Archive for the ‘physics’ Category

News tidbit: Water bottle light bulbs

Saturday, September 24th, 2011

How do you light the inside of a windowless room? With a bottle of water, of course! Driven by the outrageous price of electricity in the Philippines, Illac Diaz developed this economical and environmentally-friendly alternative. And in just four months, more than 15,000 bottles have been installed. How does it work? Imagine cutting a hole in the roof. Light enters, but so does the rain. Now plug the hole with a bottle of water. Sure, the bottle allows light in and not the rain, but the sunlight entering the bottle refracts in the water, spreading out into the room below! See these water bottles in action here.

The Physics of Dance

Monday, September 19th, 2011

arabesque.jpgOriginating in the elaborate courts of the Italian Renaissance in the 1400s, it developed into an art form during the 17th century in France under the reign of Louis XIV. But the elegant arabesques, exhilarating grand jetés, and energetic fouettés en tournant of ballet that we know today grew out of the Romanticism of the late 1800s, when ballerinas portrayed fairy-like creatures and almost seemed capable of floating in the air.

Have you ever wondered how a dancer can seem to defy gravity while your own feet are so firmly planted on the ground? Let’s take a closer look at gravity and discover the secrets behind some of these beautiful movements.

An article about dance should make you move, right? Here’s an experiment. Stand against a wall with your heels touching the wall. Now bend over and touch your toes. Did you make it?

Why did it suddenly become so difficult to do this simple task? The problem is the location of your center of mass: the average location of all the matter in your body. When standing straight, your center of mass lies within your body just below your belly button. It is situated above your feet, so you have no trouble standing.

But your center of mass can move depending on the position of your limbs. What if your body is horizontal? In a pas de deux, a male dancer may lift a ballerina into the air. Have you ever noticed where his hands are placed? Rather than clasping her waist or her thighs, he clasps her hips. Not only do her hipbones provide support, this is the point where her body is balanced; this is the location of her center of mass. Any closer to her belly or her thighs and the balance is upset; her center of mass is no longer above him, and he won’t be able to hold her aloft.

If your body is not straight, however, your center of mass is different. Try the experiment again. What happens to your center of mass as you bend over? By moving your torso away from the wall, you move some of your mass forward. Your center of mass also moves forward to a point somewhere in front of your upper thighs, not inside your body! Continue bending forward and at some point it will have moved out beyond your toes and you risk falling over. What do you do to keep from landing face-first on the floor? Try it and see. Can you figure out why standing against the wall makes such a difference?

Dancers instinctively know that to execute a perfect turn, their center of mass needs to be over their feet. Imagine trying to execute a turn, like a pirouette, on one foot. What happens if your center of mass is not directly over your feet? You end up with a wobbly turn, or worse, falling over!

grandjete.jpgThe center of mass also helps explain those big leaps, or grands jetés, that seem to hang effortlessly in the air. After taking a few quick steps, a dancer takes a leap, one leg leading and one trailing. During the leap her head rises a certain amount. (For some numbers and more physics, check out Dr. George Gollin’s Physics of Dance website.) As soon as she starts the leap, however, she raises her legs, i.e. some mass, to be parallel to the floor, which raises her center of mass some more. During the jump, her center of mass rises more than her head, making the leap seem even higher. What is more, her center of mass moves the most at the very beginning and end of the jump; it moves very little through most of the leap, giving the impression she is hanging in the air or floating.

We are so familiar with gravity’s pull attaching us to the ground that the light airy movements in ballet take us by surprise. The movements seem much more possible, however, when we apply a little physics and see how ballet has developed to work with gravity. The result? An art form that becomes even more exquisite!

PS. Here is another experiment. Sit in a chair, with your knees at a 90° angle, your feet flat on the floor. Now stand up without moving your feet or bending forward. How did you do? Our natural instinct is to bend forward, but try it again, without bending forward! When you sit in a chair, your center of mass lies at a point above your thighs in front of your lower belly. It is impossible to stand up in the second experiment unless you move your center of mass closer to your feet, which is what happens when you bend forward.

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!

Peering Into the Body

Tuesday, June 28th, 2011

x-ray.jpgOn 8 November 1895, Wilhelm Röntgen discovered an unknown type of electromagnetic radiation. He called this radiation X-rays, using the mathematical symbol x to represent something unknown. Not only did he win the first Nobel Prize for his work in 1901, he also ushered in a new era in medicine, one where it was no longer necessary to cut open the body to investigate an ailment. In fact, he unwittingly realized this potential early on when he used his wife’s hand to make the first X-ray image. With the devastation of World War I and II, X-rays became widely used and have become a vital instrument for doctors and dentists ever since.

Compared to today, medical diagnosis in the late 1800s was very primitive. To investigate ailments, doctors were limited to their own five senses. The senses of sight and smell were able to detect exterior signs of disease. (We hope they didn’t taste their patients too often.) Investigating the interior without dissection the body was more difficult. The sense of touch helped with broken bones or foreign objects lodged within the body, but swelling at the site could make diagnosis difficult. Aiding hearing, the stethoscope magnified sounds in the body. However, diagnoses relying on touch or sound were always dependent on a mental image the doctor created of the patient’s innards. And this mental map could look quite different from reality.

With X-rays, however, doctors could make a real image of a patient’s insides, which, as you can imagine, greatly improved medical treatment.

In our post about archaeology, we mentioned the electromagnetic spectrum and some uses of infrared radiation — radiation with wavelengths slightly longer than visible light. In this post, we jump to the other end of the electromagnetic spectrum. X-rays have wavelengths much shorter than visible light.

In order to make an X-ray image of a patient’s insides, doctors first need a source of X-rays. To make X-rays, a heated piece of metal called the cathode, and a collector — a metal plate called the anode — are placed within a glass tube from which all the air has been removed. The cathode and anode are connected to a high voltage power source and a beam of electrons is created in the tube between the cathode and anode. X-rays are produced when electrons hit the anode. This setup, called an X-ray tube, is nearly identical to the cathode-ray tubes used in older television sets and computer monitors. (In fact, the word set refers to the set of cathode-ray tubes making up the television.)


In medical uses, a tube like this is used to create short pulses of X-rays that are aimed at the patient. Some photographic film is placed behind the patient. X-rays are blocked somewhat by denser materials like bones and pass more easily through less dense materials like tissues. A shadow forms on the film where X-rays are blocked. When developed, the film turns darker where more X-rays have hit it, so denser objects like bones appear lighter on the final X-ray.

As useful as this simple technique is, more advanced techniques have also been developed. A CT (computed tomography) scan, for example, is a series of images made by passing the X-ray tube in a circle around a patient. Thousands of images are made from many directions and these images are then compiled to form a 3D image.

Now, the next time you visit the dentist, or go through security at an airport, or break a bone, you can thank Mr Röntgen for his discovery!