The Obedient Ray Puzzle Journey
The Obedient Ray
Penguin Book of Curious and
Interesting Puzzles No. 378
The Obedient Ray
Two mirrors are fixed at O and a ray of light enters,
bounces around and goes out on the same path.
Given distance OX, what is the height of the ray
above the base mirror (to which it is parallel)?
What is the angle between
the mirrors?
The Obedient Ray
The Obedient Ray
The Obedient Ray
The Obedient Ray
The Obedient Ray
The Obedient Ray
RESOURCES
The Obedient Ray
Two mirrors are fixed at O and a ray of light enters,
bounces around and goes out on the same path.
Given distance OX, what is the height of the ray
above the base mirror (to which it is parallel)?
What is the angle between
the mirrors?
SIC_42
Delve into a series of curious and compelling puzzles involving ray reflections between two fixed mirrors. Discover the heights, angles, and intricate relationships within this fascinating optical challenge.
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Presentation Transcript
The Obedient Ray Penguin Book of Curious and Interesting Puzzles No. 378
The Obedient Ray Two mirrors are fixed at O and a ray of light enters, bounces around and goes out on the same path. Given distance OX, what is the height of the ray above the base mirror (to which it is parallel)? What is the angle between the mirrors? ? ? ? ?
The Obedient Ray Considering the angle, ? , first: 90 + 4? = 180 ? = 22.5 ? 90 ? 2? normal ? ? 2? 2? ? ? ? ?
The Obedient Ray From similar triangles: 2? 2 =? ? So ? = ? ? 45 2 2? 45 ? 90 ? 45 ? 45 ? ? ?
The Obedient Ray In the scenario previously shown we can define ? = 2, i.e. the number of times the ray reflects off the upper mirror. What would the value of ? be if ? = 3,4,5, ? 90 5? Can you generalise? 90 3? 90 ? ? ? 6? 2? 10? 4? 8?
The Obedient Ray For ? = 1 , 90 ? is equal to ? 90 5? 90 3? 90 ? ? ?
The Obedient Ray For ? = 1 , 90 ? is equal to ? For ? = 2 , 90 3? is equal to ? 90 5? 90 3? 90 ? ? ?
The Obedient Ray For ? = 1 , 90 ? is equal to ? For ? = 2 , 90 3? is equal to ? For ? = 3 , 90 5? is equal to ? 90 5? 90 3? 90 ? ? ? We can infer that for ? reflections: 90 2? 1 ? = ? ? =45 ?
SIC_42 The Obedient Ray Two mirrors are fixed at O and a ray of light enters, bounces around and goes out on the same path. Given distance OX, what is the height of the ray above the base mirror (to which it is parallel)? What is the angle between the mirrors? ? 10?? ? ?
