Light is simply a name for a range of electromagnetic radiation that can be detected by the human eye. What is electromagnetic radiation, then?

Electromagnetic radiation has a dual nature as both particles and waves. One way to look at it is as changing electric and magnetic fields which propagate through space, forming an electromagnetic wave. [illustration] This wave has amplitude, which is the brightness of the light, wavelength, which is the color of the light, and an angle at which it is vibrating, called polarization. This was the classical interpretation, crystallized in Maxwell’s Equations, which held sway until Planck, Einstein and others came along with quantum theory. In terms of the modern quantum theory, electromagnetic radiation consists of particles called photons, which are packets (“quanta”) of energy which move at the speed of light. In this particle view of light, the brightness of the light is the number of photons, the color of the light is the energy contained in each photon, and four numbers (X, Y, Z and T) are the polarization.

Which interpretation is correct? Both of them, actually. It turns out electromagnetic radiation can have both wave-like and particle-like properties as demonstrated in experiments such as the dual slit experiment. In this exploration of light, we will primarily take the wave viewpoint as it is a more useful description of the everyday properties of light, but keep in mind that both viewpoints are valid, and sometimes we will use the quantum viewpoint too.

On to the numbers! Light ranges from wavelengths of 7×10-5 cm (red) to 4×10-5 cm (violet) and (like all electromagnetic radiation) travels at the speed of light, 299,792,458 meters per second or 186,282 miles per second. (Interesting fact: the speed of light is actually defined to be 299,792,458 meters per second and scientists combine this with the definition of a second to create the definition of a meter! As stated at the 17th General conference on weights and Measures, “The meter is the length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second.”)

The frequency (number of wavelengths per second) of a light wave may be calculated using the equation c=ln where l is the wavelength, n is the frequency and c is the speed of light. In quantum theory, a photon has energy equal to hn, where h is Plank’s constant and n is the frequency of the light in classical theory.

The Electromagnetic Spectrum

The “electromagnetic spectrum” is simply a phrase used to describe electromagnetic radiation of all wavelengths. This includes radio waves, microwaves, infrared, visible light, ultraviolet, x rays, gamma rays, and other electromagnetic radiation of longer and shorter wavelengths. Note that the names given to various portions of the spectrum are simply arbitrary labels imposed by humans; there is no definite wavelength where “radio waves” cease to be radio waves and suddenly become “microwaves”. Rather, the various portions of the spectrum blend into one another and waves in between radio waves and microwaves interact with matter in a manner in between radio waves and microwaves. It is important to remember that there is no fundamental difference between any portion of the electromagnetic spectrum other than wavelength (and its dependent properties, frequency and energy). A radio wave is electromagnetic radiation of a long wavelength, and x rays are electromagnetic radiation of a shorter wavelength, but they are both electromagnetic radiation and their behavior is governed by the same laws.

If all electromagnetic radiation is fundamentally the same thing, you might ask, “Why don’t we see radio waves like we see light?” or “Why do we need special infrared light bulbs to heat things up?” Although all portions of the electromagnetic spectrum are governed by the same laws, their different wavelengths and different energies allow them to have different effects on matter. Radio waves, for example, have such a long wave length and low energy that our eyes can’t detect them and they pass through our bodies. It takes a metal antenna with special electronics to capture and amplify radio waves. Likewise, infrared radiation is of wavelengths that are easily absorbed by matter and turned into heat, and x rays are radiation of wavelengths that can pass through soft tissue but are stopped by bone. The wonderful variety of the electromagnetic spectrum is all a result of the same laws, applied to different wavelengths and energies.

Huygens’ Principle

In many cases, light waves are very much like water waves. One distinct difference, however, is that water waves are waves on a 2 dimensional plane (surface of the water) while light waves are waves within 3 dimensional space.

The wave theory, proposed by the Dutch physicist Christiaan Huygens, viewed light as an impulse moving in all directions. Consider a point P in space. If an impulse starts at P, then the effect of the impulse, after some time, will be equidistant from P in all directions — one can visualize this impulse as an expanding sphere with center P.

