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.
1 Answer
$\begingroup$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 :)
$\endgroup$ 10
