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Re: Spherical Mirrors



R. W. T.!


Tanks for finally bring up the steady state case.

I presume which loss (surface of sphere or entrance exit hole) will be greater (determine
the saturation light level) depends on the reflectivity and ratio of surface areas (hole
and interior sphere). This system is (was?) in very common use by lighting engineers.
They use integrating spheres, for example, to determine the efficiency of light sources.
In another particular case Ron. Ruby (emeritus UCSC) used one to measure the absorption of
chlorophyl at its active wave length ~ 700 nm. The sample was in the center of the
Ulbrich(t) sphere (v. ~ 30 cm D.). A collimated beam from a monochrometer entered through
a small (relative to sphere area) hole incident on sample. At right angle was a hole
through which an MPT looked. Finally, a stop blocked the light directly reflected by the
sample. The inside of the sphere and stop was painted with matte white paint. This
method accurately measures the total non absorbed light (transmitted and diffusely
reflected). The key is diffuse reflection. Such a sphere is unnecessary for measuring
specular reflectivity. R. R. reports this method become obsolete soon after his work (30
yr. ago?) Perhaps this explains why none of you kids mentioned this use.

bc

P.s. An altavista search will result in 30 pages. One is of a mfg'd. photometer for sale;
it hinges open to install the to be measured lamp.


"Richard W. Tarara" wrote:

----- Original Message -----
From: "Van E. Neie" <ven@PHYSICS.PURDUE.EDU>

Jennifer S wrote:

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

The most significant flaw is that you really can't get perfectly
reflecting
surfaces, so even if the surfaces were almost perfect, the light intensity
would essentially decay to zero in a very small fraction of a second.

I've been asked the same question in a slightly different way: "If I
shine
light into a box that has mirrors on the inner surface, then shut the lid,
will I trap the light inside?"


But what about the fact that light could keep entering through the hole.
The energy inflow should be greater than the decay rate within the sphere,
at least at first. Eventually, with enough light bouncing around inside and
each reflection losing some small percentage of energy to the walls, we
should reach an equilibrium. The actual level of illumination within the
sphere is then a function of the reflectivity. There _is_ the complication
of light eventually leaking out the hole. Consider the related problem
however. Place a single light bulb within a fully mirrored box (better to
keep it off any 'focal' point). Assume a reflectivity (99% say), figure
what the effective illumination would be. Maybe this is the way to save
electrical energy! Light an auditorium with a single 60 Watt light
bulb--just totally mirror the inside walls, ceiling, and floor! ;-) {OK,
I'm sure not, but what would be the 'effective' illuminating power of the
bulb? Seems we would have to know how many bounces--someone did that
calculation--but then figure the intensity of each bounce that passes
through a given point in space and combine all those. We know this works in
principle because we use parabolic reflectors to intensify the illumination
from headlights, with the once reflected light combining with the direct
light from the bulb or filament. }

Rick

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Richard W. Tarara
Associate Professor of Physics
Department of Chemistry & Physics
Saint Mary's College
Notre Dame, IN 46556
219-284-4664
rtarara@saintmarys.edu

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