Huygens called this sphere a front. Most importantly, every point on a front can be a source of new wavelets (act just like point P), and the envelope around those wavelets forms another front. In other words, a second front can be created from the first by making each point of the first front the origin of another impulse. All these impulses combine and appear as if the original front is expanding.

This model of light propagation through space by formation of spherical fronts is called Huygens’ Principle.

Making Light

There are two basic types of light sources. Incandescence involves the vibration of entire atoms, while luminescence involves only the electrons.

Incandescent light is produced when atoms are heated and release some of their thermal vibration as electromagnetic radiation. It is the most common type of light that you see everyday sunlight, regular light bulbs (not florescent) and fires are all incandescent sources of light. Incandescent light is also known as “black body radiation.” This seemingly self-contradictory name arises from the history of physics-scientists studying this type of light emission modeled their theories on ideal materials that would absorb all colors of light, hence appearing to be “black bodies”. Depending on how hot the material is, the photons released have different energies, and therefore, different colors. It was found that at lower temperatures, these materials would emit radiation in the infrared wavelengths which we feel as heat (fires, for example, emit most of their energy in the infrared). As temperatures are increased, increasingly more energetic radiation is emitted, so these materials would glow red, then orange, then yellow, and eventually “white-hot.” Although ideal black body materials don’t exist in reality, most substances are close enough that this color sequence can be observed. This is why a fire tends to be redder than a halogen lamp-the filament in a halogen lamp is heated to a higher temperature than normal fires. Likewise, the hottest stars appear to be a blueish-white while cooler stars such as our sun are more yellowish in appearance. Some sources of incandescent light are: the sun, fire and light bulbs.

Unlike incandescence, luminescent light occurs at lower temperatures, because it is produced when an electron releases some of its energy to electromagnetic radiation, not an entire atom. It turns out that electrons like to have energy at specific “energy levels.” Thus, when an electron jumps down to a lower energy level, it will release a specific amount of energy which becomes a photon, or light of a specific color. Therefore, continued luminescence requires something to continuously give the electrons a boost to a higher energy level to keep the cycle going. This boost may be provided by many sources: electrical current as in florescent lights, neon light, mercury-vapor street lights, light emitting diodes, television screens and computer monitors; chemical reactions as in Halloween light sticks and fire-flies; or radioactivity as in luminous paints, to name just a few examples.

Colors

In 1665-1666, Isaac Newton studied sunlight and discovered that it could be broken down into a rainbow of colors by a prism. Today, we know that the rainbow of colors one gets from a prism is a consequence of refraction and the different wavelengths of different colors. “White” sunlight is not really white-there is no wavelength of light that is white. Rather, it is a mixture of many different colors that appears white to our brains after being processed by our eyes. (Seeincandescent light) In the same way that the sun can produce light of many different wavelengths that appears white when mixed, televisions and computer screens also mix light to produce different colors. If you examine your computer screen or television with a magnifying glass, you will see tiny dots, probably red, green and blue. By mixing these colors in different amounts, a large range of colors can be produced. [applet!]

Did you know that long before color television was invented, artists did the same thing? The pointillists and post-impressionistic artists painted with many many little tiny dots of color. Up close, their paintings didn’t appear to be anything, but when you stepped back and let your eye mix the dots into other colors, you would see the subject of painting. By letting the eye mix the colors, they were able to achieve a brighter, more vibrant palette.

Reflection

Reflection of light is very predictable. The Law of Reflection describes it simply as “The angle of incidence is equal to the angle of reflection.”

Law of reflection:
‘ = where is the angle of incidence and ‘ is the reflected angle from the normal.

Yeah, that is great for flat surfaces but what about curved surfaces? It works the same way. Simply draw the tangent line to the point of the curve and reflect the light according to the tangent line.

There are actually two types of reflections: specular and diffused.

Specular reflection is reflection from a smooth surface. When light strikes this smooth surface, all the reflected rays are in line with each other.

Diffused reflection is reflection from a rough surface. The small bumps and irregularities on a rough surface will cause each of the light rays to reflect in different directions, all following the law of reflection of course.

