Archive for the ‘Daily Science’ Category

On Rainbows and Diamonds

Sunday, July 17th, 2011

Yesterday a quick rainstorm came through.  Shortly after it passed, a beautiful rainbow appeared in the sky, a perfect arc that touched down somewhere this side of the distant hills. While my 2-year-old nephew thought the rainbow very pretty, he would have none of the explanation, so I offer it here to you.

In our last post, we talked about why the sky is blue, and in particular, we mentioned that light from the Sun contains “all the colors of the rainbow.” We also mentioned that the atmosphere contains water vapor, the amount of which is obviously higher just after a rainstorm.

To these two elements we add a third: the refraction of light. Light refracts, or changes direction, when it enters a different material, and the amount and direction of refraction depends on a property of the material called the index of refraction. For example, light traveling from air into water refracts less than light traveling from air into glass because the index of refraction of water is lower.  Refraction depends on the wavelength as well, with blue light refracting more than red light. This is known as dispersion, and it also depends on the material.

So given some sunlight, a raindrop, and a bit of physics, what happens? The figure below shows a raindrop. See how the colors separate when sunlight enters the raindrop? This results from refraction and dispersion. Look now at what happens when the light in the raindrop tries to get out the other side. It reflects! If light incident on this part of the raindrop is not perpendicular enough to the surface, it will reflect instead of refract; this is known as internal reflection.


So light enters the raindrop and reflects off the inside, hitting another part of the raindrop. This reflected light now refracts a second time when it leaves the raindrop (the light is more perpendicular to the surface this time). Blue light again refracts more than red light, meaning the colors spread out even more.

If you’ve looked carefully at the diagram, you’ll notice the blue light ends up on top. But rainbows don’t look like this! To observe a rainbow, you need to stand with the Sun at your back, facing the raindrops. Looking straight ahead, there is a band of raindrops where the blue light is directed at your eyes. The raindrops further up will be in a position where the green light reaches your eyes, and finally the raindrops even higher are in a position where red light reaches your eyes. So we see red on top!

What about that pot of gold? I’m sorry to say you’ll never reach it. The rainbow’s location is not fixed, but rather depends on the your position and that of the Sun. If either you or the Sun moves, so does the rainbow! In fact, the rainbow’s semicircular shape also depends on these positions. Sunlight reflects off of all the water droplets in the sky; it just happens that the reflected light that reaches your eyes comes from a position 40-42° from the line connecting the Sun and your head. (This diagram may help clarify things.) Consequently, rainbows can only be seen when the Sun is within 42° from the horizon, or if you are high off the ground.

And double rainbows? This is caused by light internally reflecting twice within the water droplet. This secondary reflection also causes the colors to be inverted, with red on the bottom and blue on the top. Between the two rainbows lies a dark band known as Alexander’s Band, after Alexander of Aphrodisias, the Ancient Greek philosopher who first described it.

And last question… Why mention diamonds in the same article? Because they sparkle for pretty much the same reasons!

“Not that I give a hoot about jewelry. Diamonds, yes. But it’s tacky to wear diamonds before you’re forty.” ~Holly Golightly, Breakfast at Tiffany’s

Diamonds have high dispersion, which separates the colors a lot giving diamonds that characteristic fire. But diamonds can’t sparkle if light doesn’t internally reflect twice and exit out the top of the diamond. This depends on the index of refraction: the higher the index of refraction, the more likely it is that light will be internally reflected in a material. Diamonds have a very high index of refraction, making internal reflection very easy. This is where the cut of the diamond becomes important. If the bottom angle of the diamond is too shallow or too deep, light will not reflect, or it will only reflect once, getting lost out the lower side of the stone, as in the figure below. The magic number for this angle, as it turns out, is about 98°, depending on the way other parts of the diamond are cut.

 Diamond cuts

The next time you’re shopping for diamonds (maybe before you’re forty), you’ll now know why your purchase should have the right cut. The things nature designs are often inspiring, but it’s always amazing how they can become truly dazzling with just a little bit of tweaking by human hands!

