where is the angle measures with respect to the direction that is normal to the LED surface (in this case, the z axis), and r is the radial distance from the origin at which the power is detected. (a) In terms of P0 , find the total power in watts emitted in the upper half-space by the LED ; (b) Find the cone angle, , within which half the total power is radiated, that is, within the range 0 < < ; (c) An optical detector, having a 1-mm2 cross-sectional area, is positioned at r = 1 m and = 45 , such that it faces the LED. If one milliwatt is measured by the detector, what (to a very good estimate)
is the value of P0?