Inside A Spherical Mirror

Hey, Vsauce. Michael here. But you are actually right there. Well, at least the camera is. Mirrors are amazing.

In fact, the word "mirror" comes from Latin "mirari", meaning "to wonder at, to admire." It's also where we get the word miracle. Mirror-acle. Like when mirrors face each other and transform a toilet room into infinity. I love this kind of stuff. But what if instead of a rectangular prism, the room was a sphere, mirrored
all the way around? What would it look like? What would you see floating around in such a room?

The first question we should ask involves
the light source. If you were in this room using a flashlight and you turned the flashlight off, would the light keep bouncing around off of the mirrored walls, illuminating the room until your body absorbed all of it? Or if you left the flashlight on, would light continue bouncing around, building up, getting brighter and brighter until you lost your vision and cooked?

Probably not. Every time light hits a mirror and reflects off, a tiny tiny amount is absorbed. Even if your mirror spherical room was the size of a giant stadium and its walls reflected
99.99% of light on each reflection, light speed is just too fast, meaning that the reflections will happen rapidly, a little bit of light being lost each time. The room will go dark in a fraction of a fraction of a second. To you and me, it would seem instantaneous.

As for what it would look like, let's pretend you begin with your face up against a wall of the sphere and float backward toward and past the centre. At first, you would see your face quite clearly.
The surrounding reflections would be very distorted. As you moved away, at a certain point your face would cease to shrink away in appear smaller in mirror and instead would grow larger and become magnified until you reach the center at which point your face would fill your field of view. As you continued on past the center, your image would flip upside down and continue receding away.

It would look a bit like this. But don't get too enamored with your reflection because mirrors don't show you as you really are. Have you ever wondered why you liked the way you look in a
mirror but don't like how you look in photographs or video? It might be because of the mere-exposure effect. You prefer what you are used to and most mirrors you look into don't show
the real you, the you that other people in cameras see. Instead, a mirror shows you a reversed version of yourself and you've become more comfortable with that version of you. A version of you that is flipped left to right. Mirrors reverse along axes perpendicular to their surfaces, like left and right. They don't also flip things upside down, they don't also reverse up and down because those directions are parallel to the surface of the mirror. When it comes to the way you and other people look,
the difference can be startling. NPR pointed out that Abraham Lincoln looked like this. Mirrored he would have looked like
this. Now to us, something seems noticeably strange about it but it is the Lincoln Lincoln would have preferred. It's what he saw every day in the mirror. But here's something really cool. You can take a flexible mirror and unreverse its image by folding the mirror into a cylindrical shape. Take a look at this. Here I am with a reflective material and there is the camera with some text taped underneath, as you can see everything is flipped left to right. But as I fold the sheet into a cylindrical shape the image separates, revealing an unreversed version. It becomes a true mirror.

Finally, here is one last piece of every day mirror trickery. When you look into a mirror, how big is your reflection, your image on the surface of the mirror to you? Surely, it depends on how far away you are from the mirror. But it doesn't. When you look into a mirror your reflection on the surface of that mirror is always the exact same size. In fact, it is always about half of your actual size. This is because when light reflects off a mirror, it comes in and reflects back out at the same angle, which means that in order to reach your eyes at the top of your body, light from your feet at the bottom must hit the mirror halfway between the two. The triangles you form with a mirror are similar, regardless of where you stand. You can demonstrate this effect by outlining the size of your own head as it appears on the surface of a mirror using a bar of soap.

Now, because you aren't here let's pretend that this phone is your head and its camera is your eye. We begin up close. The camera looks really big from this perspective. Let me just carefully trace around the outside, so we can compare later. Good, good, good. Okay. Now, I'm going to pull away from the mirror. Clearly the phone is smaller, right? Well, if I reach out and once again carefully trace the edges. There we go. I will find that I have drawn a rectangle that is the exact same size. Your image on the surface of a mirror from your own perspective is always the same size, whether you are a few centimeters away from the mirror or a few kilometres away. Your image on the surface of a mirror in fact is always half your actual size.

Okay, enough about light returning to our eyes. What about light
that never returns? Could we use a telescope to resolve individual
aliens on a planet light years away? Well, over on Vsauce3, Jake investigates this question with Star Wars. And my friend Rusty investigates the potential for Star Wars becoming real in his episode of Science Friction. And Vsauce2 has a brand new lüt all about cool Star Wars stuff. Check them all out.
And as always,
thanks for watching.