Why is the sky blue?

Sunday, July 10th, 2011

It’s a very common question, and you’ve probably asked it at least once yourself, but do you have the answer?

To explain, let’s start with the source of the light: the Sun. The Sun emits a lot of energy – light – spanning the electromagnetic spectrum from X-rays to radio waves. Most of this is either visible light (44%) or infrared (48%) radiation. Much of the remaining 7% consists of ultraviolet light. Wait… only 7%? I know what you’re thinking. Even though it makes up only a small fraction of the Sun’s light, we most often hear about this type of light because it is so damaging to our skin.

The Sun emits all colors – wavelengths ­– of visible light, from short blue wavelengths (0.4 mm) to long red wavelengths (0.7 mm), but it emits more of some colors and less of others. If we plot the intensity, or amount of light, versus the wavelength, we end up with the figure shown below, called a spectrum. The familiar colors of visible light are shown as well for comparison with the wavelength. What do you notice? The Sun emits all the colors of visible light, but the color it emits most is green. But the Sun doesn’t look green! All those colors emitted by the Sun get blended together and the result is a Sun that appears white from outer space.


This light leaves the Sun and speeds along its 8.3-minute trip to the Earth, where it hits the atmosphere. The atmosphere is composed of different atoms and molecules, most of which are nitrogen (N­­2, 78.1%), oxygen (O2, 20.9%), and argon (Ar, 0.9%). The remaining 0.1% is made up of a mix of different trace gases like neon (Ne), helium (He), methane (CH4), carbon dioxide (CO2), and ozone (O3). There is also some water vapor in the air, about 1–4% at the Earth’s surface, as well as some dust.

When sunlight hits the atmosphere, it interacts with the particles in the air, and the way it interacts depends on the size of the particles. For large particles like water vapor or dust, all wavelengths of light reflect off the particles equally. The interaction of light with smaller particles, however, is much more dramatic. This interaction is called Rayleigh scattering. When light hits a particle, the particle absorbs the light and then releases it in a different direction. Rayleigh scattering depends strongly on the wavelength of light, which means that shorter wavelength, blue light is scattered much more than longer wavelength, red light. Blue light gets scattered in all directions, so it reaches your eyes from whichever part of the sky you view. Red, orange, and yellow light gets scattered less, so if you glance at the sky near the Sun (don’t look directly at the Sun!), that portion of the sky will look yellower.

Okay, so if the Sun emits more green light, why isn’t the sky green? It isn’t green for the same reason the Sun itself isn’t green: the colors that scatter the most create the blue color you see when they’re blended, or averaged, together.

And if shorter wavelengths are scattered more, why isn’t the sky purple? This is simply because there isn’t much purple light coming from the Sun. There is much more blue and green light making the average scattered light appear blue. But here’s an interesting thought. If the surface temperature of the Sun were about 1500 K hotter, we would have a purple sky!

Come back next week for a physical description of how rainbows form and why diamonds sparkle!

About Eggs

Tuesday, May 17th, 2011

eggs.jpgWe eat them cooked any one of half a dozen ways in the morning.  We use them in cakes and cookies and as a meringue on lemon pies.  The particularly ambitious cook may use them in a mousse or a soufflé.  (For eggs in cooking, revisit Physics in the Kitchen.)  But have you ever stopped to think about how amazing the egg really is?

We all know that eggs should be handled carefully because their shells are incredibly thin.  Drop an egg a short distance and you have a gooey mess to clean up.  One simple tap on the edge of the counter is enough to crack open the shell.  But try this experiment: hold an egg in the palm of your hand and curl your fingers around it.  Now squeeze with all your might.

Did it break?  If you didn’t believe me and didn’t squeeze with all your strength, go back and try again.

What on Earth…?  The key to an eggshell’s strength is the fact that its whole surface is curved.  The strongest shape is a sphere, and an egg is a close approximation of this.  (The reason it’s not exactly a sphere in just a moment.)  With no corners or flat sides to weaken it, the forces you apply to the egg by curling your fingers around it are distributed equally over the egg rather than concentrating at any one point. 

