2 Doggone It!When the “dog days” of summer give way to the “three dog nights” of winter, inhabitants of colder climates are often treated to spectacular apparitions like that shown in the accompanying photo.On brisk days when the Sun is near the horizon and the sky is filled with thin clouds of ice crystals, one often sees bright patches of light flanking the Sun at an angular distance of about 22.
3 Doggone It!These patches frequently exhibit rainbowlike coloration and are variously called mock suns, parhelia, or sundogs.Next to rainbows themselves, sundogs are among the most common atmospheric optics effects seen at midlatitudes and above.
4 Doggone It!This phenomenon, like that of rainbows and halos, touches us with its beauty, but it also stirs our intellectual curiosity about what naturally occurring circumstances conspire to produce such an exquisite display.What are the underlying physical principles governing the processes that lead to such striking visualizations?How, if at all, might they be related to other optical phenomena often seen in the sky such as rainbows?
5 Doggone It!The wonder and fascination afforded to us by Nature in the form of sundogs can be enhanced by finding answers to these questions.A primary ingredient in the mix that provides the answers we seek is the law of refraction.By applying this principle and paying close attention to the relationship between the natural elements in play, you should be able to frame responses to the questions posed above.
6 Doggone It!In this chapter, we will investigate the law of refraction together with its counterpart, the law of reflection, to discover that they comprise two important elements in the study of light and its interaction with matter–the field of optics.These laws also provide the basis for many practical devices, such as cameras, telescopes, and liquid-crystal displays, as well as for many of the most striking natural phenomena, such as rainbows, soap-bubble iridescence, and, of course, sundogs.
7 9.1 Light WavesLight generally refers to the narrow band of electromagnetic (EM) waves that can be seen by human beings.These are transverse waves with frequencies from about 4×1014 hertz to 7.5×1014 hertz.
8 9.1 Light WavesThe corresponding wavelengths are so small that we will find it useful to express them in nanometers (nm).One nanometer is one billionth of a meter:
9 9.1 Light WavesThe wavelengths of visible light (in a vacuum or in air) range from about 750 nanometers for low-frequency red light to about 400 nanometers for high-frequency violet light.Keep in mind two important points:1. different frequencies of light are perceived as different colors, and2. white light is typically a combination of all frequencies in the visible spectrum.
10 9.1 Light WavesAs with sound and water ripples, we will use both wavefronts and rays to represent light waves.Recall that a wavefront shows the location in space of one particular phase (peak or valley, for example) of the wave.
11 9.1 Light WavesFor a light bulb or other spherical light source, the wavefronts are spherical shells (not unlike balloons) expanding outward at the speed of light.
12 9.1 Light WavesA light ray is a line drawn in space representing a “pencil” of light that is part of a larger beam.Rays are represented as arrows and indicate the direction the light is traveling.A laser beam can often be thought of as a single light ray.The light from a light bulb can be represented by light rays radiating outward in all directions.Be careful not to confuse these light rays with the electric and magnetic field lines discussed in the previous chapters.
13 9.1 Light WavesSome of the general characteristics of wave propagation, such as reflection, are readily observed with light waves.But other phenomena are more rare in everyday experience because of two factors:1. The speed of light is extremely high (3×108 m/s in a vacuum).2. The wavelengths of light are extremely short.
14 9.1 Light WavesWe must turn to distant galaxies moving away from us at high speeds to easily observe the Doppler effect with light.The Doppler effect with sound, on the other hand, is quite common because the speed of sound is only about 350 m/s and the wavelengths of sound (in air) are in the centimeter to meter range.In these first two sections, we will describe some of the phenomena that can occur when light encounters matter.The remaining sections of the chapter deal with important things that occur after light has traveled inside transparent material.
