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• How a glass prism resolves light into its rainbow components, which can be recombined to create white light.

• The difference between spectral colors and the colors perceived by the eye.

• That hot solids (or dense gases) radiate a continuous spectrum, related to their temperature.

• That the colors of a glowing rarefied gas are characteristic of the atoms emitting them, with examples.

• That cold atoms in a gas absorb the same colors as the ones they emit when hot, and that such absorbtion causes dark lines in the Sun's spectrum.

• That light is a wave spreading through space, with a very short wavelength, or the order of a few microns (0.001 millimeter).

Note: This lesson can also be embedded in a course on optics. At this level, the student is told that the wave nature and wavelength are deduced from the way parts of a beam of light resonate with each other. The question of why these waves are called "electromagnetic" is left for the next lesson.)

Terms: [Refraction of light, dispersion of light], spectrum, spectral color, perceived color, 3-color theory, black body spectrum, spectral lines, diffraction grating, wave, wavelength, absorption spectrum.

Stories: Discovery of helium.

Starting the lesson:

(One way of introducing the subject of color is through the rainbow. Accordingly, unless time is short, the teacher may devote the beginning of the class to the phenomenon of the rainbow. The discussion here also extends into optics--the study of light.)

One striking phenomenon involving color is the rainbow. People generally divide the rainbow into 7 colors. Anyone knows what they are, in the order in which they appear?

(Students may answer--put on board, make sure class copies). Red, orange, yellow, green, blue, indigo, violet

(All of you know "indigo"? It is the name of a dye. What color are blue jeans?

• dark ones are indigo, light ones are blue)

We obtain the same sequence when light passes a prism--red is bent least, violet the most (draw on board). Anyone knows why? (students may answer)

Because (draw on board, students copy) light hitting a flat surface of glass gets bent by an angle. (That is known as refraction--"The beam of light is refracted.")
  However, different colors are bent by different amounts. (That feature is known as the dispersion of light).

When a beam of light hits a glass windowpane (draw on the board) with two parallel sides, the beam is refracted one way as it enters the glass, then the opposite way as it leaves. The net result is that it emerges with the same direction as before. So, inside the glass diffect colors may be separated, but when they emerge again they all move again in the same direction, and no separation remains.

In a prism (refer to drawing already on the board), the entry side and the exit side are inclined, not parallel, and therefore the direction is changed--by a different amount for each color.

      How about rainbows? When do you see rainbows?

• We see rainbows when the Sun is shining on falling rain. Typically, a rain cloud has passed over you and you are now in the sunlight again. (Students may also mention rainbows in sprays from large waterfalls or from garden sprinklers.)

Has anyone noticed where in the sky the rainbow appears?

• Always on the side opposite the Sun. In fact, it is part of a circle whose center is exactly in the opposite direction from the Sun. And the outermost color is always red.

Now, the big question: why the colors?

Raindrops are tiny spheres (draw on board) and act very much like prisms. The light that is reflected inside is separated into colors, and when it comes out--at a point where the angle of the surface is different, just as it is in a prism--the different colors are separated.

    Let me give you a hint. When a beam of light goes through a windowpane (refer the drawing on the board), not all the light goes through. Some of it, instead of being refracted the second time, is reflected back, as if the back of the glass was a mirror. (add the reflected beam to the drawing on the board, a broken line.)

• By light reflected once inside the raindrop, as in the drawing.

•     Answer: He used a second prism (upside-down to the first) to bring all the colors together again, and the result was white light, like the one which entered the first prism.

He then placed a thermometer on the place where the spectrum fell, and noted that the temperature rose.

He then moved the thermometer past the red edge of the spectrum, and noted that even there a higher temperature was recorded. What did this mean?

• Answer: The heating of the thermometer in the middle of the spectrum meant that light carried heat (or in our terms, carried energy).

• The heating of the thermometer past the edge of the spectrum suggested that light was shining there as well--a new invisible color which the eye could not see, but the prism was able to separate. Today we would call it infra-red ("infra" means "below"--related to "inferior")

In a TV with a black-and-white picture tube, the screen contains many small dots which glow when a beam of electrons passes them. The beam sweeps over the picture many times each second, and by controlling its strength, each dot it passes over can be made to shine brightly, dimly or not at all. This way a picture is painted on the screen. The newer flat screens have no electron beams, but the glowing dots are directly connected electrically--otherwise it is very similar.

• The screen of a color TV has 3 types of dots, each glowing in a different color, each connected separately to a source of electricity. At any time only one color is connected, and only it responds to the beam. Then the next color is switched on, then the third, and then the cycle repeats. The electrons therefore always paint, very quickly, a red picture, a yellow one and a blue one, and the eye sees the three combined.

• Our eye's ability to tell colors apart is limited. It contains three types of cell, each sensitive to a different range of colors. Any color--of the rainbow or otherwise-- is therefore seen as equal to some combination of the 3 "primary colors. " Color printers, too, need only use inks in three colors.

• To the eye, yes. In spectrograph, an instrument where colors are separated by a prism orange creates one response, red plus yellow, a completely different one. Orange is one color, red and orange, two.

• Tell about James Clerk Maxwell. (see story from the web page)

• A combination of the 3 colors produced white. (and that is how a color TV or computer screen produces white, too.)

• A distribution of colors, as obtained (for instance) by a prism.

From now on we only discuss "spectral color" as seen by a prism instrument ("spectrometer"), rather than color observed by the eye.

• The light of a glowing filament has a smooth continuous spectrum ("black body spectrum"), most intense at a color which depends on temperature. (see here; much but not all of sunlight is of this type, too.)

• The light of glowing rarefied gas, like that in a fluorescent tube, has a "line spectrum" concentrated in "spectral lines" of well-defined colors, characteristic of the gas. If you see them in the spectrometer, the light source in the box is a fluorescent tube; if they are absent, the light comes from a hot filament.