Mirrors

When you focus on an object, a single point, your eyes are receiving light waves diverging from that point. This must be true for an object, or an image of an object, to be visible. To put it simply, if our eyes detect light waves diverging from a point, that point will be visible. As you will see, this is very important in terms of how mirrors work.

For plane (flat) mirrors, light is reflected according to the law of reflection. When the eyes receive these light waves, it looks as if the waves are diverging from behind the mirror, making it appear as if the object is behind the mirror as well. This type of image is called a virtual image, because light waves do not actually pass through that point, it only appears so. The distance between the object and the mirror is called the object distance and the distance between the virtual image and the mirror is the image distance. Notice that on plane mirrors, the object distance is equal to the image distance.

Curved mirrors are slightly more complicated. There are basically two types of curved mirrors: concave and convex. A concave mirror curves toward the incoming light while a convex mirror curves away from the incoming light. For now, we will assume that light waves striking the lens are from an object infinitely far away, therefore, the light waves will be parallel with the principal axis.

When light strikes a concave mirror of curvature radius R, the light waves will reflect and converge at a point on the principal axis that is 1/2 * R in front of the mirror. This point is called the focal point. Since light is converging at the focal point, it is also diverging from that point on the other side. Therefore, the image of the object is created at the focal point, appearing as if the object is actually there. Notice that this image is not like the image of the plane mirror, light actually pass through where the image is. This type of image is called a real image.

When light strikes a convex mirror of curvature radius of R, the light waves will reflect and appear to diverge from a point on the optic axis that is 1/2 * R behind the mirror. Just like that of the concave mirror, this point is also called the focal point. The image of the object, even if the object is infinitely far away, will appear as if it is 1/2 * R behind the mirror.

Notice that the focal point of both the concave and convex mirrors are 1/2 * R away from the mirror. This distance between the mirror and the focal point, 1/2 * R, is called the focal length. The focal length of a concave mirror is always positive while that of the convex mirror is always negative.

Now, obviously, objects can not be infinitely far away, so we can not have it so easy as to have all the light waves always being parallel to the principal axis. If the light waves are not parallel to the principal axis, what then? No sweat! We can still locate the image, where the light waves converge then diverge off, by using three principal rays and finding where they converge.

Notice that the first and second set of principal rays are essentially the same, so any one of the first two principal rays along with the third is all that is required to determine the image location.

The image of an object from a concave mirror is a smaller, inversed version of the object. From a concave mirror, the image is a smaller, upright version of the object.

The object distance, image distance, and focal length are all related by the image equation: 1/do + 1/di = 1/f

Scattering

Excited electrons emit light waves, and just so happens, the opposite is true: light waves can excite electrons. When electrons are excited by light waves, they jump to a higher energy level. When they fall back to their original energy level, the electrons reemit the light. This process is called scattering. However, when the light is reemitted by scattering, not all of the energy is given back to the light wave, but instead, some is lost to the particle. This will result in a light wave of lower frequency and wavelength as described by Compton’s shift formula:

When light is scattered on an object smaller than the wavelength of light, the process is called Rayleigh scattering. Because of the nature of Rayleigh scattering — light waves scattered by objects smaller than its wavelength — it is very frequency dependent. Higher frequency, shorter wavelength, light are scattered the most while lower frequency, longer wavelength, light is scattered the least by very small particles.

The color of the sky is the direct result of Rayleigh scattering of the sunlight. Lower frequency light waves, such as red, are able to pass though a network of air particles better than higher frequency light waves, such as blue. During the day, the particles in the atmosphere will scatter the sunlight and lower its frequency to somewhere in the blue range. At sunset, the light waves from the sun have to travel a greater distance to reach us. Because of that, all of the light waves have been scattered so much that it lowers the frequency to the other end of our visible range: red.

Diffraction

Diffraction is the bending of light as it passes the edge of an object. An example of this property is the shadow. If observed carefully, the edges of shadows are not solid, but slightly fuzzy.

So, what is going on? Diffraction can be easily explained with Huygens’ Principle. Just as the front of a wave passes the edge of an object, the wavelets will cause the succeeding front to bend around the edge.

