Light & Optics

[7.1] THE DISCOVERY OF LIGHT / ELECTROMAGNETIC RADIATION

The ancient Greeks had some confused ideas about light, such as failing to understand that the eye operated by passively receiving the light that fell on it, instead believed it took some active role. Nonetheless, they got some things right. The philosopher Empedocles speculated that light had a finite speed, and the great philospher Aristotle correctly linked the occurrence of rainbows to the reflection of light from raindrops, though he had no real idea of the mechanism. The mathematician Euclid correctly understood the rules of reflection of mirrors.

The confusion over the operation of the eye was finally resolved through experiments performed by the Egyptian scientist Ibn Al Haythen, known in Europe as "Alhazen", in the Middle Ages. However, the modern understanding of optics did not begin until the 17th century, as researchers began to determine the precise rules of reflection and refraction, leading to the introduction of optical equipment, such as telescopes, microscopes, and eye-glasses.

In 1803, the English polymath Thomas Young published studies of the behavior of a light source when passed through two narrow slits. If light were a particulate phenomena, the light falling on a surface beyond the slits should have been concentrated directly behind the slits, but what he observed was a pattern of alternating light and dark lines, the product of wave interference. That seemed to resolve the debate in favor of the wave theory, though it still left open the problem of the medium that light used for propagation.

The interference effects observed by Young are in practical use. They are the basis of "interferometers", highly sensitive instruments in which two light beams sent through alternate paths are allowed to interfere, with any slight change in the relative paths of the two beams causing alternations in the intensity of light output.

An interferometer can be used as an "optical gyroscope" by arranging the two light paths as alternate routes from one vertex of a square to the opposite vertex, with the rotation of square around its center causing the effective path of light along one side to shorten and around the other side to lengthen. Another scheme is to fit some class of sensor into one of the paths, with the sensor's optical properties changing with the parameter to be measured.

Interference effects are also used in "holography", with interference patterns from the reflections of light off an object recorded in photographic film as a "hologram". Shining light through the hologram will reconstruct the image in three dimensions, and the image will seem to float in space.

Scientists had known for decades there were forms of light that were invisible to the eye. Early in the 19th century, the Anglo-German astronomer Sir William Herschel used a prism to break sunlight up into its rainbow spectrum, and then moved a thermometer through the spectrum to see how much warmth it contained. The temperature rose steadily from the blue end of the spectrum to the red end of the spectrum, and then surprisingly continued to rise as Herschel moved the thermometer past the red end of the spectrum. This invisible form of light was named "infrared" light.

Maxwell's analysis extended this concept by showing that electromagnetic radiation existed over an infinite range of frequencies, and that only a small range of these wavelengths were visible to the eye. Visible light quickly became only a small subset of the entire "electromagnetic spectrum". Long wavelength electromagnetic radiation became identified as "radio waves" that could be generated and detected with electronic gear, leading to the foundation of radio communications.

In 1676, the Danish astronomer Olaus Roemer noticed that the timing of the eclipses of the moons of Jupiter shifted relative to the position of the Earth, advancing when the Earth was on the same side of the Sun as Jupiter and falling back when the two planets were on opposite sides of the Sun. He was able to perform a crude calculation of the speed of light by measuring the delay and using an estimate of the size of the Earth's orbit.

In the 19th century, improved technologies permitted a much more accurate measurement of the speed of light. The French experimentalist Armand Fizeau used a system of rotating toothed wheels, intercepting a light beam that was routed between them over a roundabout path with a set of mirrors to increase the path length. The speed of rotation of the wheels was increased until the light was blocked, allowing calculation of the speed of light from the path length, the size of the gap between the teeth of the wheels, and the rate of rotation.

His colleague Jean Foucault performed even better measurements using a system that was based on spinning mirrors rather than toothed disks. The value turned out to be very close to 300,000,000 meters per second.

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[7.2] THE ELECTROMAGNETIC SPECTRUM

                   300,000,000
    wavelength  =  -----------
                    frequency
 
 

The visible light that humans can sense is only a very small part of the full EM spectrum. The spectrum extends through longer wavelengths, down through the "infrared", "microwave", and "radio" regions, and through shorter wavelengths, including the "ultraviolet", "X-ray", and "gamma-ray" regions.