(The fluorescent coating inside the tube absorbs light and re-emits it in a broad continuous spectrum, so in addition to spectral lines, you will also see a continuous spread.)

• The Sun is hotter than Antares, not as hot as Sirius.

• Because the battery cannot supply as much electric current as before, the filament in the lightbulb isn't as hot as it should be.

• Heat easily makes sodium atoms emit a distinct yellow "spectral line" (actually two lines, very close in color). Firewood, paper, candle wax and most other combustible materials contain at least traces of table salt (sodium chloride), which colors the flame.

    The polar aurora or "northern lights" is emitted by the high atmosphere (around 100 km or 60 miles) when beams of fast electrons from space hit the edge of the atmosphere. These electrons are guided by the Earth's magnetic field lines and therefore are generally observed only in an "auroral zone" around the magnetic pole, typically 2500 km from the pole. At locations like Fairbanks, Alaska, aurora is not all that rare. (See here for more about the aurora, and here about the auroral zone.)

    Light is emitted when those electrons collide with atoms, a bit like the way light is emitted when a beam of fast electrons inside a TV picture tube hits the screen. Different spectral lines are observed, but the brightest and most common one is a green spectral line at a wavelength of 0.5577 micron. A red line at 0.6300 micron is also sometimes emitted.

    These emissions used to puzzle scientists, because they failed to match any spectra in the laboratory. Did the upper atmosphere contain any new unknown substance?

    Around 1925, the answer was found--both colors came from oxygen. When an oxygen atom was activated ("excited") by a collision in a certain way, it took about half a second before it emitted light, an unusually long time. In laboratory experiments, the gas used was so dense that other atoms usually collided with the excited atom and carried away its extra energy. Only high in the atmosphere could the emission process proceed undisturbed.
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lines.)

    The grating acts like many closely spaced slits: the light hitting between the slits is scattered irregularly, and only what hits the slits goes through. If light acts as a wave, one can show mathematically that each slit acts as a new source of the wave.

(By the way--the "slits" are really the ridges between the grooves of the grating, which transmit light like a windowpane, not the grooves themselves)

    Suppose light arrives at the grating from a direction perpendicular to it. Waves have peaks and valleys, and when the arriving wave-front is at a peak, all slits also start their "local waves" with a peak.

    Suppose we continue in the same direction 1, 2, 3... wavelengths. The wave from each slit will then also have a peak at those locations. These peaks would be in the same distances if the wave passed intact through the grating, as if it wasn't there, suggesting that much of the wave goes straight through, with no modification.

But wait! If each slit is the source of a wave spreading in all directions, what about the part spreading in slanted directions?

   Consider the part spreading at an angle θ to the original direction of light. The wave front of a wave moving in that direction would be along the drawn slanted line. However, the distances of the points on that line from the various slits--each a separate "light source"--are all different! If at the slits the wave has a peak, at the wavefront, different parts of it are in different parts of the cycle. They are at a peak if the distance to a slit is an exact multiple Nλ of the wavelength (N is some whole number), at a peak in the opposite direction if the distance is (N+0.5)λ, and in other parts of the cycle for other distances. The sum total--say 2000 slits, 2000 different distances--is close to zero, so we get very little light scattered in the direction of θ. (That cancellation of peaks is called "destructive interference between the waves.")

    Except... if the angle θ is such that the distances of the wave-front from two neighboring slits differ by exactly one wavelength λ . In that case, the distances from the next slits in line are 2λ, 3λ ... and so forth, and the waves continue propagating "in step." That is "constructive interference" between the waves, and in those directions, you will see a fairly bright beam of light.

    Note that the angle θ at which the light undergoes constructive interference depends on the wavelength λ, that is, on the spectral color of the light. Each color is therefore bent by a different angle--just as it is in a prism. Because most of the beam goes straight through, the light may not be as bright as in a prism, but the separation of neighboring colors may be much more sensitive.

    The above formula allows the light's wavelength to be calculated. For example: you observe the yellow line of sodium with a grating having 1000 lines per centimeter, and find that light is brightest at an angle θ =36°. What is the wavelength λ?

    In fact, methods based on interference have measured wavelengths with such accuracy, that the international meter--originally defined by two scratches on a bar, kept in a vault in Paris--was at one time redefined in terms of the wavelength of a certain emission.

    Laser disks for recording songs, videos or data for computers, shimmer in colors, because they contain many closely spaced grooves, which make them act like a grating. The light is reflected from the grooves (with the help of an aluminum backing), rather than passing through, but the effect is very similar.

    Another interference effect are the colors seen when a thin layer of kerosene floats on a puddle of water--layers with a thickness of the order of a wavelength of light. Some light is reflected from the top of the kerosene layer, some from its bottom (which is the top of the water), and the two reflected waves interfere with each other. For some colors the interference is destructive, for others, constructive, leading to a shimmering of colors.

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• The continuous spectrum? ... It tells that the temperature of the photosphere is about 5780° Kelvin.

• The bright lines in the spectrum?... They tell us about the composition of the photosphere--mostly hydrogen, some helium, a bit of oxygen, carbon and heavier stuff (some lines, carefully recorded and analyzed, can also tell of the presence and strength of the local magnetic field).

• The dark lines of the spectrum?.... They identify cooler material in the higher levels of the photosphere.

• The spectrum of the corona, for instance, the presence of iron that has lost 13 electrons? ... It tells us the corona is very hot, and provides an estimate of its temperature.

• How was helium discovered? (The teacher can tell more about the discovery. The helium line was in the yellow part of the spectrum, and at first some astronomers credited it to sodium--but it had a slightly different wavelength, and it was gradually recognized that in no way could sodium produce it.)