Answer Happy

Problem 1.24 (Focusing of waves). Suppose you have an incoming electro- magnetic wave along the y-axis which should be focused on a receiver sitting at the origin (0,0). What is the optimal shape for the mirror? (Hint: An incoming ray, hitting the mirror at (x, y) is given by х Rin(t) (*) - 0). t, t€ (-0,0). At (x, y) it is reflected and moves along х Ruf(t) = () (1 -t), te[0,1]. = – 0] The laws of physics require that the angle between the normal of the mirror and the incoming respectively reflected ray must be equal. Considering the scalar products of the vectors with the normal vector this yields 1 -Ꮖ Vito -011 (-3) (1")= 0) () = x2 + y2 which is the differential equation for y mend the substitution u= 2.) = y(x) you have to solve. I recom-