Exercises
1. Rearrange the letters in the anagrams to form equivalents for the Russian words:
Зеркала |
rorsmir |
|
|
Линзы |
seslen |
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Усиление |
ficationmagni |
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|
Увеличение |
largementen |
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Фокус |
Calfo ntipo |
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|
2. Match the words in A with the words in B to form word combinations:
A |
B |
Real |
reversal |
Concave |
lenses |
Convex |
image |
Chromatic |
mirror |
Diverging |
aberration |
Left-right |
mirror |
3. Fill in the gaps with the missing words from the list:
ray diagrams, magnification, thin-lens equation, image, focal point
1.The _____ formed by an object placed in front of a flat mirror is as far behind the mirror as the object is in front of the mirror.
2.Note that the word _____, as used in optics, doesn't always mean enlargement, because the image could be smaller than the object.
3.The _____ is not the point at which light rays focus to form an image, the focal point of a mirror is determined solely by its curvature - it doesn't depend on the location of any object.
4.The equation, called the _____, can be used with both converging and diverging lenses if we adhere to a set of sign conventions.
5._____ are essential for understanding the overall image formation by a thin lens or a system of lenses.
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UNIT 24
WAVE OPTICS
Read the following texts. Study the thesaurus on fig. 24, answer the questions after the texts
Colors swirl on a soap bubble as it drifts through the air on a summer day, and vivid rainbows reflect from the filth of oil films in the puddles of a dirty city street. Beachgoers, covered with thin layers of oil, wear their coated sunglasses that absorb half the incoming light. In laboratories, scientists determine the precise composition of materials by analyzing the light they give off when hot, and in observatories around the world, telescopes gather light from distant galaxies, filtering out individual wavelengths in bands and thereby determining the speed of expansion of the universe.
Understanding how these rainbows are made and how certain scientific instruments can determine wavelengths is the domain of wave optics. Light can be viewed as either a particle or a wave. Geometric optics, the subject of the previous Unit, depends on the particle nature of light. Wave optics depends on the wave nature of light. The three primary topics we examine in this Unit are interference, diffraction, and polarization. These phenomena can't be adequately explained with ray optics, but can be understood if light is viewed as a wave.
Conditions for interference
In our discussion of interference of mechanical waves in Unit 13, we found that two waves could add together either constructively or destructively. In constructive interference, the amplitude of the resultant wave is greater than that of either of the individual waves, whereas in destructive interference, the resultant amplitude is less than that of either individual wave. Light waves also interfere with each other. Fundamentally, all interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine.
Two sources (producing two traveling waves) are needed to create interference. To produce a stable interference pattern, the individual waves must maintain a constant phase with one another. When this situation prevails, the sources are said to be coherent. The sound waves emitted by two side-by-side loudspeakers driven by a single amplifier can produce interference because the two speakers respond to the amplifier in the same way at the same time - they are in phase.
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If two light sources are placed side by side, however, no interference effects are observed, because the light waves from one source are emitted independently of the waves from the other source; hence, the emissions from the two sources don't maintain a constant phase relationship with each other during the time of observation. The result is that no interference effects are observed, because the eye can't follow such short-term changes. Ordinary light sources are said to be incoherent.
Currently it's much more common to use a laser as a coherent source to demonstrate interference. A laser produces an intense, coherent, monochromatic beam over a width of several millimeters. This means that the laser may be used to illuminate multiple slits directly and that interference effects can be easily observed in a fully lighted room.
Thomas Young first demonstrated interference in light waves from two sources in 1801. Light is incident on a screen containing a narrow slit. The light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits. These slits serve as a pair of coherent light sources because waves emerging from them originate from the same wave front and therefore are always in phase. The light from the two slits produces a visible pattern on screen consisting of a series of bright and dark parallel bands called fringes.
Another simple, yet ingenious, arrangement for producing an interference pattern with a single light source is known as Lloyd's mirror.
