The sugar water barber pole effect | Optics puzzles 1

Summary

The video explores an intriguing visual phenomenon - shining polarized light through a cylinder of sugar water creates colorful spiral patterns down the tube and a kaleidoscope of hues out the other end. To deeply understand the reasons behind the twisting light waves and changing colors requires diving into several key concepts about the nature of light itself - such as circular polarization, frequency dependence, and the directionality of scattering. By building an intuition for what light truly is, the explanations for the patterns emerge organically, transforming abstract facts into inevitable discoveries.

Takeaways

• 😀 The setup involves shining polarized light through a cylinder of sugar water and observing the resulting colors and patterns.
• 👉 Key questions: Why does the sugar cause the light to twist? Why does twisting rate depend on frequency? Why diagonal stripes from the side?
• 🤔 Need solid intuitions about circular polarization, frequency-dependence of refraction, and directionality of scattering.
• 🌈 Different colors twist at different rates, separating the polarization directions.
• 🔀 A second polarizing filter causes an imbalanced combination of colors.
• 🎡 Rotating the first filter changes which colors pass through the second filter.
• 🔬 Sucrose is a chiral molecule, interacting differently with left/right circular polarization.
• ⚗ Mathematical understanding of refraction explains dependence on frequency.
• 🎯 Scattering direction depends on polarization direction, causing diagonal stripes.
• 💡 Aim is for intuitive understanding of what light actually is, not just facts from authority.

Q & A

What causes the twisting of the light as it passes through the sugar water?

The key is that sucrose is a chiral molecule, meaning it has a handedness and is different from its mirror image. This causes slightly different effects on right-handed versus left-handed circularly polarized light, resulting in the twisting.

Why does the rate of twisting depend on the light frequency?

The rate of twisting depends on how much the light appears to slow down in the material. This slowdown is ultimately explained by the frequency of the light, with higher frequencies slowing down more.

Why do you see diagonal stripes when viewing from the side if the light is still white at each point?

The direction light scatters depends on its polarization direction. So even though the overall light is still white, the components scatter differently, allowing you to see the separated colors from the side.

What causes circularly polarized light?

Circularly polarized light consists of two perpendicular plane waves with a phase difference. This causes the electric field vector to trace a helical path, rotating uniformly around the propagation direction.

Why does light appear to slow down in materials?

Light interacts with the electric charges in the material, which causes it to effectively take a more "zig-zag" path, increasing the time it takes to traverse the material.

What exactly is "wiggling" or oscillating in a light wave?

For visible light, it is the electric and magnetic fields that are oscillating perpendicular to the direction of propagation. The oscillation causes the fields to drive oscillations in charges they encounter.

How can you create polarized light at home?

You can create linearly polarized light by shining light through a polarizing filter, which only allows through waves oscillating in one direction.

What causes light to scatter?

Light scatters when it encounters inhomogeneities - variations in composition or density. This causes some of the wave to change direction.

What is a chiral molecule?

A chiral molecule lacks internal symmetry - it cannot be superimposed with its mirror image. Common examples are DNA, proteins, and sugars.

Why does rotating the filters change the observed color?

Rotating the filters changes the alignment with the separated polarization components in the tube. This changes how much of each color passes through the second filter.

Outlines

00:00

🎥 Setting up the polarized light demonstration

The paragraph describes the initial setup for a demonstration using polarized light shined through a cylinder of sugar water. There are two polarizing filters, one at the start and one at the end. The narrator asks viewers to predict what will happen when the light is turned on based on this setup.

05:00

👀 Observing the intriguing effects of polarized light in sugar water

When viewed from the side, rotating the polarizing filters creates colorful diagonal stripes moving up the tube. The rate of 'twisting' depends on light frequency, causing separation of colors. To fully explain these effects requires understanding fundamentals about light including polarization, scattering, and how materials impact propagation.

Keywords

💡polarized light

Polarized light refers to light waves that vibrate in a single plane. The video mentions that the light first passes through a linear polarizer, which filters the light to vibrate in one direction only (e.g. up and down). This polarized light then passes through the sugar water and undergoes further changes. Understanding polarization is key to explaining the visual effects seen in the cylinder.

💡twisting

As the polarized light passes through the sugar water, the direction of vibration rotates or 'twists' around the axis of the cylinder. The rate of twisting depends on the light's frequency, with higher frequencies twisting faster. This differential twisting of colors is what leads to the separation of colors and visual effects.

💡circular polarization

The twisting of the polarized light results in circular polarization, where the light vibrates in a helical pattern. The handedness of circular polarization relates to the chirality or handedness of the sugar molecules, which interact differently with right vs left circularly polarized light.

💡frequency dependence

A key effect is that the twisting rate depends on the light's frequency, with higher frequencies (violet, blue) twisting faster than lower frequencies (red, orange). This leads to separation of colors down the length of the cylinder.

💡chirality

Many molecules like sucrose sugar are chiral or 'handed', meaning they are distinct from their mirror image. This molecular handedness relates to the different effects on right vs left circularly polarized light, inducing the twisting.

