Buckets of water

I was asked why a bucket full of water looks shallower than an empty one, so I pulled out an old physics book to find the answer. It's been many years since I've taken optics, although recently I've developed a new interest for it.

Refraction occurs because the speed of light changes based on the density – something I discussed here. The refractive index is the ratio of the speed of light in a vacuum to the speed in the medium. If we think about water with its refractive index of 1.33, we find that light travels 1.33 times faster in a vacuum than the water. The denser the medium, the greater the difference in speed of light and the bigger the refractive index.

Not only does light slow down, it also bends. When a ray of light hits a surface at an angle (angle of incidence) it gets bent to a new angle (angle of refraction) inside the surface. With a little trigonometry applied to these angles, we find that their ratio is also the refractive index, a trick discovered by Willebrod Snellius (of Snell's law fame) in 1621 – although an Arab scientist figured this out almost 500 years earlier.

So, what fun can we have with the refractive index? Ever looked into a still pool of water? Due to light rays bending in the water, the pool will look ¾ the depth it actually is. If a post sticks up through the water, it will look oddly disjointed at the surface – appearing to extend at one angle above the water and another below the surface even through the pole is straight.

From another point of view, what does a fish see when it looks up? A fish sees a lot more than expected. By looking up in a cone of 98 degrees, a fish gets a 180 degree view above the water due to refraction. The view above the water would be strange – someone fishing on the shore would look excessively squat, standing at an odd angle and probably distorted due to ripples on the surface. But, the fish would see the fisherman, making it much more difficult to be successful at fishing (spear fishing is even more complex due to refraction). By the way, if you put on your goggles and hopped into the local swimming pool, you would see what the fish sees.

The physics of salad dressing

Ever made your own salad dressing? For a vinaigrette, ever wondered why the result is opaque even though most of the ingredients are clear? Vinegar is typically clear, as is oil – a trick of optics makes the results opaque, which is easily demonstrated at home (In case you want to check this one out for yourself).

Put oil and water (as a stand in for the vinegar) together in a jar (see picture). Oil floats on water with an easily seen interface. The background of my blue cutting board shows through for both layers. Vigorous shaking of the jar creates a emulsion of the two liquids. An emulsion is not the same as mixing, since the oil and water don't actually mix. Instead, both liquids form tiny bubbles that co-exist beside each other – over time they would separate back out into two layers. Once the emulsion forms it become opaque (see picture number 2).

An opaque liquid like mud (tiny dirt particles suspended in water) operates differently – mud's opaque because it absorbs much of the light incident upon it. Our oil and water looks opaque because of back reflection. Each tiny drop of oil and water remains clear. Now gizillions of surfaces form, separating the oil and water and each interface reflects light. Since the drops are round, the light isn't reflected perfectly back where it came from like a mirror, instead it scatters in all directions. This scattering creates a matte look to the emulsion – like the look of white paper.

As a tangent, under high magnification, white paper consists of random criss-crossing fibers that also scatters the light incident upon it. So a vinaigrette and white paper have something in common.

If you sit your vinaigrette on the counter for a few moments, the two layers will reform quite quickly. To keep an emulsion emulsified for a longer period of time, an emulsifier can be added. Mustard or honey are often added to vinaigrettes for this reason and their tastiness. Egg yokes can also be used and they typically act as an emulsifier for mayonnaise.

fabrics with a fishy twist

Since I love the effect of structural colours, when I came across a story that could have me wearing them a few years from now, I had to share. Check out this.

A flash of green

The spectrum of sunlight peaks in the green wavelengths (520-570 nanometers), explaining why most plants are green: an attempt to optimize the available energy for photosynthesis. Our vision's colour sensitivity also peaks in the greens – the better to hunt green vegetables. With so many greens surrounding us, it would be easy to overlook a rare optical phenomenon in the sky: the green flash at dusk.

Just after the sun's final moment in the sky, a flash of brilliant green may be seen for a brief moment, but - only if the conditions are exactly right. A corresponding flash of green may occur just before the sun rises over the horizon. I've never been lucky enough to see either of these phenomenon. I assume folks saw this flash as soon as they started looking at the sky, however, the first conclusive scientific sighting occurred in 1865 by W. Swan. He described the sight as a 'dazzling emerald green' flash at sunrise. In 1926, a PhD thesis was written on the topic by P.F. Keuper. As I haven't been able to find a copy, I don't know if he found it dazzling or not.

