Computing light output

In illumination problems, it is often necessary to compute the solid angle of a light beam in steradians in order to determine the total flux emitted by the source in lumens. When the plane angle of divergence of the beam is small and, hence, the half angle is small, the use of the common relationship ω = 2π(1 – cos α) becomes quite cumbersome. Slide-rule computation of the cosine term is valueless and even the use of four-place trigonometric tables may result in large errors. If, however, the cosine term is expanded in an infinite series, the following result may prove helpful.