💡index of refraction

The slowing down of light in a medium is quantified by its index of refraction. The frequency dependence of the index explains why different color light twists at different rates in the sugar water.

💡scattering

The diagonal stripes of color seen from the side are due to scattering of light. The polarization direction affects the scattering direction, causing the color variations seen from the side.

💡white light

Although the colors separate along the cylinder's length, the light remains white at any given point since it still contains the full spectrum. Side viewing shows the color effects by scattering particular polarizations.

💡second polarizer

By passing the output light through a second polarizing filter, particular colors/polarizations are filtered out depending on the filter alignment. This selects particular imbalanced color combinations to be viewed.

💡intuition

The video emphasizes building an intuitive understanding for optical phenomena like polarization, scattering, chirality etc. vs just stating facts. This intuition is key for fully explaining what causes the observed visual effects.

Highlights

Understanding what polarized light is and how it interacts with sugar water leads to an intriguing visual effect with colorful spiral bands.

Polarized light can be thought of as a wave propagating in one direction while wiggling perpendicular to that.

The key questions are: why does sugar cause the twisting, why does twist rate depend on frequency, and why do diagonal color stripes appear from the side?

Sucrose is a chiral molecule, meaning it interacts differently with right or left circularly polarized light, causing the twisting.

The frequency dependence comes from light slowing down at different rates in the material, separating colors.

The side view shows stripes because scattering direction depends on polarization direction in a structured way.

To fully understand this requires intuitions about polarization, circular polarization, scattering, and how materials affect light speed.

White light contains many frequencies, and they twist at different rates to end up with different final polarizations.

A second polarizing filter lets through different amounts of each twisted color, giving a new combined color.

Rotating a filter changes which colors pass through the second filter, changing the final mixed color.

You can recreate this at home with sugar water and polarizing filters, rotating to see different colors.

It's unclear why side view would show stripes since at each point colors are still balanced white light.

Key question is why scattering would discriminate between frequencies when light is still white at each point.

Understanding what light fundamentally is allows these phenomena to emerge inevitably rather than be facts from authority.

Need to revisit the basic question of what is light and what exactly is wiggling as an electromagnetic wave.

Transcripts

The setup here starts with a cylinder full of sugar water,

basically, and we're about to shine some white light into it,

but before it gets there, it passes through a linearly polarizing filter.

And what that means, basically, is that if you look at all of

the light waves beyond the point of that filter,

those waves are only going to be wiggling in one direction, say up and down.

And don't worry, in a few minutes we're going to go into much more detail

about what specifically is wiggling and what the significance of that

wiggling direction is, but skipping to the punchline first,

the demo also includes a second linearly polarizing filter coming out the other end,

and I want you to predict what we're going to see once we turn the light on.

Now I suspect some viewers might already have a little bit of a sense for

what's going on, because a few years ago Steve Mould made a really excellent

video about this phenomenon of shining polarized light through sugar water.

It was really well done, which is no surprise because everything Steve makes is,

but even if you watched that, this is a rich enough phenomenon

that there's still more to be explained.

In fact, even if you made that video, this is a rich

enough phenomenon that there's more to be explained.

I'm curious, Steve, when you made that video, did you happen

to get a good view of the side of the glass, probably when the

rest of the lights in the room were off or something like that?

No.

No, I didn't think about the side view.

Great.

So given the setup that we're looking at now, once we turn off the room lights

and turn on the lamp, I'm curious if you have a prediction for what you might see.

Well, there will be some scattering, I suppose,

but then if we're just looking at the tube, we're not applying any kind of filter

to just looking directly at the tube.

So, I mean, my instinct is nothing will happen.

That would have been my guess too, but let me just show you what it

looks like when we turn off the room lights and we turn on the lamp.

Ooh.

And then if you turn the initial polarizer, you can kind of see those.

Wow.

Stripes, those diagonal stripes seem to walk up the tube.

Oh, wow.

But why diagonal?

Exactly, why diagonal?

But why anything?

I mean, why anything?

Something about the interaction with sugar water separates the light out

into these different bands of color, but it does so in this really intriguing way,

where the colors appear to form these spiral helixes down the tube.

And the other thing I want to draw your attention to is the color

that's coming out of the tube after it passes through that second filter.

As we rotate the first filter, you rotate through a family of distinct hues.

And it doesn't have to be the first filter if you rotate that second filter,

you also rotate through these various different colors.

That's Quinn, by the way, who kindly set up this whole demo.

And what I love about this setup is that if you want to really understand what you're

looking at with that deep to your bones satisfying sense of what's going on,

it requires having very solid intuitions for a number of different fundamental concepts

about light, like polarization, how scattering works,

and how an index of refraction works.

To kick things off, let me show you the overall structure for the explanation of what's

going on here, and along the way record various questions that we still need to answer.

A basic premise to the whole thing is to think about polarized

light as a propagating wave which is wiggling in just one direction.

