Leo Moser studied the effect that two face-to-face panes of glass have on light reflected through the panes. If a ray is not reflected, 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. Make a conjecture about the number of paths for n reflections.
A) 1, 2, 3, 5, 7,....
B) 1, 2, 3, 4, 7,....
C) 1, 2, 3, 4, 5,....
D) 1, 2, 3, 5, 8,....
E) 1, 2, 3, 6, 12,....

Question

Quizplus · Accepted Answer

The pattern appears to be a Fibonacci sequence. The first two terms are 1 (no reflection) and 2 (one reflection). Each subsequent term is the sum of the two previous terms. Therefore, the sequence is 1, 2, 3, 5, 8, 13, 21,.... Choice D is the closest to this pattern.

Leo Moser Studied the Effect That Two Face-To-Face Panes of Glass