Reflection of Radiation from an Infinite Plane. Part V. Hemispherical Source (Correction due to Shadowing),
BUREAU OF AERONAUTICS (NAVY) WASHINGTON DC
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In an earlier section of this report, it was noted that as an approximation the shadow area produced by the finite hemispherical source had been excluded in the derivation of the equation for the reflected radiation. For most practical purposes, as will subsequently be shown, the simplicity of the equation derived by omitting the shadowing effect far outweighs the error introduced by its exclusion. However, it is still of some interest to determine an expression for the reflected radiation which does include the shadowing effect so that the regions for which this effect may be safely neglected can be readily determined. Furthermore, should controlled laboratory experiments be undertaken, a more refined expression for the reflected radiation would prove to be of value. In this supplement, the limits of the mathematical integration are modified to account for the portion of the plane obscured by the source. In addition, the mechanics of evaluating the modified integral are indicated. A few numerical results are listed to give an indication of the magnitude of the reduction of the reflected radiation due to the shadowing effect.