight pierces it to great depth.
That the ending of the beam appears close at hand is no doubt partly due to the brightness distribution, but is also a matter of perspective arising from the manner in which the beam is adjusted. Searchlight operators in the army were instructed to adjust the light to throw a parallel beam. Accordingly, the adjustments were so made that the beam appeared the same width at its outer extremity as at its base. The result seems to be a short parallel shaft of light, but is really a divergent cone of infinite extent, its angle of divergence being such as exactly to offset the effects of perspective.
If the beam were a truly parallel one it would seem to come to a point, just as the edges of a long straight stretch of country road seem to meet at the horizon. If the sides of the road were not parallel, but diverged from the observer's eye at exactly the rate at which they ordinarily would appear to converge, then the road would seem to be as wide where it passed out at the horizon as at the observer's feet. If there were no other means in the landscape of judging the distance of the horizon than by the perspective afforded by the road, it would likely be inferred that the road only extended a short distance on the level, and then went down a hill, that is, passed abruptly from the observer's view.
These conditions obtain ideally in the case of the searchlight beam. There is no other means of judging the position in space of the "end" of an unobstructed searchlight beam than by the perspective of the beam itself, and the operator in adjusting it to appear parallel eliminates the perspective.
The angle at which the beam must diverge to appear parallel to an observer depends upon the distance of the observer from the searchlight. A beam which seems parallel to a person close to it will not appear so at a distance. This fact probably accounts for the difficulties encountered during "searchlight drill" in the army in getting a beam which satisfied both the private operating the lamp and the officer down the field as to its parallelity.
To summarize, the apparent abrupt ending of a searchlight beam is purely an optical illusion. It really has no ending; it extends to infinity.
Chapter 10 - Lighting:
Lighting and Color
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