Atmospheric refraction causes the green flash (although other not yet understood phenomenon may be involved). As we know, sunlight is composed of many different wavelengths. In the vacuum of space, all wavelengths of light travel at the same speed (the speed of light, a speed we cannot exceed). Once they hit the atmosphere, some wavelengths are absorbed and some pass through. For now, let's consider the visible spectrum as most of it passes through the atmosphere without being absorbed.

Since the atmosphere is contains more stuff than the vacuum of space, when light enters it slows down. If the incoming light hits the atmosphere straight on, all the wavelengths pass through, albeit at a slightly slower speed. At an angle, the light is forced to bend as it enters the atmosphere – an effect called refraction. This allows us to see things slightly over the horizon, like a ship, because light is refracted the same direction as the earth curves.

The amount light slows differs for the different wavelengths resulting in slightly different bent angles. Higher frequency light (blue/green) bends more than the lower frequencies (red/orange). In the extreme angled case, like a setting sun, the sun's image separates by colour (difficult to see because the sun is so bright and dangerous to look at). If you could slow the sunset down, first red would set, followed by yellow, then green with a remaining glint of blue/violet. Typically, just a flash of green is seen, or if the conditions are exceptional a flash of blue.

If you are setting out to see a green flash, the ideal conditions include a sharp horizon (ie, far away from buildings), perfectly clear air (get even further from those buildings) and a homogeneous atmosphere (a remote desert might work).

For more info, check out wikipedia or Sunsets, Twilights, and Evening Skies by Aden and Majorie Meinel (1983), or The Field Guide to Natural Phenomena by Keith Heidorn and Ian Whitelaw.

Bubble colours

Who hasn't blown bubbles outside on a sunny day? If you haven't, devote some time to blowing bubbles the next time the sun is out - it's fun. As a bubble floats gracefully through the air, sunlight creates a virtual rainbow (actual rainbows are formed by a different process) of colours across the bubble's surface. The colour-making phenomenon at work is the same as what creates the colours on a slick of oil, a rooster's tail, a cardinal tetra or hummingbird's gorget – it's iridescence.

Bubble walls are constructed of several thin layers, two soap layers sandwich a layer of water between them. This wall encases a volume of air. As sunlight shines on a bubble, some of it reflects off the surface and some enters the soap film. Inside the bubble wall, light travels slower because both water and soap are denser than the air. At the interface between the soap film and the water, again some light reflects and some passes through. The reflected light may bounce back and forth between the two surfaces a few times or it may just pass back out of the bubble. Reflection or transmission of light occurs at every interface. Most of the light emerging from the interior of the bubble wall will be out of phase with the light that reflects off the interface. Out of phase means that the troughs from one wave line up with the crests from another so that the waves cancel each other out. Some of the emerging light will be in phase, that is, the crests and troughs line up with each other. These two light waves amplify each other, resulting in brilliant iridescent colours.

Layer thickness determines what wavelengths (thus colour) will be amplified. If you move and look at the bubble from a different angle, the colours will change. This is because your viewing angle has changed in relation to the layers. From different angles the distance the light has to traverse to reach you changes, thus the wavelengths that amplify each other also change.

Unfortunately, soap bubbles last only a short time. It doesn't take long before gravity pulls the liquid to the bottom and evaporation whisks fluid away. Bubble colours change as the bubble changes. When the bubble walls are thick, only red gets canceled out leaving blues and greens. As the walls thin, yellow is also canceled out leaving blue. Next green is removed and the bubble looks magenta. Blue goes last making the bubble look golden yellow. As the bubble wall's continue to thin, all the waves in the visible region cancel out and the bubble looks just clear. When the walls reach about 25 nanometres thick the bubble is in serious risk of popping.

Since the thickness of a bubble's walls aren't constant - the walls thicken towards the bottom (remember gravity acts to pull the water down), bands of colours seem to fall downwards on the surface. That pesky gravity also prevents us from dyeing bubbles. The dye will only mix with the water and drain to the bottom of the bubble. However, when gravity is absent dyeing bubbles becomes possible – so if you head out on a long voyage to Mars bring lots of bubble making supplies as you'll have years to perfect your bubble dyeing technique.