Derive the differential equation(s) describing the given physical situation. Light stri...

Derive the differential equation(s) describing the given physical situation.

Light strikes a plane curve C in such a manner that all beams L parallel to the y-axis are reflected to a single point 0. Determine the differential equation for the function y = f(x) describing the shape of the curve. (The fact that the angle of incidence is equal to the angle of reflection is a principle of optics.) [Hint: Inspection of Figure 1.22 shows that the inclination of the tangent line from the horizontal at and that we can write (Why?) Also, don't be afraid to use a trigonometric identity.]