Problem of the Week 1195
The Legacy of H. G. Wells
Work in the usual xyz coordinate system. Consider a 30-30-120 triangle ABC with apex A and placed with BC rising vertically from
Rotate this object around the z-axis to get a 3-dimensional body W the outer boundary of which is a cylinder. Assume that the inner part of W consists of perfectly reflecting surfaces (angle of
Now suppose a ray of light rises vertically from below.
If it is outside the cylinder or inside a radius 1/4 cylinder around the z-axis, it will simply rise, never striking W.
But suppose the ray strikes W on a face that faces downward. What will happen to the ray of light?
Suggested by: Nikolai Andreev, and an item at the fascinating www.etudes.ru web site.