September 30, 2013

Over One Year Hiatus...Over?!

I have not blogged in many many moons...mostly because I started working at a start-up and lost site of most all personal endeavors.

The biggest news of the year was the passing of my father, Sy. This has proved to be confusing, as I often refer to my step-father (Jim) as my "dad". Jim and I are very close, whereas Sy and I not so much. I would often say that as the youngest of his many kids, and having spent the least time actually living with him as a child, he always felt more like a grandpa...but nonetheless he was my dad and I loved him very much.

I will probably write more on the subject at some point but for now I will say I am on a quest to clear out my email inbox and am finally reading some emails my sister, Rebecca, forwarded to me. She took it upon herself in recent years to ask my dad sciencey questions, since she knew his in-depth answers would educate and amuse. I am SO glad she did, as this is precisely the information I want to pull out when I have a kid and they ask about these things...proudly saying it was their grandfather who wrote it especially for his kids/grandkids.

Here is his answer to her question about rainbows (warning - its LONG):

Hi Rebzy,Ah, rainbows!

In empty space light travels at the same speed, regardless of the color. That speed (about 186,000 miles per second) is a constant of nature, commonly designated by lower case "c". We won't get into details but they are an outgrowth of Einstein's Special Theory of Relativity. It requires ninth grade algebra to understand but we'll skip that here. What IS important for understanding rainbows is that when light travels in a material substance, i.e., in a non-vacuum, different colors travel at different speeds. Light color = light energy. When we see different colors, that just our way of perceiving different energies.

Light seems to have a dual nature, depending on what kind of experiment we use to study it. It has a "wave" nature and a "particle" nature. Nobody can understand how it can "be" a wave AND particle. That's because our intuition developed in the corner of the world humans are familiar with. Waves are like water waves (the waves are pure form or structure, and the wave moves forward but water molecules don't; they just bob up and down) But we think of particles as solid objects (like hard balls), and they can certainly move forward and hit things. But each half of the wave/particle duality is just a different "model", described by different types of mathematical equations, so we tend to think that a real phenomenon "should" behave one way or the other, exclusively. Our "models" are distinct, so why should nature perversely mush them together? Nature, however, does not feel constrained by our limited intuition. Since things are the way they are, whether we like it that way or not, any mismatch between intuition and reality is entirely due to the inadequacies of intuition. Math also has limitations, but the limitations are much further out than our intuitive limitations. That's why there inevitably comes a time during the education of a physicist when one has to give up on intuition and rely on math instead. Usually, that happens at or about the time one studies electromagnetic theory, which is borderline understandable intuitively.

You can learn about waves by standing on a pier and watching water waves moving toward the shore. If you have a stopwatch you can time the interval between successive waves, measured from crest-to-crest or from trough-to-trough. Suppose you determine that 12 waves travel past your position on the pier in a single minute. In physics-speak, you might say that the wave frequency is 12 per minute, which means one wave every 5 seconds, or a fifth of a wave per second. A fifth is two-tenths, so on a "per second" basis, that's a "frequency" of 0.2 per second. That's how "frequently" waves go past your location. The frequency (call it "f") is said to be 0.2 Hertz, or 0.2 per second. (Hertz is the standard unit of frequency, in honor of the first person to generate radio waves in a lab.)

Suppose you could measure or estimate the wavelength of the ocean waves passing you as you stand on the pier. Let's say it's 25 feet (from the crest of one wave to the crest of the next wave). Then it's easy to see that the wave velocity is 5 feet per second.  If 1/5 of a wave rolls past you in a second, that amounts  to 1/5 of a 25-foot long wave, or 5 feet worth of wave. This is just math, as Bill Clinton would say:

Velocity = Wavelength times frequency, or V = L x f, or V=Lf.

The same relationship applies to light waves traveling in a vacuum. As I said earlier, the velocity of light in a vacuum is a universal constant, often called "c". Since c is constant, to say that c=LF means that L and f are inversely proportional to each other. The frequency is always just c/L, and the wavelength is always just c/f. So if you know the value of c, you can determine the frequency of a monochromatic beam of light once you know its wavelength. And if you know its wavelength you can determine its frequency.

