Why are 8 images formed for a object kept symmetrically between two mirrors kept at angle 50°? Let us consider two mirrors $M_1$ and $M_2$ kept at $50^\circ$ with each other.
An object $O$ is kept symmetrically between the mirrors making angles $25^\circ$ with each.
Now the number of images is given by the formula:
$$n = \frac{360}{\theta},$$
where is $n$ is odd. The number of images is $n$ for a asymmetrically placed object and $n-1$ for a  symmetrically placed object.
If $n$ is even, the number of images is $n-1$ for all positions of the object.
Applying the formula to this case we get
$$n=\frac{360^\circ}{50^\circ} = 7.2,$$
ignoring the decimal part. As the object is symmetrically placed, number of images becomes $n-1 = 6$.
But the ray diagram I have drawn shows otherwise.

Here 8 images are formed. So which one should I follow, the ray diagram or the formula?
 A: The formula 
$n = \frac{360}{\theta}$ 
has on one side an integer and on the other a continuous variable. This should give you pause. For correctness, we may either restrict $\theta$ to precisely those values which give integral $360/\theta$ or modify the formula.
So, for $50^\circ$, the formula doesn't hold.  Truncating the decimal isn't something the formula can do and so it can't be expected to yield a right answer.
Anyways, for the symmetric case, 
the general formula would be
$n=2\left\lfloor m\right\rfloor+
\lceil\{m\}\rceil(1+\lceil\{m-1/2\}\rceil)$ 
where
$m=\frac{\pi-\phi}{2\phi}$
$\theta=2\phi$ 
and {} denotes fractional part.
This, indeed, gives $n(25^\circ)=8$.
For $\theta=\frac{2 \pi}{k}$, $k$ integrer,  
$n\left(\frac{2 \pi}{k}\right)=k-1$
as expected
Extending continuous variables to discrete casses can sometimes be tricky.

The first term in the formula is just the ordinary "above the mirror" reflections. The $\lceil\{m\}\rceil$ is to terminate the formula in case the reflection falls on the mirrors. The "$(1...$" is for those last two reflections just below the mirrors. The last factor$\lceil\{m-1/2\}\rceil$, corrects for $\theta=\frac\pi2,\frac\pi3,\frac\pi4,\frac\pi5,...$ when those two last reflections coincide.
$\lceil\{x\}\rceil$=$0$ for $x$ positive integer, $0$ otherwise
