Solution: Two light sources of identical strength are placed 10 m apart. An object is to

Chapter 4, Problem 62

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Two light sources of identical strength are placed 10 m apart. An object is to be placed at a point on a line parallel to the line joining the light sources and at a distance meters from it (see the gure). We want to locate on so that the intensity of illumination is minimized. We need to use the fact that the intensity of illumination for a single source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. (a) Find an expression for the intensity at the point . (b) If m, use graphs of and to show that the intensity is minimized when m, that is, when is at the midpoint of . (c) If m, show that the intensity (perhaps surprisingly) is not minimized at the midpoint. (d) Somewhere between m and m there is a transitional value of at which the point of minimal illumination abruptly changes. Estimate this value of by graphical methods. Then nd the exact value of .