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Re: Cat's eyes



John Denker wrote:

At 05:07 PM 9/3/00 -0400, Ludwik Kowalski wrote:

Sorry I missed this part, a lens with a flat mirror in the focal
plane (whose normal is parallel to the lens axis) does indeed
send the beam of parallel light backward.

OK.

But only when the beam is strictly parallel to the lens axis.

Really? That's news to me. Strictly?? Zero degrees????

Perhaps your ray-tracing muscle needs exercise:

1) Derive a general expression for how the efficiency of
retroreflection falls off as a function of angle (and of
numerical aperture). ...

Here is an illustration, a flat mirror and an ideal
(no aberrations) thin lens.

Case 1

Mirror is horizontal, incident beam at 45 is reflected
by 45 degrees (on the other side). A lens of f=10 cm is
intercepting the beam and the focal point is on the
mirror's surface. The beam intercepted by the lens is
reflected and does not pass through the lens. That
what I had in mind by saying that the mirror must
be perpendicular to the beam in order to produce
the retroreflection.

Case 2

Same as above but the angle of incidence is much
smaller than 45, say 5 degrees. In this case the
central (co-axial) ray will hit the mirror at 5 degrees
and will be reflected at 5 degrees, on the other side.
Will it be refracted to be "retroreflected"? Yes, by
the principle of reversibility (the principle would be
violated if the answer were not). The same is true
for any other ray which passes the lens twice.
.........................................................

But what is true for an idealized system may not be
true for real eyes. I do not know the anatomy of a
cat's eye and I do not have a good ray tracing
software to demonstrate that the explanation is
actually correct (rather than making sense). Why
don't we observe the same "glowing eyes" effect
in people?

Thick short focus lenses are likely to be much
different from thin lenses, as far as the
retroreflection is concerned. Try to make a
retroreflector from a microscope objective in
front of a flat mirror which is not strictly
perpendicular. How large deviation from
perpendiculatiy can the system tolerate? It
is not easy to answer such question, for me.

Our cat did not cooperate but I was lucky to meet
another cat on the street. No effect was observed.
My face was illuminated by the sodium (?) street
lamp, just in front of me (~45 degrees up). The
cat was also in front of me, in the darkness below
a parked car. I was about 12 feet from his eyes and
the animal was looking at me. Then a car passed
by and this ended the experiment.
Ludwik Kowalski