Interference in thin films
Interference effects are commonly observed in thin films, such as the thin surface of a soap bubble or thin layers of oil on water. The varied colors observed when incoherent white light is incident on such films result from the interference of waves reflected from the two surfaces of the film.
Another method for observing interference in light waves is to place a planoconvex lens on top of a flat glass surface. With this arrangement, the air film between the glass surfaces varies in thickness from zero at the point of contact to some value. The circular fringes, discovered by Newton, are called Newton's rings.
Compact disks (CD's) and digital video disks (DVD's) have revolutionized the computer and entertainment industries by providing fast access; high-density storage of text, graphics, and movies; and high-quality sound recordings. The data on these disks are stored digitally as a series of zeros and ones, and these zeros and ones are read by laser light reflected from
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the disk. Strong reflections (constructive interference) from the disk are chosen to represent zeros and weak reflections (destructive interference) represent ones.
Inter-ference effects
Diffraction
Wave Optics |
Polari-zation |
Coherent |
Constant |
Interference |
urces |
phase |
pattern |
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Resultant am- |
Destructive |
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plitude |
interference |
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Constructive |
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|
interference |
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Laser |
Illuminate mul- |
|
|
tiple slits |
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Monochromatic beam |
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Incoherent |
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|
sources |
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|
Young's dou- |
Fringes |
Lloyd's mirror |
ble-slit ex- |
|
|
periment |
|
|
Thin films |
Newton's |
Plano-convex |
|
rings |
lens |
|
Compact |
Digital video |
|
disks (CD's) |
disks (DVD's) |
Fraunhofer |
Path |
Diffraction |
diffraction |
|
grating |
Transverse |
Unpolarized |
Superposition |
nature |
wave |
of waves |
Linearly polarized |
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|
Selective ab- |
Polaroid |
Polarizer |
sorption |
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Analyzer |
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Malus's law |
Polarization |
Polarizing |
Brewster's law |
by Reflection |
angle |
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Scattering |
Reradiation |
|
Optical activ- |
Liquid crys- |
LCD’s(liquid |
ity |
tals |
crystal displays) |
Fig. 24. Thesaurus for Unit 24
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Diffraction
Suppose a light beam is incident on two slits, as in Young's double-slit experiment. If the light truly traveled in straight-line paths after passing through the slits, the waves wouldn't overlap and no interference pattern would be seen. Instead, Huygens's principle requires that the waves spread out from the slits. In other words, the light bends from a straightline path and enters the region that would otherwise be shadowed. This spreading out of light from its initial line of travel is called diffraction.
One type of diffraction, called Fraunhofer diffraction, occurs when the rays leave the diffracting object in parallel directions. Fraunhofer diffraction can be achieved experimentally either by placing the observing screen far from the slit or by using a converging lens to focus the parallel rays on a nearby screen.
The diffraction grating, a useful device for analyzing light sources, consists of a large number of equally spaced parallel slits. A grating can be made by scratching parallel lines on a glass plate with a precision machining technique. The clear panes between scratches act like slits. A typical grating contains several thousand lines per centimeter.
Polarization of light waves
In Unit 21, we described the transverse nature of electromagnetic waves. The phenomenon of polarization, described in this Unit, is firm evidence of the transverse nature of electromagnetic waves. An ordinary beam of light consists of a large number of electromagnetic waves emitted by the atoms or molecules of the light source. The vibrating charges associated with the atoms act as tiny antennas. Each atom produces a wave with its own orientation, corresponding to the direction of atomic vibration. However, because all directions of vibration are possible, the resultant electromagnetic wave is a superposition of waves produced by the individual atomic sources. The result is an unpolarized light wave.
It's possible to obtain a linearly polarized beam from an unpolarized beam by removing all waves from the beam except those with electric field vectors that oscillate in a single plane. The most common technique for polarizing light is to use a material that transmits waves having electric field vectors that vibrate in a plane parallel to a certain direction and absorbs those waves with electric field vectors vibrating in directions perpendicular to that direction.
In 1932, E. H. Land discovered a material, which he called Polaroid, that polarizes light through selective absorption by oriented molecules.
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