Can the Formula for the Number of Images by Two Inclined Mirrors Be Proven?

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Discussion Overview

The discussion revolves around the formula for calculating the number of images formed by two inclined mirrors, specifically the expression [360/$]-1. Participants seek to explore proofs for this formula, particularly for general angles of inclination between the mirrors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the formula for the number of images and requests a proof.
  • Another participant suggests considering the angle range 360/(n+1) < θ < 360/n and proposes finding image positions from principal images, indicating a personal intent to explore this further.
  • Several participants express a desire for a proof applicable to general angles, emphasizing the need to establish that the number of images is independent of the observer's position.
  • It is mentioned that any angle can be shown to satisfy the criteria for a suitable choice of n, though specifics are not provided.
  • A participant notes that the angle of incidence increases by β/2 at each reflection when considering the inclination of the second mirror.

Areas of Agreement / Disagreement

Participants generally agree on the need for a proof of the formula for various angles, but multiple competing views and approaches remain regarding how to establish this proof and the conditions under which it holds.

Contextual Notes

There are limitations regarding the assumptions made about the observer's position and the specific conditions under which the formula applies. The discussion does not resolve these aspects.

Who May Find This Useful

Individuals interested in optics, geometry, and mathematical proofs related to mirror reflections may find this discussion relevant.

shashank010288
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The formula for no. of images by two mirrors inclined at $ angle is

[ 360/$]-1
can anybody prove it?
 
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Consider an angle

[tex]360/(n+1) < \theta < 360/n[/tex]

Find the positions of the images, starting from each of the pricipal images. When two images have the same position, stop.

I'll try this myself, when I find the time.
 
I want a proof for general angle
 
shashank010288 said:
I want a proof for general angle

Well, the first goal is to prove that the number of images is independent of the poistion of the observer, or perhaps you could specify the position of the observer.
 
shashank010288 said:
I want a proof for general angle

Any angle Ccan be shown to satisfy the above criteria for a suitable choice of n.
 
If the inclination of the second mirror with respect to the first is [itex]\beta[/itex] then the angle of incidence is increased by [itex]\beta / 2[/itex] at each reflection.
 

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