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Diffraction and Interference Figu These expar new .5 wave oday Isaac Newton is most famous for his new v accomplishments in mechanics—his laws of Tmotion and universal gravitation. Early in his career, however, he was most famous for his work on light. Newton pictured light as a beam of ultra-tiny material particles. With this model he could explain reflection as a bouncing of the parti- cles from a surface, and he could explain refraction as the result of deflecting forces from the surface Interference colors. acting on the light particles. In the eighteenth and nineteenth cen- turies, this particle model gave way to a wave model of light because waves could explain not only reflection and refraction, but everything else that was known about light at that time. In this chapter we will investigate the wave aspects of light, which are needed to explain two important phenomena—diffraction and interference. As Huygens' Principle origin; 31.1 pie is I constr In the late 1600s a Dutch mathematician-scientist, Christian Huygens, dimen proposed a very interesting idea about waves. Huygens stated that light waves spreading out from a point source may be regarded as die overlapping of tiny secondary wavelets, and that every point on ' any wave front may be regarded as a new point source of secondary waves. We see this in Figure 31.1. In other words, wave fronts are A made up of tinier wave fronts. This idea is called Huygens' principle. Look at the spherical wave front in Figure 31.2. Each point along the wave front AN is the source of a new wavelet that spreads out in a sphere from that point. Only a few of the infinite number of wavelets are shown in the figure. The new wave front BB' can be regarded as a smooth surface enclosing the infinite number of over- lapping wavelets that started from AA' a short time earlier. 480 Chapter 31 Diffraction and Interference Figure 31.1 A These drawings are from Huygens' book Treatise on Light. Light from A (left) expands in wave fronts, every point of which (right) behaves as if it were a new source of waves. Secondary wavelets starting at to,13,b,12 form a new wave front (d,d,d,ch; secondary wavelets starting at d,d,d,d form still another new wave front (DCEF). 4 Figure 31.2 Huygens' principle applied to a spherical wave front. WAVE FRONT NEW WAVE FRONT As a wave front spreads, it appears less curved. Very far from the original source, the wave fronts seem to form a plane. A good exam- ple is the plane waves that arrive from the sun. A Huygens' wavelet construction for plane waves is shown in Figure 31.3. (In a two- dimensional drawing, the planes are shown as straight lines.) 4 Figure 31.3 WAVE FRONT Huygens' principle applied to a A plane wave front. / \ ll \ I a ---_.--,_____--_.--,____--.. - \ r NEW WAVE FRONT ‘‘‘ Figure 31.4 A Huygens' principle applied to (a) reflection and (b) refraction. Figuri Straigh The laws of reflection and refraction are illustrated via Huygens' openin. principle in Figure 31.4. You can observe Huygens' principle in water waves that are made to pass through a narrow opening. A wave with straight wave fronts can be generated in water by repeatedly dipping a stick lengthwise into the water (Figure 313;. A ruler works well. When the 31. straight wave fronts pass through the opening in a barrier, interest- ing wave patterns result. Any bt is calif of stra Figure 31.5 S is with Making plane waves in a tank of As the water and watching the pattern more they produce when they pass light though an opening in a barrier. the wa When a pica out likt is diffn When the opening is wide, you'll see straight wave fronts pass through without change—except at the corners, where the wave fronts are bent into the "shadow region" in accord with tiltiyg^^-' opening, less of the wave principle. If you narrow the width of the _ gets through, and the spreading into the shadow region is more pro- nounced. When the opening is small compared with the wavelength SI of the waves, Huygens' idea that every part of a wave front can be regarded as a source of new wavelets becomes quite apparent. As the waves move into the narrow opening, the water sloshing up and down in the opening is easily seen to act as a point source of circular other side of the barrier. The photos in waves that fan out on the Figuro Figure 31.6 are top views of water waves generated by a vibrating Lightfr c. stick. Note how the waves fan out more as the hole through which ig is they pass becomes smaller. ton it 482 Chapter 31 Diffraction and Interference ...i.umm.d..••••••••••1. ^ ..... Figure 31.6 A Straight waves passing through openings of various sizes. The smaller the opening, the greater the bending of the waves at the edges. 31.2 Diffraction Any bending of a wave by means other than reflection or refraction is called diffraction. The photos of Figure 31.6 show the diffraction of straight water waves through various openings. When the opening k wide compared with the wavelength, the spreading effect is small. • As the opening becomes narrower, the spreading of waves becomes more pronounced. The same occurs for all kinds of waves, including light waves. When light passes though an opening that is large compared with the wavelength of light, it casts a rather sharp shadow (Figure 31.7). When light passes through a small opening, such as a thin razor slit in a piece of opaque material, it casts a fuzzy shadow, for the light fans out like the water through the narrow opening in Figure 31.6. The light K" is diffracted by the thin slit. I I ;Si? LIGHT LIGHT SOURCE SOURCE WIDE WINDOW Figure 31.7 A J.ightcasts a sharp shadow with some fuzziness at its edges when the open- g is large compared with the wavelength of the light. Because of diffrac- ion, it casts a fuzzier shadow when the opening is extremely narrow. Diffraction is not confined to the spreading of light through narrow slits or other openings. Diffraction occurs to some degree for all shad- object ows On close examination, even the sharpest shadow is blurred at the ' waveli edge. When light is of a single color, diffraction can produce diffraction fractu fringes at the edge of the shadow, as shown in Figure 31.8.1n white light struct the fringes merge together to create a fuzzy blur at the edge of a shadow , amou The amount of diffraction depends on the size of the wavelength • defeat compared with the size of the obstruction that casts the shadow Tc (Figure 31.9). The longer the wave compared with the obstruction, hs the greater the diffraction is. Long waves are better at filling in shad- \gavel( ows. This is why foghorns emit low-frequency sound waves—to fill in than t "blind spots." Likewise for radio waves of the standard AM broadcast electri band. These are very long compared with the size of most objects in The d their path. Long waves don't "see" relatively small buildings in their that o path. They diffract, or bend, readily around buildings and reach Tl Figure 31.8 • more places than shorter waves do.* wave!' Diffraction fringes around the I011/11i scissors are evident in the shad- I 4 4 4 4 4 I 4 4 1 1 4 4 4 long-v ows of laser light which is of a in its s single frequency. These fringes of sho would be filled in by multitudes to doll of other fringes if the source gas-fl were white light • tumor the de the mi 4 4 devia a. b. C. Figure 31.9 A (a) Waves tend to spread into the shadow region. (b) When the wavelength is about the size of the object the shadow is soon filled in. (c) When the wave- length is short compared with the width of the object, a sharper shadow is cast. FM radio waves are shorter, don't diffract as much around build- ings, and aren't received as well as AM radio waves are in mountain canyons or city "canyons." This is why many localities have poor FM reception while AM reception comes in loud and clear. TV waves, which are also electromagnetic waves, behave much like FM waves." TV antennas are often put on rooftops to improve recep- tion. Both FM and TV transmission are "line of sight," meaning that diffraction is not significant, whereas AM transmission diffracts 'round hills and buildings to reach places that would othen,deo he shadowed. Diffraction can be helpful. * The ofte * On the other hand, a framework of connected steel girders in a building or bridge can an t act as a "polished" surface for long-wavelength radio waves, reflecting them away from the structure. That's why you lose reception when you drive onto a steel bridge rep while listening to an AM station. So although long waves get around a steel structure, phi, they don't get into it. aco dol ** Most TV channels have wavelengths shorter than FM wavelengths, and therefore even oft less diffraction than FM, but some (channels 2-6) have wavelengths longer than FM , COr wavelengths. Is 484 Chapter 31 Diffraction and Interference Diffraction is not so helpful when we wish to see very small objects with microscopes.