Derive:
Number of images formed by two plane mirrors inclined at an angle of $\theta$ is given by $$\frac{360}{\theta} -1 $$
What I think: Inclined mirror forms images in the circle and one image lies in one sector.
No of images = Number of sectors=$\frac{360}{\theta}$
And $1$ is subtracted from $\frac{360}{\theta}$ because a sector is occupied by the object.
I think this is not a proper derivation. How to prove that Inclined mirror forms images in the circle?
I saw an answer but I didn't understand it.
How to derive it formally?
What's correct:
Let $$n=\dfrac{360}{\theta}$$
where $\theta$ is the angle between the two mirrors
If $n$ is even: $$\mathrm{Number\ of\ images}=n-1$$ If $n$ is odd and the object is placed symmetrically: $$\mathrm{Number\ of\ images}=n-1$$ If $n$ is odd and the object is not placed symmetrically: $$\mathrm{Number\ of\ images}=n$$ If $n$ is in decimal then only integral part is taken and above rules are followed.
It should be noted that above the 'number of images' means the number of images formed.
Experiment work:
$\color{red}{\theta=30^\circ}$
Simulator:
Plus corner:
I don't think there exists a derivation to the above formulae. Maybe it was found by experiments.
Note: A very tiny change in the angle can spilt the farthest image.
Reflection of light in mirror is the same as reflection of the world in the mirror. See this
So, just do that... Let us consider your $\theta=60^o$. The original setup looks like this...
Now... REFLECT THE WORLD !!!!
There you go! Cheers :)