Viewing you full length in a mirror

[user1252452035]

Hey guys, I've got a quick question if you don't mind.

I understand that in order to view your full length in a mirror, that only a half-length mirror is needed; however, I'm wondering if this is true to just only see your face (if it was held up in front of you). So if my face is 15 inches, I would, theoretically need a mirror that is 7.5 to see my entire face, right?

The reason why I'm asking is that I don't know how the reflections will interact with "what I see." Is it the top half of my face (above the eyes) that can be disregarded of the mirror?

I'm not sure.

Thanks in Advance!

 

[Doc Al]

...to view your full length in a mirror, that only a half-length mirror is needed...

If you understand why that's true, you should be able to answer your own question. Here's how to understand it: If you stand a distance D away from a plane mirror, your mirror image (which is the same size as you) appears to be a distance 2D away from you. Draw a diagram of you, the mirror, and your image. Then draw lines representing your eyes looking at your feet (in the mirror), at the top of your head, then anywhere in between. Any part of the mirror that you don't need in order to see everything from your feet to the top of your head can be cut away. How big is what's left?

Then apply the same reasoning to viewing just your face.