15 9.1 Light Waves Reflection Reflection of light waves is extremely common:Except for light sources such as the Sun and light bulbs, everything we see is reflecting light to our eyes.There are two types of reflection:specular and diffuse
16 9.1 Light Waves Reflection Specular reflection is the familiar type that we see in a mirror or in the surface of a calm pool of water.A mirror is a very smooth, shiny surface, usually made by coating glass with a thin layer of aluminum or silver.Specular reflection occurs when the direction the light wave is traveling changes.
17 9.1 Light Waves Reflection By changing the angle of the incident (incoming) light ray and observing the reflected ray, we see that the light behaves somewhat like a billiard ball bouncing off a cushion on a pool table.
18 9.1 Light Waves Reflection The figure shows an imaginary line drawn perpendicular to the mirror and touching it at the point where the incident ray strikes it.This line is called the normal.The angle between the incident ray and the normal is called the angle of incidence, and the angle between the reflected ray and the normal is called the angle of reflection.Our observations indicate that these angles are always equal.
19 9.1 Light Waves Reflection The following law, first described in a book titled Catoptrics and thought to have been written by Euclid in the third century BCE, states this formally.Law of Reflection: The angle of incidence equals the angle of reflection.So specular reflection of light is much like sound echoing off a cliff.
20 9.1 Light Waves Reflection The other type of reflection, diffuse reflection, occurs when light strikes a surface that is not smooth and polished but uneven like the bottom of an aluminum pan or the surface of this paper.The light rays reflect off the random bumps and nicks in the surface and scatter in all directions.
21 9.1 Light Waves Reflection The law of reflection still applies, but the rays encounter segments of the irregular surface oriented at different angles and therefore leave the surface with different directions.That is why you can shine a flashlight on the aluminum and see the reflected light from different angles around the pan.With specular reflection from a mirror, you could see the reflected light from only one direction.
22 9.1 Light Waves Reflection Except for light sources and smooth, shiny surfaces such as mirrors, every object we see is reflecting light diffusely.This diffuse reflection causes light to radiate outward from each point on a surface.You can see every point on your hand as you turn it in front of your face because each point on your skin is reflecting light in all directions.
23 9.1 Light Waves Reflection Things can have color because light actually penetrates into the material and is partially reflected and partially absorbed along its way into and out of the material.The reflected light that leaves the surface will have color if pigments in the material absorb some frequencies (colors) more efficiently than others.
24 9.1 Light Waves Reflection A white surface, like this paper, reflects all frequencies of light nearly uniformly.If you shine just red light on it, it will appear red.With just blue light, it will appear blue.A colored surface, like that of a red fire extinguisher, “removes” some frequencies of the light.
25 9.1 Light Waves Reflection A red surface reflects the lower frequency light (red) most effectively and absorbs much of the rest.If you shine red light on it, it will appear red.With blue or any other single color, it will appear black:very little of the light will be reflected
26 9.1 Light Waves Diffraction As with all waves, diffraction of light as it passes through a hole or slit is observable only when the width of the opening is not too much larger than the wavelength of the light.
27 9.1 Light Waves Diffraction This means that light doesn’t spread out after passing through a window nearly as much as sound does, but diffraction is observed when a very narrow slit (about the width of a human hair) is used.The narrower the slit, the more the light spreads out.
28 9.1 Light Waves Interference Recall that when two identical waves arrive at the same place, they add together. If the two waves are “in phase”—peak matches peak—the resulting amplitude is doubled.This is called constructive interference.At any point where the two waves are “out of phase”—peak matches valley—they cancel each other.This is destructive interference.
29 9.1 Light Waves Interference Interference of light waves is an important phenomenon for two reasons.First, in experiments conducted around 1800, British physician Thomas Young used interference to prove that light is indeed a wave.Second, interference is routinely used to measure the wavelength of light.We will consider two types of interference: two-slit interference and thin-film interference.
30 9.1 Light Waves Interference When a light wave passes through two narrow slits that are close together, the two waves emerging from the slits diffract outward and overlap.If the light consists of a single frequency (color), a screen placed behind the slits where the two light waves overlap will show a pattern of bright areas alternating with dark areas.
