# Contest Problem

The walls of an angle $0$< $\theta$< $\pi$ are mirrors. The angle sits in the plane, with its vertex at the origin, first wall along the positive x-axis, and second wall in the upper half plane. A ray of light originating somewhere in the upper half plane hits the first wall (away from the vertex) at angle $\alpha$ and is reflected by the mirrors $N$ times before it moves away along a line that forms an angle $\beta$ with the x-axis and never meets the walls again. Compute $N$ and $\beta$ in terms of $\theta$ and $\alpha$.

#### Full solutions by:

December: Emil Alegría, Gregory P Constantine

October: Jacob Mckibbin

September: Gregory P Constantine

#### General Information:

This is a monthly contest for Pitt undergraduate students. The monthly problem will be posted here and on the Undergraduate Contest section of the bulletin board in 705 Thackeray Hall.

Written solutions to the monthly problem should be submitted by 4PM of the last business day of the corresponding month. Please submit your solutions to the mailbox labelled "Undergraduate Contest" in 301 Thackeray Hall. Late submissions are not accepted. Please remember to include your name and e-mail address.

The winner will be selected in a random drawing from all eligible entries that contain a full and correct solutions to the month's contest problem. The winner will be notified by e-mail. The winner will receive a prize and the names of all the people that submitted a correct solution will be posted on the Undergraduate Contest section of the bulletin board in 705 Thackeray Hall.