International projectionist (Jan-Dec 1950)

as the amount of light falling on a surface 1 square foot in area, every point of which is 1 foot from a uniform source of 1 candlepower. If the opening indicated by ABCD, Fig. 3, is 1 square foot of the surface area of a sphere of 1-foot radius, the light escaping will be one lumen ; if the area of this opening is doubled, it will be 2 lumens. Since the total surface area of a sphere with a 1-foot radius is 12.57 square feet. a uniform one-candlepower source of light emits a total of 12.57 lumens. Thus a light source of 100 mean spherical candlepower emits 12.57 lumens. Since an area of 1 square foot on the surface of a sphere of 1 foot radius subtends a unit solid angle at the center of the sphere, the lumen may also be defined as the amount of light emitted throughout a unit solid angle by a source whose average candlepower is 1 throughout the solid angle. From this point of view, candlepower may be considered as the number of lumens in a solid angle and is thus a measurement of the light density in a given direction. Summarizing the foregoing definitions Light may be termed the cause, and illumination the effect or result. Since candlepower and lumens are both a measure of the cause, they therefore apply only to the light source itself and not to the effect or result obtained. For the measurement of illumination, a unit known as the "foot-candle" is used in the United States. A foot-candle represents the illumination at a point on a surface which is 1 foot distant from and perpendicular to the rays of a one candlepower light source. If the light source S in Fig. 4 has an intensity of 1 candlepower along the line SA, and if A is one foot distant from the source, the illumination on the plane CD at the point A is 1 foot-candle. The illumination at the points C or D will be somewhat less than 1 foot-candle, since the distance from the source is a little more than 1 foot and the light strikes at a slight angle. The illumination at A is 1 foot-candle only if the plane is perpendicular to the light ray which strikes the surface at that point. If the surface is tilted so that the light strikes at some angle other than *<S -p?3 3^. ytf>J*l '-■.- "?^v^ \ &* /0U ^•~\ ' /p. \' \&' ^' fo?r'~ -/f \K^\\ A >B/^ { Bjj H j^-4 — Area = 1 SQ. FT. KS^S^i' •;] III V-L===M;.W---' .£>_ «[££^ ;'.'( T \ " V ■ •' 7 D\ ~~" — r m ^■"-y^' ^<? N ' 1 i FIGURE 3 Relation of candles to lumens. of candlepower and lumen, it will be seen that candlepower measures luminous intensity or light density of a light source in one direction only. It is no indication of quantity of light flux. The lumen, on the other hand, measures this quantity of light flux and does so irrespective of direction. When the various candlepowers in any solid angle are averaged (which may be considered as eliminating direction), there is then a definite relationship of the candlepower to the lumens in that particular solid angle. This is expressed by the statement that a source of unit spherical candlepower gives 12.57 lumens. TABLE A Source Foot-Candles Moonlight 0.02 "Well-lighted street (average) 1.0 Typical Interior 5-15 Daylight — At North Window 50-200 In Shade (outdoor) 100-1000 Direct Sunlight 5000-10000 90°, there will be a corresponding decrease in illumination. 'Average' Illumination Values A foot-candle reading applies only to the particular point where the measurement is made. By averaging the footcandle at a number of points, the average illumination of any given surface can be obtained. The foot-candle is the unit of measurement most intimately associated with everyday use of light. A working idea of this unit may be obtained by holding a lighted candle 1 foot distant from a newspaper. The result will be approximately 1 foot-candle of illumination. Table A, which lists the foot-candle levels experienced in everyday life, will serve as a basis for a better understanding of the various levels of illumination. Referring again to Fig. 3-B, it will be seen that the surface ABCD fulfills the conditions for a surface illuminated to a level of 1 foot-candle. Every point of this square foot of a surface is perpendicular to the rays of a 1-candlepower source which is 1 foot away. FIG. 4. Illumination at A is 1 foot-candle. This brings out an important relationship between lumen and foot-candle. A lumen is the light flux spread over 1 foot of area to a level of 1 foot-candle, or 1 foot-candle = 1 lumen per sq. ft. This relation forms the basis of a simplified method of lighting design known as the "flux of light" or "lumen" method. When the number of square feet to be bghted is known and the desired level of illumination decided upon, it is a simple matter to determine the number of lumens which must be provided on the working plane. For example, to illuminate 100 square feet to an average level of 5 foot-candles, 500 lumens would have to be distributed uniformly over this area. This may be expressed in the form of an equation: Area (sq. ft.) X foot-candles (average) = total lumens Inverse Square Law Another method of design known as the "point by point" method is based upon the well-known but widely misused inverse square law which also plays an important part in most photometric measurements. This law is illustrated in Fig. 5. If the source of light is one candlepower, the illumination on a spherical surface 1 foot distant, as illustrated by A, is 1 foot-candle. If surface A is removed, the same amount of light passes to surface B, 2 feet away, and here covers 4 times the area of A. Since light travels in straight lines, and none of it is lost, the average level of illumination on B, 2 feet away, is XA as great as that on A, 1 foot away, or ^ of a foot-candle. If B is removed and the same amount of light falls on surface C, 3 feet away from the source, it will be spread over an area 9 times as great as it would be at A. The resulting illumination is therefore l/9th of a foot-candle. At a distance of 5 feet, the illumination would only be l/25th foot-candle. Illumination decreases not in proportion to distance but in proportion to the square of the distance. This fact is referred to as the inverse square law. It should be emphasized that this law is based upon a point source of light from which the light rays diverge as shown in Fig. 5. Practically, it applies with -16 INTERNATIONAL PROJECTIONIST • January 1950