16 - Light placed above the center of circular area

Tags: 
maxima and minima
light
illumination
trigonometric functions

Problem 16
A light is to be placed above the center of a circular area of radius a. What height gives the best illumination on a circular walk surrounding the area? (When light from a point source strikes a surface obliquely, the intensity of illumination is

$ I = \dfrac{k\sin \theta}{d^2} $

where $ \theta $ is the angle of incidence and $ d $ the distance from the source.)
 

Solution 16

 
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