And I suppose question number zero is for us to be clear about what exactly is wiggling.

Postponing that for the moment, we'll just say if we think about

it as propagating in one direction, say along an x-axis,

the wiggling happens perpendicular to that, say in the z-direction.

What's going on when it passes through this tube of

sugar water is that that wiggling direction gets twisted.

And so the first key question is why?

What is it about interaction with sugar that causes this twist?

And just so that it's crystal clear what I mean by twisting,

if you focus your attention on a single slice perpendicular to the axis of the cylinder,

and draw a line indicating how the light is wiggling on that slice,

then if you were to move that slice down the cylinder,

the relevant wiggling direction slowly turns about the axis of the cylinder.

Critically, the rate at which it's getting twisted depends on the frequency of the light.

Higher frequency light, say violet, actually gets

twisted more quickly than low frequency light, like red.

So the second key question we need to answer is

why would that twisting rate depend on the frequency?

Whatever explanation we come to for why the twisting happens in the first place,

it should offer some intuition for where the dependence on frequency would come from.

Let's take a moment to think about what it means that

different colors of light are getting twisted at different rates.

In the demo we're shining in white light, and white light is not a clean pure sine wave,

it's something more complicated.

And you typically think about it as a combination of many different pure sine waves,

each one corresponding to one of the colors in the rainbow.

For this animation I will schematically represent the

wiggling direction for each pure frequency, just with a line.

So the key idea is that as all of those different waves propagate down the tube,

with different pure frequencies twisting at different rates,

purple light twisting the fastest and red light twisting the slowest,

then the polarization directions for each one of those pure colors get separated out.

For example, by the time you reach the end of the tube,

they all have their own distinct wiggling directions.

But one thing that's important to understand is that this is still white light.

If you were to put your eye at the end of the tube and look towards the lamp,

it wouldn't look colored in any way, because even if the wiggling directions are

all different, they're still the same amount of each color as there was at the start.

In order to see any evidence of this separation,

one thing you could do is pass it all through a second linear polarizing filter,

say in the vertical direction.

The effect that has is that the amount of light of a given frequency passing through

is equal to the component of its polarization direction that lines up with the filter.

So colors which happen to align very closely with that filter

pass through almost completely, whereas colors which end up

more perpendicular to the filter pass through only very weakly.

So the light coming out the other end of this filter is some imbalanced

combination of all of the pure frequencies, which is why what we see

coming out the other end is no longer white, but some other color.

And notice if we rotate the whole setup, say by twisting the initial polarizing filter,

then that changes the components of each pure frequency that happen to be vertical,

resulting in a different balance of all those colors,

which is why rotating the initial filter changes the color you see coming out

the other end.

And this is something you can do at home, by the way.

You don't need a very fancy setup.

Start by creating a pretty dense mixture of sugar water,

and then you'll need to get your hands on some polarizing filters so that you can

pass light first through one of those filters, then through the sugar water,

and then through a second filter.

And if you look at this whole setup from the top,

as you rotate one of those filters, you'll see different colors.

But even if you understand this, the thing that really had me

scratching my head when Quinn showed me this demo was why you

would see diagonal stripes when you view the cylinder from the side.

I mean, take a moment to think about this.

At any point down the tube, even though all the colors have been rotated differently,

again, the light at that point is still white.

It's still an equal balance of all the different colors.

If you were to stick your eye inside the tube and look towards the lamp,

you would see white.

So why would viewing it from the side change what you see?

The way I've made this animation, I've just left a faint shadow representing

the wiggling direction for each color along the way down the tube.

But that's just a cartoon.

It's a schematic representation.

Why is it that the actual way that light interacts with the molecules

within the tube would discriminate between the colors in any way?

And why would the stripes be diagonal?

Wouldn't you think the setup should be completely symmetric from top to bottom?

So these are the main questions we need to answer.

Why would sugar cause the light to twist?

Why would the rate at which it twists depend on the frequency of the light?

And why, even if you understand both those facts,

would you be seeing different colors appear in these diagonal stripes?

You can answer these questions if you have a handful of key intuitions about optics.

The first question requires understanding circularly polarized light,

since the key is that sucrose is a chiral molecule,

which is to say there's a handedness to it, it's different from its mirror image,

and the slightly different effects that it has on right-handed versus left-handed

circularly polarized light ends up explaining the twist.

The second question requires understanding why light

appears to slow down when it passes through a material.

A sufficiently mathematical understanding for where that

slowdown comes from ultimately explains the color separation here.

And the third question comes down to the fact that when light scatters off of a material,

it's not like some projectile bouncing in any old direction.

The direction of scattering depends on the direction of polarization,

and there's a very good reason for it.

My aim is for all of these answers to feel less like facts that I'm

handing down from on high, and more like inevitable discoveries

emerging from a fundamental understanding for what light actually is.

For that, we'll begin by returning to that question number zero, what exactly is wiggling?

Which is to say, what is light?

If you're curious about how the full explanation unfolds, come join me in the next video.