Lecture 6 6 Color, Waves, and Dispersion Reading Assignment: Read Kipnis Chapter 7 Colors, Section I, II, III 6.1 Overview and History In Lecture 5 we discussed the two different ways of talking about light: One is is the "particle" theory expressed in part by the word photon and the other was the "wave" theory, expressed by the term light wave. In 1807, Thomas Young backed up Huygens' wave theory by showing that when light passes through a very narrow opening, it can spread out, and interfere with light passing through another opening. Young shined a light through a very narrow slit. What he saw was a bright bar of light that corresponded to the slit. But that was not all he saw. Young also perceived additional light, not as bright, in the areas around the bar. If light were a stream of particles, this additional light would not have been there. This experiment suggested that light spread out like a wave. In fact, a beam of light radiates outward at all times. Albert Einstein advanced the theory of light further in 1905. Einstein considered the photoelectric effect, in which ultraviolet light hits a surface and causes electrons to be emitted from the surface. Einstein's explanation for this was that light was made up of a stream of energy packets called photons. Modern physicists believe that light can behave as both a particle and a wave, but they also recognize that either view is a simple explanation for something more complex. In this work we will talk about light as waves, because this provides the best explanation for most of the phenomena we will discuss. 6.2 Electromagnetic Waves and Wave Theory Why is it that a beam of light radiates outward? What is really going on? To understand light waves, it helps to start by discussing a more familiar kind of wave -- the one we see in the water. One key point to keep in mind about the water wave is that it is not made up of water: The wave is made up of energy traveling through the water. If a wave moves across a pool from left to right, this does not mean that the water on the left side of the pool is moving to the right side of the pool. The water has actually stayed about where it was. It is the wave that has moved. When you move your hand up and down in a filled bathtub, you make a wave, because you are putting your energy into the water. The energy travels through the water in the form of the wave. All waves are traveling energy, and they are usually moving through some medium, such as water. You can see a diagram of a water wave in Figure 1. A water wave consists of water molecules that vibrate up and down at right angles to the direction of motion of the wave. This type of wave is called a transverse wave.
Light waves are a little more complicated, and they do not need a medium to travel through. They can travel through a vacuum. A light wave consists of energy in the form of electric and magnetic fields. The fields vibrate at right angles to the direction of movement of the wave, and at right angles to each other. Because light has both electric and magnetic fields, it is also referred to as an electromagnetic wave. Light waves come in many sizes. The size of a wave is measured as its wavelength, which is the distance between any two corresponding points on successive waves, usually peak-to-peak or trough-to-trough (Figure 1). The wavelengths of the light we can see range from 400 to 700 billionths of a meter. But the full range of wavelengths included in the definition of electromagnetic radiation extends from one billionth of a meter, as in gamma waves, to centimeters and meters, as in radio waves. Light is one small part of the spectrum. Light waves also come in many frequencies. The frequency is the number of waves that pass a point in space during any time interval, usually one second. It is measured in units of cycles (waves) per second, or Hertz (Hz). The frequency of visible light is referred to as color, and ranges from 430 trillion Hz, seen as red, to 750 trillion Hz, seen as violet.
Again, the full range of frequencies extends beyond the visible spectrum, from less than one billion Hz, as in radio waves, to greater than 3 billion billion Hz, as in gamma rays. As noted above, light waves are waves of energy. The amount of energy in a light wave is proportionally related to its frequency: High frequency light has high energy; low frequency light has low energy. Thus gamma rays have the most energy, and radio waves have the least. Of visible light, violet has the most energy Light not only vibrates at different frequencies, it also travels at different speeds. Light waves move through a vacuum at their maximum speed, 300,000 kilometers per second or 186,000 miles per second, which makes light the fastest phenomenon in the universe. Light waves slow down when they travel inside substances, such as air, water, glass or a diamond. The way different substances affect the speed at which light travels is key to understanding the bending of light, or refraction. So light waves come in a continuous range of wavelengths, frequencies and energies. We refer to this continuum as the electromagnetic spectrum shown in Fig. 4. Fig. 4. 6.3 Colors 1. The Naming of Colors Isaac Newton named the colors of the spectrum we use today. He made 7 names of the colors of light to correspond to the seven named musical notes in an octave. Instead of
do-re-me-fa-so-la-te he named them ROYGBIV, red, orange, yellow, green, blue, indigo, violet 2. Non-spectral colors Notice that yellow and cyan appear in the spectrum of the slit however, magenta is not a color of the spectrum. This is because humans perceive yellow as the color produced by a single wavelength of light in the spectrum, they also perceive yellow as the mixture of two different single wavelengths, red and green. The same is true for cyan. No single wavelength of light produces the perception of magenta, red plus blue wavelengths must be combined. Therefore magenta is not a color of the spectrum. This means that white is not a color of the spectrum since at least three different wavelengths must be mixed to produce a perception of white. 6.4 The Primary Colors of Light and Color Algebra A prism breaks white sunlight up, spreading its component colors out into a spectrum of light visible to the human eye stretching from red through yellow, green and blue to violet as shown in Fig. 4. Scientists analyzing these colors find that they have a wave nature, and that one given wavelength of light is perceived as one color when viewed by a person. However, there are colors, which do not occur in the spectrum, such as magenta, these colors can only be created when two different wavelengths hit the same spot on the retina at the same time. Without human perception there is no color magenta. Indeed there is no white either. Thus to understand color we must understand the human retina. The human retina has three types of color receptors called cones; long wavelength called red (responds to light near 600 nanometers), medium wavelength green (responds to light near 550 nanometers), and short wavelength blue (responds to light near 450 nanometers). Because of this, almost all of the colors which we can perceive can be created by adding together three different wavelengths of light, these three colors: red, green, and blue, are called the primary colors of light. You can remember how the primary colors combine by recalling Fig. 5. By adding various combinations of red, green and blue light, you can make all the colors of the visible spectrum. This is how older computer monitors and televisions (RGB monitors) produced colors.
