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AT THE
BLACKBOARD II
Ihe illnazinU Hl'aholoid
Double reflection and redistribution of energy
by M. l. Feingold
HE "PHYSICAL" DEFINITION
of the optical properties of aparabola
can be based on the following
property: a beam oi
light that strikes a parabola parallel
to its axis of symmetry Passes
through its focus after reflection.
From the principle of reversibility of
light it follows that abeam coming
from the focus of a parabola will
travel parallel to its symmetry axis
after reflection. In this article we'Il
look at some purely "physical" features
of light reflection from a paraboloid-that
is, the surface formed
by revolving a parabola about its axis
of symmetry. The paraboloidal mirror
is a paraboloid with a reflective
interior surface. I{ light falls on such
a mirror parallel to the axis of symmetry
of the paraboloid, after reflection
all the beams pass through its
focus as if they were being collected
there. On the other hand, rays ema-
Figure 1
nating from a point source at the
focus wili propagate as a parallel
beam after reflection on the mirror
surface.
I should point out that both of
these effects are the result of only
one reflection of the rays from the
paraboloidal surface. If a paraboloid
is rather deep, most of the entering
rays willbe reflected twice (fig. 1).
AIter the first reflection each beam,
having passed through the focus,
will again be re{lected from the opposite
side of the paraboloid. In
other words, the focus becomes a
kind of point source of light.l But
the rays of such a source leave the
paraboloid as a parallelbeam. Thus,
we come to the conclusion that the
paraboloid converts the incoming
beam, which is parallel to its symmetry
axis, into an outgoing beam
that is also parallel to this axis.
The incident and reflected beams
do differ, however, with regard to
their energies. To understand this,
let's look at figure 2. It shows the results
of a very simple experiment.
Photographic film is placed pe{penficular
to the mirror's qrmmetry axis,
with the photosensitive layer facing
the reflective surface. The mirror is
illuminated by a Light beam parallel
to the symmetry axis with homogelln
reality the designation "point
source" is appropriate only to a certain
extent/ in the sense that the
dimensions are small. Later we'II see
how this source differs from the point
source.
neous energy distribution over the
cross section-that is, an equal
amount of energy passes Per unit
time through a unit area placed at any
location perpendicular to the beam.
The incoming light would strike the
film homogeneously. However, in
our experiment the film is struck bY
reflected light, which produces the
result shown in figure 2.
',",i
Figure2
(a) Intensity distribution over the
cross section of the outgoing beam;
(b) plot of the intensity as a function
of distance from the beam's axis.
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