This works even in the following way. Hold the top and bottom of the egg with your thumb and forefinger and squeeze.  Did it break this time?  In physics terms, we say that the egg has a high “compression strength” — you’re compressing the egg, but it doesn’t break!  In fact, an egg has such high compression strength, that (with the proper setup) it can support the weight of a small personwithout breaking.

So why aren’t eggs spherical?  The oval shape is created as the bird lays it, and this turns out to be an advantage for the hen.  The shape prevents the eggs from rolling away!  Spherical eggs would roll and roll and roll… and never return.  For birds like ostriches that nest on the ground, this isn’t an issue, and their eggs are generally more spherical.  But birds that nest on cliffs often lay very conical eggs, which roll in a tight circle around the narrow end and remain on the ledge.

What else?  How can you tell if your egg is fresh?  Eggs contain an air pocket that forms when its contents shrink as it cools after being laid.  As the egg ages, moisture evaporates and the air cell grows larger, reducing the average density of the egg.  An object floats in a liquid if it is less dense than the liquid and an object denser than the liquid sinks.  We can therefore use the egg’s density as a handy measure of the egg’s freshness!  Here’s how it works.  Place your egg in a container of water.  A fresh egg with a small air pocket will rest horizontally on the bottom.  The air pocket in a 1-week-old egg is slightly larger — its density is less — and the end will hover slightly off the bottom, and an egg that’s 2-3 weeks old — even less dense — will rest vertically on the bottom.  Don’t eat any eggs that float!

Now that you know so much about eggs, here’s a bonus question: what do eggs and Roman arches have in common? 

PS. When squeezing your egg: don’t wear any rings, and make sure your egg doesn’t have any cracks already.  My “research” egg was blessed with a crack and I ended up with a handful of broken shell and raw egg oozing between my fingers and onto the floor!

Numbers and Nature

Wednesday, May 11th, 2011


banana2.jpgDid you know that bananas have five sides?  Not sure?  Pick up a banana and count the sides.  Bet you there are five.

How many one- or two-petalled flowers have you ever seen?  Probably not many.  They are relatively rare in nature.  Flowers with three petals are more common, those with five petals more common still.  But flowers with four or six petals are few and far between.

What’s the deal?  The answer lies with Fibonacci.

Leonardo Fibonacci was born in Pisa, Italy, around 1170 and spent several years in Algeria with his father, a wealthy merchant.  Roman culture had spread widely in Europe by the Middle Ages and the Roman numeral system was commonly used for arithmetic.  While addition and subtraction are relatively easy with the system, anything more advanced — even multiplication or division — is difficult; the lack of zero poses a particular problem.  In Algeria, Fibonacci learned of the Hindu-Arabic numeral system and recognized the simplicity and efficiency of mathematics in this system compared to the Roman system.  He traveled throughout the Mediterranean, studying under many leading Arab mathematicians, and returned to Pisa around 1200.  The publication of his book Liber Abaci (Book of Calculation) two years later helped to popularize the Hindu-Arabic numeral system in Europe, becoming the numeral system we still use today.

In Liber Abaci, Fibonacci introduced a number sequence that solved a problem relating to the growth of a population of rabbits generation by generation assuming some idealized constraints.  This number sequence had been known to Indian mathematicians since the 6th century, but after publication of his book, it became known as the “Fibonacci sequence.”

In the Fibonacci sequence, each number is the sum of the two preceding numbers, starting with 0 and 1:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …

(In mathematical terms, we can write this as Fn = Fn-1 + Fn-2, with F0 = 0 and F1 = 1.)

The amazing thing about the Fibonacci sequence (aside from rabbit populations, of course) is that numbers in the sequence occur regularly in nature.  Look at your banana again.  Five sides – a Fibonacci number.  The most common flowers have 3, 5, 13, 21 petals – again, Fibonacci numbers.

In other cases, pairs of consecutive Fibonacci numbers determine the pattern of seeds in a sunflower, fruitlets on a pineapple, or scales on a pinecone.  Let’s look at the chamomile flower as an example.


