Calculation of Luminance (L) of a Diffuse Reflecting Surface The luminance (or brightness) of a surface largely depends on the character of the surface, if it is itself not the emitter. In the case of a polished surface, the luminance depends on the angle of viewing. But if the surface is matt and diffusion is good, then the luminance or brightness is practically independent of the angle of viewing. However, the reflectance of the surface reduces the brightness proportionately. In Fig. 3.4 is shown a perfectly diffusing surface of small area Suppose that at point on a hemisphere with centre and radius A. M O R, the illuminance is cd/m2. L Obviously, at point is = (or lumen/steradian). luminous intensity M L A cosө candela Now, the hemisphere can be divided into a number of zones as shown. Laws of Illumination or I luminance The illumination (E) of a surface depends upon the following factors. The source is assumed to be a point source or is otherwise sufficiently away from the surface to be regarded as such. (i) is directly proportional to the luminous intensity (I) of the source or E EI (ii) The illumination of a surface is inversely proportional to the Inverse Square Law. square of the distance of the surface from the source. In other words, 1/r2 E α Proof In Fig. 49.5 are shown portions of the surfaces of three spheres whose radii are in the ratio 1 : 2 : 3. All these portions, obviously, subtend the same solid angle at the source and hence receive the same amount of total flux. However, since their areas are in the ratio of 1 : 4 : 9, their illuminations are in the ratio 1 : 1/4 : 1/9 (iii) According to this law, is directly proportional to the cosine of Law. E Lambert’s Cosine the angle made by the normal to the illuminated surface with the direction of the incident flux.
Calculation of Luminance (L) of a Diffuse Reflecting Surface The luminance (or brightness) of a surface largely depends on the character of the surface, if it is itself not the emitter. In the case of a polished surface, the luminance depends on the angle of viewing. But if the surface is matt and diffusion is good, then the luminance or brightness is practically independent of the angle of viewing. However, the reflectance of the surface reduces the brightness proportionately. In Fig. 3.4 is shown a perfectly diffusing surface of small area A. Suppose that at point M on a hemisphere with centre O and radius R, the illuminance is L cd/m2. Obviously, luminous intensity at point M is = L A cosө candela (or lumen/steradian). Now, the hemisphere can be divided into a number of zones as shown. Laws of Illumination or I luminance The illumination (E) of a surface depends upon the following factors. The source is assumed to be a point source or is otherwise sufficiently away from the surface to be regarded as such. (i) E is directly proportional to the luminous intensity (I) of the source or EI (ii) Inverse Square Law. The illumination of a surface is inversely proportional to the square of the distance of the surface from the source. In other words, E α 1/r2 Proof In Fig. 49.5 are shown portions of the surfaces of three spheres whose radii are in the ratio 1 : 2 : 3. All these portions, obviously, subtend the same solid angle at the source and hence receive the same amount of total flux. However, since their areas are in the ratio of 1 : 4 : 9, their illuminations are in the ratio 1 : 1/4 : 1/9 (iii) Lambert’s Cosine Law. According to this law, E is directly proportional to the cosine of the angle made by the normal to the illuminated surface with the direction of the incident flux.
40-Calculation-of-Luminance.docx