Re: Refraction at Constant Speed

[brian whatcott <inet@INTELLISYS.NET>]

If a tractor travels at a speed of two towards a sheet dragged in the
opposite direction at a speed of one, the tractor's relative speed to
the interface is three, and then if their directions are not
exactly at 180 degrees, a refraction of the tractor onto the opposing
sheet towards the normal is seen where the tractor travels at a
relative speed of two, and on leaving the "optically denser' sheet,
compensating refraction is noted.

 But this is not a good model for the constant (if reduced) speed of a
 wave in such a medium. The relative speed of the tractor varies with
its angle of incidence.

Perhaps a Maxwell arrangement of springs in a space filling lattice with
balls at the corners could be used. If the matrix has a plane beyond
which the springs have a softer spring constant, the propagation speed
drops, and diffraction effects occur (I assume).


At 14:41 4/20/01 -0400, you wrote:
> > From early PSSC days, the "constant speed vehicle" has been portrayed as a
> track-laying bulldozer of some sort. If the expected congruences apply, it
> is a constant velocity vehicle as well. Relative motion in two dimensions
> is often undertaken by having one dozer pull a large flat sheet on which a
> second dozer is moving to be examined in the room's frame of reference.
>
> But if the second dozer is started from off the large sheet, on the carpet
> let's say, and made to intercept the moving sheet, an interesting
> refraction occurs at the interface. The reason is simple. One track is
> getting traction on the moving sheet before the other. Depending on the
> angle of incidence, refraction can be observed either towards the normal or
> away from it. This behavior can be predicted by noticing which track would
> enter the moving sheet first or leave it last since this is what produces
> the couple that turns the vehicle.
>
> If the towed sheet has parallel edges, it is observed that the refracted
> dozer makes parallel paths on the carpet before and after being transported
> by the sheet. One presumes the shape of a prism or lens section could be
> towed.
>
> The question for the list is:
>
> What physical systems could be usefully modeled with such an arrangement?
> It is typical, but not necessary for both dozers to have the same speed.
> The dozer blade might be regarded as an element of a wavefront or the path
> of the dozer, a ray, e.g.
>
> Tom Ford


brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!