From the diagram have a similar construct that is reflectant to radiation on the inside and have a airtight seal at the entrance of the construct that allows radiation to pass through. Then have a complete vacuum on the inside. Now All the coloured arcs have origins at the similarly coded numbers. Then where the arcs meet the edge , the edges must be rounded incliding the edges of the flat slate. Then at the point E a ray of radiation S enters the construct and as it reflects around the loop, the angle of reflection becomes more and more acute, until it strikes the flat slate and then becomes more obtuse such that it does not exit the loop.
That no ray of radiation that enters the construct can ever exit as long as it is reflecting.
Take the most acute possible angle of reflection and allow it to reflect just inside the beginning of the flat slate and then show that it cannot exit.
So we prove it by taking an even more acute angle of teflection, a straight line from the origin of the circle on the inside of the construct.
Now just such a line is drawn in the diagram marked in red, and after reflecting against the slate it does not exit the construct.
Please note the diagram is saved in Illustration #1.