    THE EM SPECTRUM
    __________________________________________________________________
 
    radio                 30 centimeters or longer
    microwave             1 millimeter to 30 centimeters
    infrared              0.77 microns to 1 millimeter
    visible               0.39 to 0.77 microns
    ultraviolet           10 nanometers to 0.39 microns
    X-ray                 10 nanometers to 10 picometers
    gamma ray             10 picometers or shorter
    __________________________________________________________________
 
    A "micron" is a micrometer, or millionth of a meter.  There is actually
    overlap in the definitions of all the bands except the visible band, and
    the figures given here are useful simplifications.
 
 

The visible light region of the spectrum is divided into "color subbands". These range from low-energy red and orange bands, to more energetic and longer-wavelength yellow and green bands, to high-energy blue, indigo, and violet bands. Light emitted by the Sun and by incandescent light bulbs consists of a mix of these bands, and is known as "white light".

    COLOR SUBBANDS 
    __________________________________________________________________
 
    red visible           0.622 to 0.770 microns
    orange visible        0.597 to 0.622 microns
    yellow visible        0.577 to 0.597 microns
    green visible         0.402 to 0.577 microns
    blue visible          0.455 to 0.402 microns
    violet visible        0.390 to 0.455 microns
    __________________________________________________________________
 
 

[7.3] LIGHT EMISSION

The continuous spectrum emitted by a solid or liquid object generally approximates that produced by a "perfect emitter" or "blackbody". In a blackbody, the intensity of the light across the frequency spectrum rises to a peak corresponding to a specific temperature, and then declines rapidly for higher frequencies.

As a blackbody is heated and grows hotter, it first emits in the infrared, then glows dull red, next turning orange as it gets hotter, then yellow, then white, and finally bluish-white, with the colors corresponding to increasing peak frequencies. As the blackbody is heated even more, emission begins to occur in the ultraviolet, then in the X-ray region and finally the gamma-ray region of the spectrum.

The blackbody would still appear to be bluish-white to the eye, though anyone close enough to inspect it once it got that hot would probably want to be someplace else. The total energy output of the blackbody increases at approximately the fourth power to temperature, meaning that if the temperature is doubled, the energy output is increased by sixteen times.

Stars are a good approximation of blackbody emitters. Relatively cool stars are red, while very hot stars are bluish white. Small cool red stars have relatively low energy output and live for a very long time, while large hot stars use up their energy rapidly and so have short lives. A more mundane example of thermal emission is the ordinary incandecent light bulb, which glows by heating a filament with an electric current.

Most of the thermal emission in our surroundings is in the infrared. This emission allows infrared scopes and cameras to detect objects in the dark. The appearance of objects seen from their thermal emission can be confusing as it is very different from that seen in daylight, and such infrared "imagers" often have a switch to flip the scene from "light on dark" to "dark on light" to help a user figure out a scene.

Gas-filled lamps used in front-window displays of bars and other commercial establishments are filled with gases excited by an electric current, with the color determined by the type of gas. Neon, for example, gives an orange light.

Interestingly, if white light is shined through a cool gas, the gas will absorb light at these specific frequencies, forming a "line absorption spectrum" that consists of dark lines across the rainbow spectrum in the background. The specific pattern of lines in an emission or absorption spectrum can be used to determine the chemical composition of everything from atmospheric gases to distant stars. This technique is known as "spectroscopy".

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[7.4] LIGHT POLARIZATION

A "filter" can be designed to pass light of one polarization, but not another. For example, the lenses of "Polaroid" sunglasses contain long-chain molecules that are all oriented in a straight line in one direction. Light can pass through the lens if the polarization is in the same direction as that of the molecules, but not at other polarization angles.

One of the interesting applications of polarized light are "3D" or "stereo" movies, a common feature in theme parks, where the audience puts on special glasses to see objects coming out of the screen.

The illusion of depth is created by displaying a different image of the same scene to each eye, with the images originally filmed by a two cameras spaced apart. For example, an acquaintance of mine makes his own "still" stereo images by taking a picture of a building, then stepping several paces to one side and taking another picture of the building. He then pastes the prints onto cardboard to display in a World War I-vintage handheld stereo viewer.

It is not practical to use two distinct screens in a movie theater, so in that case the trick is to display the two images on the same screen and give the audience special glasses to sort them out. Early stereo movies played in the 1950s projected a blue and a red image onto the movie screen, and the audience wore glasses with one red and one blue lens to filter the appropriate image to each eye.

This scheme could also be performed with printed images, and is still in occasional use. Modern stereo movies project the two images using different polarizations at 90 degrees to each other, and the glasses used by the audience similarly have two polarized lenses with the plane of polarization at right angles to each other.

