We computed the radiance emitted from each point of a spherical uniform source of radius r and total power Φ in each outward direction v as Φ 4π(πr2) . Now consider some distant point P, lying on a surface that faces the center C of the spherical source, and that the distance from C to P is R >> r. We can compute the irradiance at P by computing the solid angle subtended by the spherical source, and the radiance arriving at P along each direction of that solid angle, etc.
(a) Do this computation to determine the irradiance at P.
(b) Now suppose that the total power H remains constant, while the radius r of the source shrinks. What is the limit of the expression you found in part (a) as r → 0?
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