It turns out that the ENERGY of a wave is directly proportional to its frequency. "Directly proportional" just means it's a constant times the frequency. In the case of light, the constant -- another universal constant of nature -- is called Planck's constant (traditionally symbolized by the letter "h"). This means that if you know the frequency of a lightwave, you also know its energy: E=hf. Since f and L are inversely proportional to one another, the shorter the wavelength, the higher the frequency. Combining that information with the statement in the previous sentence, we see that the higher the energy of a lightwave, the higher its frequency (and the shorter its wavelength. In the spectrum of visible light, the highest frequency/highest energy belongs to violet-colored light. The reason ultraviolet light is dangerous is because its energy is greater even than that of violet, so it disrupts cell molecules more, causing sunburn, cancer and mutations.

The low-energy end of the visible spectrum is red. Beyond red is infrared, which we can't see but we can feel it as heat radiation. Some snakes and other animals can see infrared (and bees can see ultraviolet).

Up to now I've only spoken about light in a vacuum. What happens when light travels in some material substance? To the extent that the medium is transparent, the light moves forward, though some of it is absorbed by the material, and when the light first enters the material, some of it is reflected back. But since the lightwave is a form of energy, the amount lost through absorption decreases the energy of the wave. the wave is deflected, that is, its path is bent, and the more energetic the light, the more energy it loses, and therefore the more it is deflected. The name given to this deflection by "optical folks" is REFRACTION. So violet light is bent more than red light, i.e., its angle of refraction is greater. (From these considerations it's just a short hop to understanding why the sky is blue, but that's a different story.)

Sunlight is a mixture of frequencies, extending from the ultraviolet through the infrared. Sunlight peaks in the yellow, which is why that round thing in the sky looks like a yellow disk. (Since one knows the frequency corresponding to yellow, one can easily calculate its energy, and thereby determine the temperature of the surface of the sun (around 5,600 degrees F. And since that yellow thing is almost a hundred million miles away, math can, among other astounding things, function as a mighty long thermometer.)

Back in the 1600s, Newton played with glass prisms. Let a sunbeam shine through the glass and, as you might expect, the violet and blue light gets slowed down more than the red and yellow light, so the high energy components are refracted more than the low energy components. Bingo! There's your rainbow: The mixed-color light fans out into its different-colored constituents. This phenomenon is called dispersion, but notice that  real power comes from understanding something, not from merely naming it.

Well, my beloved daughter, tiny droplets of water populating the air (especially between a rain cloud and your eye) act like a bazillion little prisms. Hence the rainbows you see when there are water droplets in the air, and the droplets are at just the right angle between your eyes and the sun.

An equally interesting thing happens with puddles on the ground -- especially when there are molecules of an oily substance that are floating as a thin film on top of the puddle. It entails another property of waves call diffraction. A material object will bend a wave into a changed direction (that terminology should sound vaguely familiar to you because refraction and diffraction are related). But what happens when the SIZE of the material object is close to the wavelength of the wave? That's when unusual and interesting things happen. The bending gets extreme. When the wavelength of a water wave is comparable to the size of a jetty, the wave gets diffracted, and it's interesting to watch. Since our topic is chasing rainbows, you should note that the human eye can see wavelengths as short as 380 nanometers (violet) and as long as 750 nanometers, which corresponds several ten-thousandths of a millimeter. Visible light has wavelengths that are tiny by normal human size standards. In essence, films that thin are of a size comparable to the wavelengths of visible light, so such films bend light, dispersing (spreading out) the different colors just like prisms do. Hence the puddle rainbows. What if you could cut tiny grooves in metal or plastic that are ten-thousandths of a millimeter apart (i.e., hundred-thousdandths of a centimeter or inch apart)? Should such groovy things produce the same rainbow effect? They should and do. They are called diffraction gratings, and you can buy them from lab supply companies. It happens, incidentally, that that size and spacing of the pits in the surface of a DVD are also of the same scale. Voila! More rainbows!

As a cranky old man I know said, "It's a joy to see the light."