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

[shashank010288]

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

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

 

[Gokul43201]

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.

 

[shashank010288]

I want a proof for general angle

 

[pervect]

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.

 

[Gokul43201]

I want a proof for general angle

Any angle Ccan be shown to satisfy the above criteria for a suitable choice of n.

 

[Tide]

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.