I wanted to know the minimum height of mirror required to be able to view a complete image of a person. I considered the following setup:
$HF$ is the person in question. $H$ denotes the head, $F$ the feet, and $E$, the eyes. For the person to see his complete image, a ray each from $H$ and $F$ has to come and reflect into his
eyes ($E$). Let $HE = 0.16m$ and $HF = 1.84m$. $KG$ is the minimum height if mirror required.
Now, since $HI = IE = \frac{HE}{2} = 0.08m$ and $FC = CE = \frac{EF}{2} = 0.92m$, $KG = 1m$.
But this doesn't make any sense. This calculation doesn't take into account the distance of the person from the mirror. It is clear that the distance matters. If I have a really small mirror, and I go far away from it, I can see my whole body; which is not the case if I'm really close to it.
Best Answer
The minimum mirror height required to see your whole body in a mirror oriented in parallel to your body is half the height of your body. The top edge of the mirror should be half in-between the level of your eyes and the top of your head, and the bottom edge of the mirror should be at a level half way between your eyes and your feet.
This is independent of your distance to the mirror. Such can easily be inferred by drawing a picture that shows straight lines from your eyes going to the top of the head and to the bottom of the feet of your mirror image.