For some time, it was believed that the bending of light was not due to light itself, but the edge of the object. Not until the British Physicist, Thomas Young, conducted the double slit experiment before light was accepted as a wave.

In his experiment, he made two slits on a barrier and allowed monochromatic light (light of a single wavelength) to pass through. The result is a series of light and dark areas on the screen that could not be explained under the particle model of light. Under the wave model of light, these light and dark areas can be explained with constructive and destructive interference of waves.

Polarization

Light waves can vibrate in many directions. Those that are vibrating in one direction — in a single plane such as up and down — are called polarized light. Those that are vibrating in more than one direction — in more than one plane such as both up/down and left/right — are called unpolarized light.

Generally, unpolarized light can be considered to be vibrating in a vertical and a horizontal plane. To polarize light, one can transmit the light through a polariod filter which will only allow light of single polarity to pass. The resulting light will be polarized light of half intensity. If two polaroid filters are used and placed so that one is rotated 90 degrees to the other, no light will be able to pass.

Some polarization will also occur during reflection, refraction, and scattering of light. When reflecting off non-metallic surfaces, the resulting light will be polarized parallel to the reflected surface. During refraction, a beam of light will be split up into two polarized beams, one polarized parallel and one perpendicular to the boundary. Scattering also causes partial polarization.

Photoelectric Effect

Although obscure to most people who aren’t scientists and students, the photoelectric effect is nonetheless an important phenomenon to know about. So much so that, in 1921, Albert Einstein received the Nobel Prize in Physics for his explanation of it, and not for the theory of relativity. What is it? In general, the photoelectric effect is whenever electromagnetic radiation is absorbed by a material, causing it to release charged particles. In practice, this is usually observed with ultraviolet light and metals, which release electrons easily.

The photoelectric effect has some curious properties that cannot be explained by classical physics. It was found that the number of electrons released by a metal was proportional to the amount of ultraviolet light, while the energy of the electrons depended on the frequency of the light. Below a threshold frequency, there are no electrons released at all, no matter how bright the light is, while above the threshold frequency, there are always electrons released, no matter how dim the light is. This contradicted classical physics because classical wave theory stated that either increased intensity or increased frequency should provide more energy in the same way, but the observed effect showed that only increased frequency provided the needed energy to eject an electron from the metal.

The implications turned out to be far-reaching. These findings were finally explained by Einstein in this Ph.D. thesis in 1905: he proposed that light could not only be waves, but could also come in packets of energy, as photons. As a photon hit an electron, it would provide it with a certain amount of energy. If it was enough, the electron would be kicked to the surface of the metal and be observed, but if it wasn’t enough, the electron would fall back to its atom. Therefore, photons with energy below the threshold had no discernible effect and the number of photons could only determine how many electrons were released, as only one photon at a time was likely to hit an electron.

The photoelectric effect was indisputable evidence of photons and thus, it kicked off the quantum physics revolution.

The Michelson-Morley Experiment

The Michelson-Morley experiment was an attempt to detect the theorized “ether.” This ether was proposed because there did not seem to be any medium for the waves of light to propagate through-light behaved as though it was composed of waves, but waves of what? Thus, scientists postulated an ether which would carry light waves, just as air carries sound waves.

If there was an ether, then the speed of light should be dependent on the ether. If the speed of light were constant with respect to the ether, then the measured speed of light in perpendicular directions should be different due to the movement of the earth through the ether. In 1887, A.A. Michelson and E.W. Morley refined an experiment that Michelson had performed a few years earlier. They split a beam of light in two, sending the two halves in different directions. Each ray of light was reflected back and the two beams combined again. By observing the interference patterns, they were able to determine the difference in the speed of light in the two perpendicular directions. It was zero. This negative result served to discredit the idea of ether and eventually led to Einstein’s 1905 special relativity, stating that the speed of light is a universal constant.

