Re: Spherical Mirrors

[Herbert H Gottlieb <herbgottlieb@JUNO.COM>]

Jennifer...

If light enters a sphere through a hole in the surface, the
far side of the sphere will not focus the light to a point
because of "spherical aberration".  To avoid this the
inside curvature of the sphere would have to
be shaped more like a parabola than like a sphere.

Then you would face the problem of trapping the light
within the sphere so it could not re-emerge throgh the
hole.  This would require having a shutter that could
open and close faster than the speed of light.

Herb Gottlieb from New York City
(Where we draw dark shades to trap the sunlight in
inside our classrooms during the daytime so the
classrooms remain lit up all night)

On Sat, 29 Apr 2000 23:43:23 -0400 Jennifer S <jmsphys@JUNO.COM> writes:
> 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
>
>
>
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