To get the most compact arrangement, the florets are arranged in a spiral pattern, and — surprise! — the number of spirals corresponds to Fibonacci numbers!  Highlighted in turquoise in the picture are the florets spiraling counterclockwise.  Count the spirals, and you get 13.  Now count the number of spirals circling in the opposite direction.  Another Fibonacci number!

The next time you have a pinecone or pineapple in hand, look for the Fibonacci numbers.  (Hint: the pineapple has three.)  Where else do you find the Fibonacci numbers in nature?  We’d love to hear from you!

A story about academic debates, Twitter and the deep emotions surrounding the Global Warming debate

Thursday, July 2nd, 2009


The Pew Center for Global Climate states that “the scientific community has reached a strong consensus regarding the science of global climate change. The world is undoubtedly warming, and the warming is largely the result of emissions of carbon dioxide and other greenhouse gases from human activities. “[1]

While the majority of scientists hold this opinion, some scientists question a number of aspects of the Global Warming debate. The disagreement primarily revolves around two areas: questions of the validity of climate models, and whether the fundamental causes of Global Warming are human-made or, as of yet, unknown.[2]

Regardless of how you view this debate, the prospect of our planet warming up is a huge threat to our environment and should be taken seriously. The costs of not proactively prevent and/or minimizing the warming of our planet would be catastrophic. 

Actions aside, I believe that it is worth our time to continue an open discussion about the underlying science behind this phenomenon, including the academic papers that cast doubt on some of our basic assumptions. Having worked with complex data before and sharing conversations with scientists who study climate, I know there is a reason this science is part of a field called Complex Systems: accurate results are difficult to predict. There are multiple articles questioning various aspects of the Global Warming problem[3] and some scientists such as Richard Lindzen[4] from MIT have expressed the “opposing side” of the Global Warming debate. Some researchers suggest that “Antarctica as a continent is actually getting cooler,”[5]“Glaciers are not melting all over the world; they’re growing in some places,”[6] and the observation that “there are large errors in Global Climate Predictions.”[7]  The sources of these articles are among the most reputable journals in the field of science: NatureProceedings of the National Academy of Science, and Science. If we are truly interested in discerning the underlying causes of Global Warming, it seems prudent to investigate these claims further.  While I am not claiming they are correct, I think maintaining an open mind in the pursuit of truth is the only way to arrive at the root of this complex problem.

This brings me to part two of the story. Recently, I had an interesting experience on Twitter, the acclaimed social networking medium where roughly 6 million users have real-time conversations through posts of less than 140 characters at a time. People who “follow” you can read your tweets, comment on them publically or privately, or re-tweet them to share them with their own followers. I am active on Twitter under the handle @thesciencebabe.

While using Twitter, I recently learned, just how difficult it is to communicate scientific concepts in 140 characters in real time, and, furthermore, how heated and politicized the discussion of global warming can be. Based on this experience I am concerned that we have so deeply enmeshed this topic with politics and emotion that we can no longer calmly discuss the facts. I am not an expert in the field of Global Warming, and I am conscious that views contesting the Intergovernmental Panel on Climate Change (IPCC)’s claims[8] are not ubiquitous. But why not keep the question open to a healthy debate?I believe in harnessing the power of social networks as a learning tool and as a means of fostering education. As Wikipedia demonstrates, knowledge is increasingly becoming a collective process. The Internet and Twitter are tools for enabling open debates that help increase our collective knowledge. This can only be the case, however, if we remain open to and respectful of those expressing new ideas.I find it wonderful that the climate change debate has incited social change by pushing many of us to conserve the beautiful planet we inhabit –a worthwhile endeavour regardless of Global Warming. Additionally, reducing our wasteful consumption of energy and searching for alternative energy sources is a necessary and sensible undertaking. However, I don’t want to see our social mediums become too averse to discussing the scientific facts behind an issue – even when “sensitive topics” are involved. Many times topics such as these are the ones directly in need of the kind of spirited debate social media can foster.