31 9.1 Light Waves Interference At each bright area, the two waves from the slits are completely in phase and undergo constructive interference.
32 9.1 Light Waves Interference Conversely, at each dark area the two waves are completely out of phase and undergo destructive interference—they cancel each other.There is a bright area at the center of this interference pattern because the two waves travel exactly the same distance in getting there, so they are in phase.At the first bright area to the left of center, the wave from the slit on the right has to travel a distance exactly equal to one wavelength farther than the wave from the slit on the left.
33 9.1 Light Waves Interference This puts them in phase as well.Similarly, at each successive bright area on the left side, the wave from the right slit has to travel 2, 3, 4, wavelengths farther than the wave from the left slit.At each bright area on the right side of the pattern, it is the wave from the left slit that has to travel a whole number of wavelengths farther.
34 9.1 Light Waves Interference At the first dark area to the left of the center of the pattern, the wave from the right slit travels one-half wavelength farther than the wave from the left slit.The two waves are out of phase and interfere destructively.At the next dark area on the left, the additional distance is wavelengths, then wavelengths at the next, and so on.
35 9.1 Light Waves Interference True constructive and destructive interference actually occurs only at the centers of the bright and dark areas.At points in between, the waves are neither exactly in phase nor exactly out of phase, so they partially reinforce or partially cancel each other.
36 9.1 Light Waves Interference The distance between two adjacent bright or dark areas is determined by the distance between the two slits, the distance between the screen and the slits, and the wavelength of the light.Because the first two can be measured easily, their values can be used to compute the wavelength of the light.The swirling colors you see in oil or gasoline spills floating on wet pavement are caused by thin-film interference.
37 9.1 Light Waves Interference Part of the light striking a thin film of oil is reflected from it, and part passes through to be reflected off the water.
38 9.1 Light Waves Interference The light wave that passes through the film before being reflected travels a greater distance than the wave that reflects off the upper surface of oil.If the two waves emerge in step, there is constructive interference. If they emerge out of step, there is destructive interference.
39 9.1 Light Waves Interference The wavelength of the light, the thickness of the film, and the angle at which the light strikes the film combine to determine whether the interference is constructive, destructive, or in between.With single-color (one wavelength) light, one would see bright areas and dark areas at various places on the film.
40 9.1 Light Waves Interference With white light, one sees different colors at different places on the film.At some places, the film thickness and angle of incidence will cause constructive interference for the wavelength of red light, at other places for the wavelength of green light, and so on.
41 9.1 Light Waves Interference Interference in thin films in hummingbird and peacock feathers is the cause of their iridescent colors.Soap bubbles are also colored by interference of light reflecting off the front and back surfaces of the soap film.
42 9.1 Light Waves Polarization The fact that light could undergo diffraction and interference convinced Young and other scientists of his time that light can behave like a wave.The other model of light elaborated by Newton held that light is a stream of tiny particles, but this approach could not account for these distinctively wavelike phenomena.Polarization reveals that light is a transverse wave rather than a longitudinal wavelike sound.
43 9.1 Light Waves Interference A rope secured at one end can be used to demonstrate polarization.If you pull the free end tight and move it up and down, a wave travels on the rope that is vertically polarized.Each part of the rope oscillates in a vertical plane.
44 9.1 Light Waves Interference In a similar manner, moving the free end horizontally produces a horizontally polarized wave on the rope.Moving the free end at any other angle with the vertical will also produce a polarized wave.Polarization is possible only with transverse waves.
45 9.1 Light Waves Interference The fact that light can be polarized reveals its transverse nature.A Polaroid filter, like the lenses of Polaroid sunglasses, absorbs light passing through it unless the light is polarized in a particular direction.This direction is coincident with the transmission axis of the filter.