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[7.5] LIGHT AND MATTER

Reflection is a simple process. If a beam of light strikes a smooth, flat reflective surface such as a mirror at an angle, it will bounce off the mirror at the same angle as it struck. Of course, if the surface is rough, it will be scattered rather than neatly reflected. The angle of reflection does not change with the wavelength of the light.

Light passing through a transparent material tends to be refracted. This can be seen by observing from certain angles a spoon stuck in a glass of water, which appears bent under the water. The amount of bending depends on the material's "refractive index". It also depends on the wavelength of the light, which is why a prism creates a tiny "rainbow" when sunlight shines through it, since the different wavelengths of light bend in a range of different directions.

The amount of bending for a material with a given refractive index is given by "Snell's Law", which is very important for the design of lenses for optical instruments. If a beam of light is passing through a medium with refractive index R1 and strikes the surface of a medium with a refractive index R2, then the angle of the beam relative to the vertical in the two mediums is given by:

    R1 / R2  =  SIN( angle1 ) / SIN( angle 2)
 

Incidentally, if light strikes a medium of different refractive index at a shallow enough angle, all the light will be reflected. This phenomenon is known as "total internal reflection". One application of total internal reflection is "optical fibers", the threads of glass sometimes used in novelties and for data-communications links. These optical fibers have a glass core with one index of refraction and an outer layer or "cladding" of another, causing light sent down the axis of the fiber to be reflected down its length with few losses.

Light is also diffracted, bending around edges of narrow openings. Diffraction, like refraction, is wavelength dependent, and can produce rainbows from a light source. Astronomers performing spectroscopy of stars and other cosmic objects normally do not use a prism to obtain the line spectra of those objects, since a prism would have a narrow field of view. Instead, they use a "diffraction grating", which is essentially a grooved mirror surface, with the reflected light diffracting around the edges of the grooves.

Objects with light-colored surfaces reflect most of the light falling on them, while those with dark-colored surfaces absorb most of the radiation falling on them, with the energy then released as as thermal emission. Some objects may selectively absorb some wavelengths and reflect others. Plants absorb blue and red wavelengths to perform photosynthesis, while reflecting green wavelengths, which is why most plants appear green.

The reflectivity of an object is also dependent on its smoothness. A very smooth surface reflects light without much scattering, and is known as a "specular" or "mirror" reflector. Calm bodies of water are specular reflectors. A rough surface scatters light, and is known as a "diffuse" reflector.

Except for the few of us who have been astronauts, we observe light that has passed through the atmosphere. The atmosphere not only blocks light through hazes and clouds, but also selectively scatters light at the shorter wavelengths. Such scattering diffuses short-wavelength blue light from the Sun, causing it to appear all over the sky and so making the sky blue.

On the other side of the coin, sunsets tend to be red because shorter "bluish" wavelengths of light are scattered, subtracting them from the Sun's light and leaving longer "reddish" wavelengths behind. Smoke from forest fires increases the level of particulates, particularly soot particles, in the atmosphere, which cause even greater reddening, resulting in dramatic "blood red" sunsets.

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[7.6] THE EYE AND COLOR

• "Blue" cones are most sensitive to short wavelengths of visible light, centered around a wavelength of 0.44 microns.

• "Green" cones have a peak sensitivity around a wavelength of 0.53 microns.

• "Red" cones have a peak sensitivity around a wavelength of 0.57 microns, which is actually in the yellow band of the visible spectrum. However, the red cones still have strong response at redder wavelengths.

The perception of colors depends on the ratio of stimulation of these three types of cones by light, or in other words on the ratio of the red, green, and blue (RGB) components. These three "primary colors" add as follows:

    ___________________________________
 
    red   + green + blue -> white 
    red   + green        -> yellow 
    blue  + red          -> magenta 
    green + blue         -> cyan 
    ___________________________________
 
 

    ___________________________________
 
    magenta + cyan    -> blue
    yellow  + cyan    -> green
    yellow  + magenta -> red
    ___________________________________
 
 

Perceived colors are also dependent on brightness, since rods tend to dominate over cones as light levels drop. The eye is very sensitive to colors, able to distinguish hundreds of thousands of different colors. However, the eye's ability to automatically compensate for changes in brightness makes it very poor at discriminating light levels, with test showing the number of levels it can discriminate as no more than about 30.

The eye's structure and the network of nerve cells that support that structure are optimized for certain tasks, such as determining the edges of objects and their motion. The eye, interestingly, is not very sensitive to changes in shade across a scene. A large square that varies gradually in shade from side to side will appear as one color.

