Stacks of Reflecting Plates

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A ray of light enters a stack of glass plates. The ray can either pass through a plate or be reflected by it. This Demonstration shows all the possible ways the ray has to leave the stack after reflections. If is even, the ray traverses the stack, otherwise it leaves the stack on the same side it entered.


With plates, the surfaces are labeled , with denoting the lower surface of the lowest plate, and a ray with reflections is uniquely determined by surface labels.


Contributed by: Adriano Pascoletti (June 2009)
Open content licensed under CC BY-NC-SA



With two plates the number of paths with reflections is the Fibonacci number . With three plates the number of paths is for , which is Sloane's sequence A006356.


R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, 2nd ed., Reading, MA: Addison-Wesley, 1994 p. 291.

Sequence A006356 in N. J. A. Sloane, ed., The On-Line Encyclopedia of Integer Sequences, 2008.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.