 ur
bicycling futurist brought the Corner Cube
home and eagerly fashioned a bracket to fit the luggage rack on his all-weather
commuter. He waited for nightfall and invited a friend to drive over
for an amazing demonstration of space-age technology. He rolled the
bike out of the workshop onto his driveway..
Illuminated by the headlights, the Corner
Cube
appeared completely dark -- a black hole! -- as viewed
from inside the car. The query in the puzzle
calls for an explanation, which will be elementary for a sophisticated
solver who understands how a Corner Cube works...
 ketches
like those above use two-dimensional views (Top, Side, Front) to depict
a three-dimensional phenomenon -- in this case the pathway traced by a
typical ray of light inside a Corner Cube.
Now, The Law of Reflection can be stated as follows:
"The angle of incidence equals the angle of reflection." It is customary
to measure both angles from a perpendicular line (normal) at the
point of reflection. In the sketches, normals are indicated
by dashed lines or by dots (for normals that are -- well, normal
to your screen).
Nota bene: Viewed from various points
in space, the two angles -- incidence and reflection -- may be foreshortened,
but their
equivalence to each other will always prevail.
As shown in the sketches, an incoming ray of light from a
given angle will be reflected from all three 'walls' of the Corner
Cube and exit at the same angle in the opposite
direction. The solution for the puzzle,
then, may be summarized as follows:
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All rays of light that enter
the Corner-Cube
from the car's headlights will be returned back into the headlights not
into the eyes of the driver.
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Which invites another question: How do normal bicycle
reflectors work? You are invited to submit your explanations here.
Epilog
Comments received from Myles
Buckley in May, 2008 are the best so far...
Upon detailed examination of the rear reflector
on my son's bicycle, with the assistance of a tunable wavelength low-wattage
laser and a sensitive photocell, I can assert the following:
-
Several plastics layers, each with differing angles of refraction
and each pressed into an overlapping bezel, form triangular segments similar
to a Fresnel lens.
-
The configuration allows a significant percentage of the
light entering the reflector medium at an incident angle between 70 and
110 degrees to be refracted and reflected back toward the light
source with a dispersion of five degrees.
-
It was noted that dispersion increases beyond five degrees
with increasing destructive interference.
-
If an automobile headlamp is considered a near point-source
of light. The angle of coherently refracted/reflected light at up
to five degrees deflection is well within a nominal 0.6 to 2.5m vertical
displacement between a car (or transport truck) headlamp and its driver's
eyes.
Fairly impressive considering the bicycle reflector is just
pile of shaped plastic on aluminum. Now, consider the effect on eye-brain
system of an interference pattern produced by the Fresnel-type structure,
featuring refraction/reflection.
-
Animal brains, including those of humans, interpret ‘moving’
light sources and ‘pulsing’ light sources differently.
-
A static light source (fixed in the background, or moving
at a relative velocity) is somewhat ignored by the visual processing in
the visual cortex.
-
Make that light “pulse” incredibly fast (much faster than
relative velocity, like having interference patterns rake-across the retina)
and suddenly the brain ‘notices’ the source much easier.
Here is a simple way to test that phenomenon: At a truck
stop, from a standstill, look for the reflector strips on a truck.
Take a jog at a tangent and observe the reflector strips. Finally
from a moving vs stationary observation point observe again. In each
case, you should note that your movement or the target's movement increases
the visibility of the reflector strips.
The effect has been exploited by the
HIRL, with life-saving
results.
-- PN
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