Question

5) An ellipsoid refraction problem (you can 't always believe everything you see in a book!) The book Optics by Eugene Hecht, 4th edition, poses the following problem (problem 5.3, somewhat paraphrased). "Referring to the figure below, provide an argument showing that if a point source is placed at the focus Fi of the ellipsoid, the light arrays that emerge from the far side are collimated. L.e., all rays AA' and BB' are parallel to each other and to the axis of the ellipsoid. Remember that an elliptical mirror reflects all the rays emitted from one of its two foci and images them onto the focus. From Hero's principle, the distances travelled by the light from Fi to curve and back to F2 are equal." medium: air Index of refraction n-1 В' axis Ellipsoid Index of refraction n2 Note: in general, when light impinges on an interface between media with two different refractive indices, part of it is reflected, part is refracted. So the elliptical surface becomes a partial mirror, but a fraction of the light is transmitted as well. Without the need for any detailed math, explain why the situation posed by Hecht cannot be correct in general. That is, provide an argument showing that we can't have a collimated beam for arbitrary values of the ellipsoid's refractive index n2.

Answer 1