What Happens to Your Reflection if You Bend a Spoon Inward?

So Derek, I have a riddle for you.

I always get roped into these things.

[LAUGHS] Look at it.

Yeah, so I'm upside down.

DEREK: Upside down right there?

Yeah, to... And then I'm right side up.

It's something that we all noticed when we were in second grade.

DIANNA: You know what?

The riddle is that you could take this spoon, and you could push it through this way until it's convex, facing you.

So what would happen to your image as you're going from upside down to right side up?

This is a tricky question.

Hey, I'm Dianna, and you're watching "Physics Girl."

If you take a spoon and you look at the scoop side, the inside, then your reflection is upside down.

When you turn it the other way so the backside is facing you, your reflection is right side up.

Have you ever seen this before?

Yeah?

No?

Cool.

Now, how the flippy image-y thing works is already a little bit tricky.

But the setup to my riddle is a step further.

Imagine you could take this spoon and go from the concave side facing you, the scoop side, to pushing it through until the convex side is facing you, got it?

So it's like pushing through one of those poppers.

So your image goes from upside down to right side up.

And at some point in between, it's going to be flat, like a regular mirror, and then it's curved toward you.

Obviously, at some point, you have to flip.

So the question is, how does your image flip?

Basically, how does your image flip when you take a concave surface and warp it through being flat all the way to a convex surface?

It would warp around.

And you'd just get larger, and larger, and larger as you approach the focal point.

My image size will blow up to infinity and essentially be kind of undefined.

I don't think the image rotates.

And as you start to flatten out the spoon, it will continue to get larger, but still be inverted, up until the point where you flatten out the spoon.

And then the moment it reaches flatness, then it's back to the right-side-up normal.

It will go back down from infinity and it'll be right side up.

All those video submissions of the answer were from my patrons, who got the riddle early.

And apparently, I have really smart patrons, because they all had the right idea on a riddle that I struggled with.

OK. Let's dig into this.

The answer has to do with how far away you are from the spoon.

So in some ways, it's a trick question because there's something that you can do to get your image to flip without even doing anything to the spoon.

This is pretty interesting to see.

If you take the spoon and move it closer, and closer, and closer, really close to your eye, you'll notice that your eyeball is right side up.

Yeah.

That's my eye.

You can tell by blinking and noticing that you blink normal direction.

Is this actually for a YouTube video, Dianna?

DIANNA: This is.

So that means that you've passed this point where you're no longer upside-down, you're now right-side-up, which seems like a significant point to keep in mind as we're going forward.

OK. Let's do a diagram.

With optics, it's necessary.

It's so confusing.

Here's the concave mirror and here's you.

If I draw a couple light rays from the top of your head to the mirror and reflect them, they'll eventually meet somewhere.

That's where the image is, where the light rays actually meet-- where they converge, as we say in physics.

That's also the definition of an image, and we've made a real honest-to-goodness image of you, as in, if you put a screen here, the light rays would project a real, visible image onto the screen.

When I turned the U-Haul truck into a camera obscura, that was a real image being projected on the wall that you could see.

There's also such a thing as a fake image, and we can see that happen if we move you closer to the mirror.

It's where the light rays look like they're converging, but they don't actually.

So there's no light over here.

It doesn't pass the mirror.

We call that a virtual image, because if you put a screen there, nothing would appear.

There are no light rays there.

So actually, a regular flat mirror creates a virtual image of your reflection, not a real image.

The only way that you can get a real image with a mirror is if you have a curved concave mirror.

So let's go back and forth between the real and virtual image in our scenario.

When does it switch from one to the other?

Right here.

Eventually, there becomes a point where the light rays are parallel to each other, so they're never going to converge, so you don't actually have any image there.

Well, let's mark that point.

This happens to be the focal point of the mirror.

And this is a pretty pedantic point, but I feel like I have to say this, anyways.

This is only for strictly parabolic mirrors, or it's an approximation for spherical mirrors that are not too curved.

Otherwise, they don't have one focal point, they have aberrations that look like this, and it gets blurry and stuff, and it's a mess.

Then OK, keep moving.

You move past the focal point and the rays diverge, but they appear to converge on the other side in a right-side-up virtual image.

This is exactly what you see if you take the spoon and move it really close to you.

Eventually, the image flips, and you see it right-side-up.

If you want to see it a little clearer, take a look at one of those makeup mirrors, like the ones that really magnify your face.

And start far away from your face.

Look at your image, which should be upside-down, and then walk towards it.

Eventually, it'll get bigger, bigger, bigger, until it flips and you're right-side-up.

Derek from Veritasium happened to have this amazing perfectly parabolic mirror in his garage, so we walked back and forth and looked at what the image does.

It's bizarre.

As you get closer and closer to the focal point, your image gets massive, and then it flips as you move back and forth across the focal point.

So it seems like the image just suddenly flips from upside-down to right-side-up, which seems like a discontinuity.

How is that happening?

Well, your eyes are actually deceiving you because it's not one image flipping.

There are two separate images.

I know.

I'm confused too.

But it was a real image and then it becomes a virtual image.

The same thing happens if we curve the mirror instead of moving you.

So that's what happens to the image.

You go from a real image to a virtual image.

But what do you see?

That's the question.

As you curve the mirror, the image gets bigger, so that's part of the answer.

But then there comes a point where the image passes you and then it's behind you, but you're in front of the focal point.

So what happens there?

Well, there's no image you can see in front of you anymore, so things are just blurry.

And then eventually, the virtual image starts coming from the other side and shrinks back down again.

So this is what you'd see with an animation.

Since it's not easy to bend a spoon, we did an animation showing what would actually happen if you looked at a curved surface bending like this.

You notice the image gets bigger and blurry, and then shrinks back down, flipped.

One of my patrons had this brilliant idea for a contraption that takes a stretchy material, and with a little pressure from a bottle, she was able to bend the surface inward and outward and see how it affects the image of four colored lights shining above.

And now your toy popper spoon is convex.

DIANNA: So smart.

So all of this isn't just stuff of riddles, it turns out bending mirrors and lenses is actually really useful.

Optical telescopes use a sophisticated version of this demo in what's called adaptive optics.

When you're imaging stars and galaxies from earth, that star light has to travel through earth's atmosphere, which distorts the light to make a blurry image.

Adaptive optics essentially deployed deformable mirrors that reverse the effect of atmospheric distortion, and this makes it possible to create high-quality images without having to launch a telescope into space beyond the atmosphere.

And then another application is in your eyeball.

The intraocular lens is used when people with cataracts or nearsightedness may choose to remove their eyes' natural lens and replace it with this intraocular lens, which focuses light on the retina to form an image.

And some models of this type of lens are deformable, meaning that they can allow the eye to focus at different distances.

That's pretty cool.

I hope you enjoyed this riddle, and if you've got any more awesome physics riddles, send them to me on Twitter, maybe, @ThePhysicsGirl, or leave them in the comments.

I love riddles.

Thanks for watching and happy physics-ing.