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 (1/√[3], 0, 0) to (1/√[3], 0, 1) and A to the left at roughly (1/(2 √[3]), 0, 1/2).

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 incidence = angle of reflection).

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.

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