Maxwell’s Equations

In words, “(1) electric field diverges from electric charge, an expression of the Coulomb force, (2) there are no isolated magnetic poles, but the Coulomb force acts between the poles of a magnet, (3) electric fields are produced by changing magnetic fields, an expression of Faraday’s law of induction, and (4) circulating magnetic fields are produced by changing electric fields and by electric currents.” (quotation from EB) The interrelationship between changing electric fields and changing magnetic fields is such that waves of changing electric and magnetic fields propagate through space, producing what we call electromagnetic radiation.

These four equations, first stated together by James Clerk Maxwell in the late 19^th century, form a complete description of electric and magnetic fields and their interaction. Their formulation was a breakthrough in the understanding of light, as they revealed the nature of light–it is really just another portion of the electromagnetic spectrum.

Relativity

One of the guiding principles of physics since Galileo’s time, the principle of relativity states that all inertial frames of reference are equally valid. In other words, an observation made by one person should be the same when made by a different person, and what is valid science here is valid science there.

This fundamental principle was called into question by Maxwell’s equations, which implied a constant speed of light. This was taken to be an indication that all light must therefore be a wave in some stationary medium, dubbed “ether” by Maxwell. Continuing this chain of logic, it followed that the frame of reference of the ether was “privileged,” being fixed with respect to the speed of light, while other reference frames were not.

Thankfully for the foundations of physics, the Michelson-Morley experiment failed to detect ether. While other scientists were unable to reconcile this result with the constant speed of light, Einstein took it as evidence of the validity of the principle of relativity.

He was able to explain the observed constant speed of light by using the Lorentz transformations which modified definitions of “observed” velocity, length and time to explain why the ether was not detected. Unlike Lorentz however, Einstein did away with the concept of ether entirely, instead assuming the observed measurements to be the actual measurements and thus taking the daring step of assuming Newtonian physics was wrong. By Einstein’s postulates, addition of velocity was no longer as simple as adding the vectors, but now required a complexnonlinear formula. In addition, some of the consequences of the Lorentz equations implied that an object shrinks in length when traveling at high speeds, that moving clocks slow down, that simultaneity at non-coincident points is impossible to determine, and that nothing can travel faster than the speed of light.

However counterintuitive, Einstein’s leap of intuition proved to be correct: later observations were able to detect the tiny changes predicted at high velocities. Both Maxwell’s Equations and the principle of relativity turned out to hold true, leading us to a more complex, but contradiction-free universe.

Quantum Mechanics

Quantum mechanics deals with the interaction of matter and energy, with the assumption that energy is only released in discrete amounts, “quanta.” It arose primarily to explain phenomenon that could not be explained by classical, or Newtonian physics. In this article, we will only cover quantum mechanics, not all of modern quantum theory, which extends the ideas of quantum mechanics into other areas of physics.

The first indications of quantum mechanics came in 1900, when physicists tried to explain the wavelength distribution of incandescent radiation. They were unable to find an answer in terms of classical theory, but Max Planck finally came up with the answer when he made the assumption that atoms may only emit of absorb energy equal to nhv, where n={1, 2, 3,…}, h is Planck’s constant (6.626 x 10^-34 Joule-seconds), and v is the frequency of oscillation of the atom. This counterintuitive assumption seemed to have no basis, but faced with a formula that predicted results within a percent of experimental data, scientists accepted his assumption and searched for explanations, the result being modern quantum theory. (Planck’s constant h determines the “graininess” of the universe. No energy can come in units smaller than hv, and this turns out to have implications for other properties too.)

While strange, quantum mechanics explains many phenomenon impossible to explain by classical physics. As stated above, the wavelength distribution of incandescent radiation was what led to quantum mechanics in the first place. Another phenomenon that tipped off scientists was the photoelectric effect, which led Einstein to propose that not only must atoms, but also light obeys quantum rules. (E=hv) Finally, another phenomenon discussed on this site caused by quantum effects is the electric discharge lamp, better known as neon light. Neon light comes only in certain wavelengths because it is produced when electrons release energy in quanta which determine the energy of the released photon. This is direct evidence for the quantum nature of radiation. (Why does incandescent light come in all wavelengths then? Incandescent light is produced by vibrating atoms, which are systems far more complex than a single electron. Thus they are able to emit many different energies because v can vary linearly, producing any E.)

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