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[7.7] INTRODUCTION TO OPTICAL TECHNOLOGY

The very first modern optical device was the one-lens microscope, or what we would now call a simple magnifying glass, and of course it is still in use. It is simply a "convex" lens, thick in the middle and thin at the edges, in contrast to a "concave" lens, thin in the middle and thick at the edges.

The magnifying power of a single convex lens is related to its "focal point". Suppose narrow beams of light are sent through a convex lens directly face-on to the lens, entering the front of the lens in parallel and then emerging from the back, bent at angles that converge on a single location behind the lens, the focal point. If you've ever used a magnifying glass to start a fire from sunlight, you move the glass until the focal point sits on the item to be ignited.

The distance to the focal point from the back of the lens is the "focal length". The focal length decreases as the curvature of the lens and the refractive index of the lens material increase. An imperfectly ground lens will not direct all light entering it on a single focal point, an error that is known as "spherical aberration". As refraction is wavelength dependent, light of different colors may come to different focal points, an error that is called "chromatic aberration".

Vision perceives the elements of some visual "target" through the shortest optical path, or "ray", to each of those elements. In direct vision, the shortest ray is a straight line.

Consider a simple visual target, consisting of four different-colored diamonds clustered side by side. To simply analysis, we'll assume that there is only a single optical path between the eye and each of the four diamonds. Of course, if the target is moved farther away from the eye, its angular size becomes proportionately smaller.

Now let's place a simple convex lens between the eye and the target. With the lens in the way, the shortest optical paths to the four target elements are no longer simple straight lines. The lens acts to bend or reroute rays that wouldn't have reached the eye in direct vision, giving a modified view of the target.

The first telescopes were based on refractive principles, with a set of two or more convex lenses "stretching" out a small and distant image and bringing it to a focus. The convex lens configuration passes light straight through the middle of the lens, where it is thickest, while bending it at an angle that increases as the distance from the center of the lens increases. This brings light to the focus. The ratio of the size of the lens to the distance of the focus is known as the "focal length" of the telescope.

Such "refracting telescopes" or "refractors" were limited in size by the difficulty of grinding large lenses, which also became impractically thick and heavy as they became bigger, and the long focal lengths of the type, which required long telescope tubes. They also suffered from "chromatic dispersion" or "chromatic aberration", since different colors of light a different angle of refraction, resulting in a colored "halo" around objects.

Although Isaac Newton had demonstrated a "reflective" telecope with a large mirror at the bottom to collect and focus light, difficulties in making mirrors that could keep their form and remain shiny kept reflectors out of use until late in the 19th century, when techniques were discovered for laying down a thin layer of silver on a glass mirror. Now "reflectors" are the norm for large telescopes, though refractors remain useful for small instruments.

A common misconception about astronomical telescopes is that their main function is to provide magnification of distant objects. This is not entirely the case. Cosmic objects may be very large but very faint. For example, the Andromeda Galaxy, the nearest major galaxy to our own, has an apparent size in the sky seven times that of the full Moon, but is is so far away and faint that only the brightest portion of its central "nucleus" can be seen, and then only on a dark night.

That means light collection is actually more important. The light collecting ability of a telescope is a function of the total amount of light collecting area, which for a reflecting telescope is the size of the mirror, or what is known as the telescope's "aperture". Magnification is simply a function of the eyepiece.

Telescopes are rated in terms of aperture size, for example as a 10 centimeter, 30 centimeter, 1 meter, or 3 meter telescope. These are the simply the diameters of the mirrors, while their light-gathering capability is a function of their area, and so the actual capability is proportional to the square of their apertures. For example, a 3 meter telescope has nine times the light-gathering capability of a 1 meter telescope. Telescopes can also be used for spectroscopy by placing a prism, or more commonly a diffraction grating, at the focus of a telescope.

Through most of the 20th century, most large astronomical telescopes recorded their images on photographic film. This not only allowed recording the images, permitting inspection at leisure and long-term archiving, but the photographic film could build up faint images over long exposures. Modern large astronomical telescopes now use electronic sensor systems, linked to computers that store and analyze the image data.

Telescopes carried on orbiting astronomical satellites may have a "turntable" that carries different sensors, for example one with a wide field of view and poor resolution, another with a narrow field of view and good resolution, and a third that performs spectroscopy. Other switching schemes may be used to divert a space telescope's image if the sensors are too large to be mounted on a turntable.

