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In the course of our classroom (high school) discussion about concave
mirrors one of my students posed the following question about a
reflective sphere. Suppose you have a sphere with a small hole in it.
The inside surface is reflective. If light passes into the sphere, would
it be possible to "trap" any and all light inside the sphere? Of course,
this is assuming that ALL wavelengths of light are reflected to the SAME
focal point.
We talked about the fact that parallel rays hitting the surface of a
concave mirror will be reflected to the focal point (F), halfway between
the suface of the mirror and the center of curvature (C). Since the
concave mirror is part of a sphere just assume that the entire sphere
exists. If parallel rays enter through the hole they will travel to the
other side of the sphere at which point they will hit the reflective
surface and pass through F. If we choose any light ray and follow its
path AFTER passing through F, will it continue until it hits the "next"
reflective surface and then pass through a focus, F' which lies on a
"new" principal axis? (That is, the principal axis of this "next"
reflective surface?) If so, would this process repeat and actually
"trap" light inside the sphere?
If there are flaws in my reasoning, please correct me (gently!) Thanks.
Jennifer