Fig. 5. Additive colors are red, blue, and green White When red, R, green, G, and blue, B light shine onto the retina in roughly equal amounts, then humans perceive white, W. So I can say that W = R+G+B. (This experiment is usually conducted by looking at a white screen illuminated by the three colored lights.) White is not a color of the spectrum. At least two different wavelengths of light (e.g. B+Y) must illuminate the retina at the same time to produce white. Remember, a color in the spectrum, by definition, can be produced by a single wavelength of light. Yellow When red and green light shine on the screen, humans perceive yellow. So Y = R+G. Now yellow is also a color of the spectrum which means that yellow is the color humans perceive when the retina is illuminated by a single wavelength of light. The single wavelength for yellow is between the wavelengths for red and green, the yellow causes both the red and green cones to fire nerve impulses. The electrical signal sent to the brain when the eye is illuminated by one wavelength of yellow is similar to the signal sent to the brain by the combination of two wavelengths R+G. Cyan Cyan, C, is a color of the spectrum. The wavelength of cyan light is midway between the wavelengths of blue and green. The crayon that used to be called blue- green is now called cyan, C. Cyan can also be created by adding blue light to green light. C = B+G. Magenta
When I mix blue and red light my eye perceives the color magenta, M. Magenta is not a color of the spectrum: no single wavelength of light can produce the color sensation called magenta. M = R + B. Mixing Colors I can use color algebra to predict the color I will create by mixing colors such as Blue and yellow: B + Y = B + (R + G) = W Two colors, which add to produce white, are called complementary colors so blue and yellow are complementary colors. I can also ask this question the other way around. What is the complementary color to red? R + X = W so R + X = R + G + B and X = G + B = C So red and cyan are complementary colors. Now figure out for yourself the complementary color to Green. Answer I could pick other colors to be my primary colors for light, such as red, yellow, and blue. However the number of colors I can produce by mixing red yellow and blue is less that the number of colors I can produce by mixing red, green and blue. Thus red, green, and blue are chosen as the primary colors of light. 6.5 The Subtractive Colors of Light Pigments remove light, usually by converting it to thermal energy. Pigments are used in: paints, dyes, pens, crayons and most colored filters. Chlorophyll of plants is a green pigment. It absorbs red and blue from white sunlight and scatters green. So the only color light that a plant does not want is? Green. In color algebra a green pigment is G = - R- B. The minus signs indicate that red and blue are removed. In terms of color algebra W - R- B = (R+G+B) - R- B = G By mixing three pigments you can create the widest range of colors by choosing magenta, cyan, and yellow as your primary colors. In terms of color algebra
* M = - G * C = - R * Y = - B. So each of the primary colors of pigment removes just one of the additive primaries. When I was in grade school these pigment primaries or subtractive primaries used to be called red, yellow and blue. However, today we know that choosing magenta, cyan, and yellow pigments can produce a wider range of colors. Fig. 6. Subtractive colors are cyan, yellow and magenta Mixing crayons Let's use color algebra to calculate what happens when we mix a yellow crayon with a cyan crayon. We shine white light on these pigments. White light on Cyan (- R) and yellow (- B) pigment W - R - B = (R + G + B) - R - B = G So yellow pigment plus cyan pigment equals green. Now I was taught that yellow plus blue crayons produced green, let's see what color algebra says. W on yellow(- B) and blue(- R- G) pigment. W - B- (R- G) = (R + G + B) - B - R - G = 0 = Black, K
yellow plus blue pigments equal black. So if a yellow crayon plus an unknown crayon equals green then the unknown crayon is cyan not blue. A Magenta light on a red apple Color algebra can also answer questions like what color will a red apple appear when illuminated by magenta light? Magenta light (R+B) on red pigment (- G- B) (R+B) - G - B = R (not - G because negative colors are not allowed to be the answer to a question "what do I see" in color algebra, and are dropped from the answer.) So the apple appears red. In cyan (B+G) light the apple appears: C - G- B = (B + G) - G - B = 0 Black. Answers: The complementary color to green is magenta. 6.6 Diffraction Grating Diffraction gratings can be used to explore the light emitted by different sources such as the sun, distant stars, "neon" tubes, and fluorescent tubes. The spectrum of light tells us what elements the light sources are made of and also what absorbing elements there are between the light source and us. Dark lines appear in the spectrum of sunlight due to light absorb by atoms in the outer atmosphere of the sun. The diffraction grating bends light away from its initial direction after passing through the grating. The angle through which the light bends is directly proportional to the wavelength. We will use the diffraction grating in this Lab to help understand the colors of light. In a later Lab we will study how the diffraction gating itself works but in this Lab we will just use it as a tool.