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By H. a. E. Keitz
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Extra resources for Light Calculations and Measurements: An introduction to the system of quantities and units in light-technology and to photometry
Sample text
10, 1948, 150-153. "The New Candle" J. W. T. Walsh, W. Barnett, R. G. Berry andJ. S. Preston, Proc. Inst. Electr. Eng. JOB, 1961, 173-181. " *) Ph. T. R. = Philips Technical R 5 r2 According to formula (II-I) w = -. Fig. 6. The value of the conical solid angle of which the half-apex angle is ex rna y be expressed in terms of ex. e. h = CD). We may now write: w 5 = -r2 = 2n =- r 2nr . CD r2 (r- r cos ex) 2n = -(MD- MC) = r = 2n {1 -cos ex). 20 [II SOLID ANGLE A conical solid angle may thus be expressed by w = 2n (I -cos ex). 5". 0404 sterad. In the above we have defined the idea of "solid angle" as the space enclosed by a conical surface. Space can also be enclosed by hyo conical surfaces having a common apex; the space thus enclosed is also called a solid angle and the definition given in section II-I should be extended accordingly. If the subtended part of the spherical surface is not equal to r 2, but may be denoted by 5, then 5 w=-. r2 (II-I ) The surface of a sphere of radius r is 4nr2 ; the solid angle enclosed by the whole sphere is thus Fig. 5. The solid angle w subtends at the surface of the sphere an areaS. When the radius of the sphere is denoted by Y and the subtended area is ,s, the solid angle is equa l to 1 steradian 4nr2 - - = 4n sterad. r2 Hence the half sphere contains 2n sterad. Example: A solid angle w subtends an area of 12 sq.