Viewing yourself in a mirror is a special situation as the object (you) and the viewer (also you!) are always at the same place!

Consider the following man looking at himself in a mirror placed on wall M.

Looking at the top of his head determines where the top of the mirror needs to be.

Looking at his chin determines where the bottom of the mirror needs to be.

Thus, to see his whole head, the mirror only needs to be of this size:

This mirror height is actually half of the height of his head.

We can see this by considering the following dimensions and applying the concept of similar triangles.

For clarity the following diagram we can see that the big blue triangle is mathematically similar to the smaller darker triangle.

Thus the mirror height, h, can be determined from:

H/2D = h/D

=> h = ½H

Note that we didn’t give a value for D, so it is the same whether the man is very close to the mirror or far from the mirror.

 

I masked off a mirror so that I can just see the whole of my body from head to feet.

I start at the back of the room…

and move closer….

and closer….

and closer….

until I get right up close to the mirror.

Notice that as I move closer to the mirror, I can still see the whole of my body from head to feet. I always completely fill the hight of the mirror.

Also note that this is not true for the rest of the image viewed in the mirror.

Far from the mirror and I can see little of the surroundings. As I move closer to the mirror, I see more and more of the room.

 

<< Back

Reflection

Next >>