There are two laws of illumination: 1. Law of Inverse Squares 2. Lambert’s Cosine Law.
1. Law of Inverse Squares:
If a source of light which emits light equally in all directions be placed at the centre of a hollow sphere, the light will fall uniformly on the inner surface of the sphere, that is to say, each square mm of the surface will receive the same amount of light. If the sphere be replaced by one of the larger radius, the same total amount of light is spread over a larger area proportional to the square of the radius. The amount which falls upon any square mm of such a surface will, therefore, diminish as the radius increases, and will be inversely proportional to the square of the distance.
A similar relation holds if we have to deal with a beam of light in the form of a cone or pyramid, as shown in Fig. 7.6 (a). If we consider parallel surfaces which cut the pyramid at different distances from the source, the areas of these surfaces are proportional to the square of these distances, and, therefore, the amount of light which falls on one unit of the area of these surfaces is inversely proportional to the square of the distance from the source. This relationship is referred to as the law of inverse squares.
Mathematically it can be proved as follows:
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Let us consider surface area A1 and surface area A2 at distances r1 and r2 respectively from the point source S of luminous intensity I and normal to the rays, as shown in Fig. 7.6(a).
Let the solid angel subtended be ω steradians = I
Total luminous flux radiated = Iω lumens
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Illumination on the surface of area A1,
Hence the illumination of a surface is inversely proportional to the square of the distance between the surface and the light source provided that the distance between the surface and the source is sufficiently large so that the source can be regarded as a point source.
2. Lambert’s Cosine Law:
Very often the illuminated surface is not normal to the direction of light as AC in Fig. 7.6 (b) but is inclined as AB. The area over which the light is spread is then increased in the ratio-
According to this law the illumination at any point on a surface is proportional to the cosine of the angle between the normal at that point and the direction of luminous flux.
Example 1:
The flux emitted by a lamp in all directions is 1,000 lumens. Calculate its MSCP.
Solution:
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Total luminous flux emitted, F = 1,000 lumens
Example 2:
State laws of illumination. A 250 V lamp has a total flux of 1,500 lumens and takes a current of 0.4 A. Calculate (i) Lumen per watt (ii) MSCP per watt.
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Solution:
Wattage of lamp = V x I = 250 x 0.4 = 100 watts
