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

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The formula for the number of images created by two mirrors inclined at an angle is given by [360/θ] - 1. To prove this, one must analyze the positions of images starting from the principal images and stop when two images coincide. The discussion emphasizes that the number of images remains independent of the observer's position, although specifying this position could be beneficial. It is noted that any angle can be accommodated by selecting an appropriate value for n. The inclination of the second mirror increases the angle of incidence by β/2 with each reflection, which is crucial for understanding the image formation.
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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

360/(n+1) < \theta < 360/n

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 \beta then the angle of incidence is increased by \beta / 2 at each reflection.
 
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