Leo Moser studied the effect that two face-to-face panes of glass have on light reflected through the panes. If a ray is unreflected, it has just one path through the glass. If it has one reflection, it can be reflected two ways. For two reflections, it can be reflected three ways.

a. Show the possible paths for three reflections.
b. Show the possible paths for four reflections.
c. Make a conjecture about the number of paths for n reflections.
d. Form a sequence of ratios of the number of successive paths. How do these numbers compare with π?

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O reflections, 1 path 1 reflection, 2 paths ## 2 reflections, 3 paths