Corner Cube

Copyright ©2008 by Paul Niquette. All rights reserved.

For background informatin see...
A Certain Bicyclist: An offbeat guide to the Post-Petroleum Age.

ur bicycling futurist brought the Corner Cube home and eagerly fashioned a bracket to fit the luggage rack on his all-weather commuter bike.  He waited for nightfall and invited a friend to drive over for an amazing demonstration of space-age technology.  He rolled the bicycle 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:
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.

Which invites another question: How do normal bicycle reflectors work?  You are invited to submit your explanations here.


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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