Problem 28 · 2021 Math Kangaroo
Stretch
Geometry & Measurement
reflectionsymmetry
Two plane mirrors OP and OQ are inclined at an acute angle (diagram is not to scale). A ray of light XY parallel to OQ strikes mirror OP at Y. The ray is reflected and hits mirror OQ, is reflected again and hits mirror OP and is reflected for a third time and strikes mirror OQ at right angles at R as shown. If \(OR = 5\) cm, what is the distance d of the ray XY from the mirror OQ?
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Answer: C — 5 cm
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Hint 1 of 2
Unfold the bounces by reflecting the wedge so the light path becomes a straight line.
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Hint 2 of 2
The incoming ray is parallel to OQ, and the final hit at R is perpendicular to OQ — relate d to OR.
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Approach: unfold the reflections into a straight path
- Reflecting the mirrors turns the three-bounce path into a single straight ray; lengths are preserved.
- The ray starts parallel to OQ at height d and ends meeting OQ perpendicularly at R with OR = 5.
- The geometry forces d = OR = 5 cm.
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