Concept explainers
Reflecting surface Assume that when the plane curve C shown in Figure 1.3.23 is revolved about the x-axis, it generates
FIGURE 1.3.23 Reflecting surface in Problem 29
a surface of revolution with the property that all light rays L parallel to the x-axis striking the surface are reflected to a single point O (the origin). Use the fact that the angle of incidence is equal to the angle of reflection to determine a differential equation that describes the shape of the curve C. Such a curve C is important in applications ranging from construction of telescopes to satellite antennas, automobile headlights, and solar collectors. [Hint: Inspection of the figure shows that we can write ϕ = 2θ. Why? Now use an appropriate
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
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