Invisible objects

There are a lot of unscience fiction stories about invisibility cloaks and so forth, bu is it possible to build an object that is for all intents and purposes invisible.

Mathematicians say it is so and we give here a very simple example of an invisible object. Our definition of invisible is different from transparent. We would say that light passes through a transparent object. We will say that light is diverted around an invisible object.

In this case we will consider light coming in from infinity so that all the light rays are parallel.




Now observe that light from infinity is diverted around the object if we have constructed the angles properly. This construction involves isosceles triangles with base angles of 30 degrees such that the bases of the two facing triangles are a distance of 1 apart and the length of each base (the vertical line) is sqrt(3)/2.

Under these circumstances, can you show that the path of the line at the beginning and end are in the same direction (or line).

See Mathematics Resolution on invisible objects for more information.