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Tadashi: So here's a mirror of sorts, it's curved.
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!
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Reflected Cats - Numberphile

15 分類 收藏
林宜悉 發佈於 2020 年 3 月 28 日
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