Images formed by a pair of plane mirrors I've been taught that if a point-sized object is placed between two plane mirrors at an angle theta with each other, then the number of images formed is $360^{\circ}/\theta$ or $360^{\circ}/\theta - 1$, depending on whether $360^{\circ}/\theta$ is even or odd.
Moreover, if $360^{\circ}/\theta$ is non-integral, we simply floor the value. So if, say, the angle between the mirrors is $65^{\circ}$, we will get ${\rm floor}\,(360/65) = 5$ images.
However, on actually drawing the figure, I'm easily able to obtain 6 images, and probably more too.
$65^{\circ}$ with 6 images" />
If the formula is erroneous, what is the correct formula?
P.S. This is definitely not a homework question. Even some books I've seen have published the formula ${\rm floor}\,(360/65)$.
 A: No. of images formed by 2 inclined mirrors:
$n=\displaystyle{\frac{360^o}{\theta}-1}$
Exceptions:
when $~\displaystyle{\frac{360^o}{\theta}}$ is an odd integer and the object is placed asymmetrically,
$~n=\displaystyle{\frac{360^o}{\theta}}$
when $~\displaystyle{\frac{360^o}{\theta}}~$ is not an integer,
$~~n=\displaystyle{\Bigg[\frac{360^o}{\theta}\Bigg]}$
where [ ] denotes the greatest integer function.
A: All the images formed by two inclined mirrors ($\theta$), of an object placed between them, are formed on a circle centred at the point of intersection of the two mirrors and with a radius equal to the distance of the object from the centre.
The first pair of images will be the direct pair and the angular separation between them will be $2\theta$.
Now there will be cross-forming of images from these direct images.
The separation between the second pair of the images will be $4\theta$ and so on.
For the $n^{th}$ pair, the separation will be $2n\theta$, only if $2n\theta\leq 360^\circ$.
If $2n\theta=360^\circ$, then out of the $2n$ images, the final pair will act as one image. Thus, the total number of images will be $\frac{360^\circ}{\theta}-1$.
When $2n\theta$ exceeds $360^\circ$, then the final pair won't form. Only the $(n-1)^{th}$ pair will form, thus $2n-2$ images in pair. Now, whatever space is remaining on the circle of images, can be utilized by one mirror or the other to form a single image.
The complete mathematical analysis can be found here.
https://thephysicist.in/understanding-inclined-plane-mirrors/
A: Actually only 5 images will be formed if more images are drawn they will overlap the existing ones if drawn with perfect geometry.
