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HYPERBOLIC GLASS For a fixed color of monochromatic light (e.g. as produced by a laser) and a given material, the
 

Summary: HYPERBOLIC GLASS
For a fixed color of monochromatic light (e.g. as produced by a laser) and a given material, the
light will move through the material at a particular speed, satisfying the relation v = c/n, where n is
the index of refraction of the material, and c is the speed of light in a vacuum. To make a chunk
of hyperbolic glass sitting on a table, make the index of refraction of the glass so that the speed of
light changes in proportion to the height of the table, i.e. the index of refraction changes inversely
proportional to the height above the table. Thus, light moves much more slowly near the table.
This could be done by doping the glass at different heights with some other material, so that the
index of refraction changes, as is done in certain types of fiber optics cables. When a laser is shined
on the glass, the rays of light will be bent, and will follow paths which are circles or lines which are
perpendicular to the table, as in figure 1. These paths are called geodesics. This is because light
follows the shortest path. Since it moves more quickly higher above the table, to connect get from
one point to another at the same height it is quicker to move upwards first where it can move more
quickly, then come back down.
PSfrag replacements
H3
n = 0
n = 1
n = 2
rays

  

Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

 

Collections: Mathematics