In fact, after the construction of the 5.1 meter (200 inch) Hale telescope at Mount Palomar observatory in the late 1940s, there was a general perception that telescopes couldn't get much bigger, because the thermal mass of the mirror would become so great that the mirror wouldn't be able to cool down and stabilize until the night was over. The mirror would also be impractically heavy to mount and use.

However, in the 1980s and 1990s new telescopes were designed that got around this limitation. The famous pair of Keck telescopes on Mauna Kea in Hawaii use a set of 36 hexagonal thin mirror segments that are fit together on a mechanical support structure that continuously adjusts the positions of the segments to ensure a good focus, with the adjustments controlled by optical sensors. Each Keck telescope has a composite aperture of 10.1 meters (400 inches), with four times the light-gathering power of the Hale telescope.

Infrared telescopes use more or less conventional optical telescope designs, but since infrared radiation is mostly absorbed by the atmosphere, infrared telescopes are usually built to be flown in balloons, high-flying aircraft, or as orbital satellites. They have to be cooled, traditionally with liquid helium in a double-dewar flask, to be sensitive to faint sources of radiation. It is impossible to pick up a faint thermal source with a detector that is warmer than the source is, because the detector's own thermal emission drowns out the emission of the source.

Short-wavelength high ultraviolet and X-ray radiation is also mostly absorbed by the atmosphere and has to be observed by satellites. These short wavelengths cannot be focused by a conventional mirror, since they are so energetic that they go right through it. However, they will "skip" over a mirror at low angles, like a flat rock skipping over the surface of water, and so they can be focused by "grazing incidence" mirrors, which look like tubes that taper to a smaller diameter in a smooth curve from front to back.

Such grazing-incidence mirrors are nested to increase the amount of radiation they focus. Typically, they consist of a primary stage with four nested cylinders with a parabolic curvature, feeding a secondary stage with four nested cylinders with hyperbolic curvature. The secondary stage focuses the radiation on an electronic detector, which has to be shielded with lead along its bottom and sides to prevent stray X-rays from introducing noise. Gamma rays cannot be focused at all, and so they are recorded by purely electronic systems.

Notice that the length of the baselines in the array only affects the resolution of the images obtained. The sensitivity of the array, or essentially the amount of radio energy it can collect, remains proportional to the sum of the areas of the individual radio telescopes in the array.

In the late 1980s, optical interferometer telescope arrays have been built as well. Due to the fact that optical wavelengths are much shorter than radio wavelengths, an optical interferometer requires extremely precise spacing and separations are no more than a few hundred meters.

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[7.8] LIGHT & A NEW PHYSICS

This was a puzzle, and it was one of the reasons that there was uncertainty as to whether light was a wave or particle until Thomas Young's two-slit experiment. A wave implies a transmission medium, while a particle flies across empty space just fine.

Since nobody could actually detect any medium that could propagate light waves, physicists had to imagine an invisible "luminiferous (light-bearing) ether" that permeated the Universe to do this job, but this was such an arbitrary construct that many were uncomfortable with it. It also led to another troublesome issue: if there was such an "ether" filling the Universe, how would the motion of the Earth, or any other object, affect the perceived velocity of light?

Albert Einstein went a bit further and wondered if were possible that the Earth or some other object might actually travel through the ether so fast that it would exceed the speed of light. Under such circumstances, a person would not be able to see his or her reflection in a mirror.

Einstein moved from this line of reasoning to create his "Theory of Special Relativity", the first of the two major revolutions in physics in the 20th century. This theory postulated that there was no ether, and that the speed of light was always the same to all observers, no matter what their speeds relative to each other might be. This led to some very non-intuitive consequences.

There were other difficulties as well. For example, if a thermal emitter produced light of wavelengths all up the EM spectrum, the energy would have been infinite, destroying the Universe in the flare of a single match. Instead, a thermal emitter produces a black body spectrum, with the energy falling off above the peak emission wavelengths.

Another issue was the nice neat spectral lines of light emitted or absorbed by atoms. It seemed like atoms were some sort of resonant chambers for light, but nobody could figure out exactly why that would be so.

These and other puzzles led to the second major revolution in 20th century physics, known as "quantum physics". Quantum physics led to even more bizarre quandaries than relativistic physics, proclaiming that particles could be wave, waves could be particles, and that there were fundamental limits on how well physical interactions could be measured.

Both relativistic and quantum physics broke the boundaries of conventional physics, and as such they leave the domain of this document. Relativistic physics is discussed in a companion document to this one, and a companion document on quantum physics is being planned.

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From Vectorsite.net.

See also: Physics