Question

please solve it ,,,,urgent

1. Cartesian Oval In the class, we learnt about the shape of the spherical interface that will mitigate spherical aberration when light enters from air (nı) into a glass (n2). Show that the defining equation is lonu +lin2 = constant And further the above equation is equivalent to n1(x2 + y2)1/2 + n2[y2 + (s. +si – x)2]1/2 = constant. (x, y) are the coordinates of point A on the air-glass interface. Read the wikipedia article on Cartesian Oval and also on Cassini oval.

Answer 1

We can apply the formad's . principle to find the shortest path from o to o' in O AO' - toni linz 05. Sti. A Since this must be the same for all positions of poin A so 2 =Constan't Now from the diagram. for ledige & 4 - Jy+ (Sit 80 - 2)2 so ni x y2 + n2 / g ² + (Sitso - 2672 = const