And in front of this mirror, I put this rectangular sheet (with something drawn on it).

And when you put it in front of the mirror

and look inside the mirror

you see a cat.

You know, with pointy ears

and side protrusions that look like whiskers and everything.

So, I am very happy with this cat.

I'm proud of this cat.

A nice cat, I will say.

But when I show this to a mathematician

and theoretical physicist colleagues

Some people like this

because they have good taste.

But others say

So?

Well, that's really sad.

I hoped that they didn't say so.

But for those of us who'd like to say so: here's the thing.

In front, you have a mirror, indeed

but that's what we call a "convex mirror."

So it's bulging out towards us.

In the back, inside of the tube

there is a concave mirror.

Which is bulging away from us.

So now, I'm going to put

another cat inside

and look at what happens.

And if you look from the correct angle

you see another cat inside.

By the way, some people might wonder

how many reflections are bouncing off before it reaches our eyes.

But in fact it is just one reflection.

It's reflecting on the back side and then coming out.

So you have a cat on the inside.

Now, the slightly odd thing is

that cat on the inside

looks very much like the cat on the outside.

Although the cat on the outside is from a convex mirror

whereas the cat on the inside is from a concave mirror.

So convex and concave

I mean they are opposite things

and you might expect the distortion effects to be the opposite

but they look very very similar.

So that's quite interesting.

It's not much of a hint

but one thing that has to do with this effect is the following.

This arrow

is pointing from left to right.

And if you look at it's image reflection

in the mirror in front, the convex part

it's still pointing from left to right.

But let's look at it on the inside on the concave mirror.

It's pointing from right to left!

So that's quite interesting

it reversed it's direction.

So, it's a matter of

where the center of focus you are placing the arrow.

As I move the arrow inside, or according to the outside, move the mirror

you see the arrow changing it's shape

and

somehow it sort of blurs out

and eventually at the end

you come to the point where you see the real image next to the original arrow.

So you can do something like this

with a cylindrical mirror

and little rectangular sheets of paper.

When I first thought of this

you know I thought something like this might be interesting to try.

The major problem I faced was

where do you find a cylindrical mirror?

I mean, if you have

a flat mirror

you know, slightly bulging out or bulging in

so it changes the size of your image

and so in a way, you can find that in cosmetic shops

and so forth.

But

where do you find a cylindrical mirror?

A tube-like mirror?

And I thought and I thought

and finally

I went to the shopping center and I found one!

These are cookie cutters!

It's a cookie cutter, you know, where you

make the cookie dough and then cut the shapes.

So you can buy 1 for $1.

And, with that

you can make a cat in the mirror!

Brady: A cat in the cookie cutter?

Tadashi: That's right!