Exploring the Obedient Ray Puzzle Journey
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.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
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?? ? ?