46 9.1 Light Waves Interference Light polarized in this direction passes through the Polaroid largely unaffected, light polarized perpendicular to this direction is blocked (absorbed), and light polarized in some direction in between is partially absorbed.
47 9.1 Light Waves Interference For simplicity, we will assume that our Polaroid filters are 100-percent efficient in absorbing light polarized in a direction perpendicular to the transmission axis.
48 9.1 Light Waves Interference The light that we get directly from the Sun and from ordinary light fixtures is a mixture of light waves polarized in all different directions.The light is said to be “natural” or “unpolarized” because it has no preferred plane of vibration.
49 9.1 Light Waves Interference When natural light encounters a Polaroid filter, it emerges polarized along the transmission axis.The filter allows only that portion of the incident light that oscillates along this direction to pass through; the rest of the radiation is absorbed.
50 9.1 Light Waves Interference Now, if the emergent light encounters a second Polaroid filter, the amount of light that passes through will depend on the orientation of the transmission axis of the second filter.If the axis of the second filter is aligned with that of the first, then the light will continue on unimpeded.If the axis of the second is perpendicular to that of the first, then all of the light will be blocked by the second filter.This is referred to as crossed Polaroids
51 9.1 Light Waves Interference When the angle between the transmission axes of the two filters is other than zero or 90, some of the light will pass through, with the intensity becoming progressively less for angles closer to 90.
52 9.1 Light Waves Interference Polaroid sunglasses are very useful because light is polarized to some extent when it reflects off a smooth surface like that of water, asphalt, or the paint on the hood of a car.In particular, the reflected sunlight is partially polarized horizontally.
53 9.1 Light Waves Interference This reflected light, called glare, is usually bright and annoying.Sunglasses using Polaroid lenses with their transmission axes vertical will block most of this reflected light, which makes it easier to see the surface itself.
54 9.1 Light Waves Interference LCDs used in calculators, digital watches, laptop computers, and video games also use polarization.The liquid crystal is sandwiched between crossed Polaroids, and this assembly is placed in front of a mirror.
55 9.1 Light Waves Interference Without the liquid crystal present, the display would be dark:Light passing through the first Polaroid is polarized vertically and would be totally absorbed when it reached the second Polaroid.No light would reach the mirror, so none would be reflected back from the display.
56 9.1 Light Waves Interference The specially chosen liquid-crystal material between the Polaroids is arranged so that in its normal state its molecules change the polarization of the light passing through it.The liquid crystal twists the polarized light 90°.
57 9.1 Light Waves Interference The polarization is changed from vertical to horizontal for light passing through from the front and from horizontal to vertical for light passing through from the rear.
58 9.1 Light Waves Interference The light that was vertically polarized by the first Polaroid is made horizontally polarized by the liquid crystal, passes through the second Polaroid, is reflected back through the display, and emerges polarized vertically.
59 9.1 Light Waves Interference To make images on the display, segments of it are darkened.Here is where the liquid crystal property is used.An electric field is switched on in the parts of the display to be darkened.This causes the molecules of the liquid crystal to rotate and become aligned in one direction.
60 9.1 Light Waves Interference As a result, they no longer change the polarization of light passing through.Light going through this segment is absorbed by the second Polaroid, and that part of the display is dark.
61 9.1 Light Waves Interference The transmission axis of the first Polaroid is oriented vertically so that you can see the display while wearing Polaroid sunglasses.If you rotate an LCD—say, like that on a digital watch—and look at it while wearing Polaroid sunglasses, at one point all of it will be dark.
62 9.1 Light Waves Interference Some color-blind animals such as squid can sense the polarization of light.This helps squid see plankton, which are transparent.Foraging honey bees use their ability to detect polarized light to help orient their waggle dances, which are used to communicate the locations of pollen sources to other bees.Even the human eye is weakly sensitive to polarized light, although to detect polarization without the use of intervening filters takes practice.