1994 AIME Problems/Problem 14
Contents
Problem
A beam of light strikes at point
with angle of incidence
and reflects with an equal angle of reflection as shown. The light beam continues its path, reflecting off line segments
and
according to the rule: angle of incidence equals angle of reflection. Given that
and
determine the number of times the light beam will bounce off the two line segments. Include the first reflection at
in your count.
Solution
Solution 1
At each point of reflection, we pretend instead that the light continues to travel straight.
Then each intersection of the extended line with the rotated segments corresponds to a reflection in the original problem. We quickly see that the extended line will intersect each rotation of the angle by until
. Thus, our answer is, including the first intersection,
.
See also
1994 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |