Advanced Optics with Laser Pointer and Metersticks

Transcription

1 Avance Optics with aser Pointer an s Roan Ya. Kezerashvili New York City College of Technology, The City University of New York 300 Jay Street, Brooklyn NY, 1101 Eail: Rkezerashvili@citytech.cuny.eu Abstract We are using a laser pointer as a light source, an etersticks as an optical branch an the screen for wave optics experients. It is shown the setup for easureents of wavelength of laser light an rating raial spacing of the CD, iffraction on a wire an a slit, observation of a polarization of light an observation of a hologra. 1. Introuction aser pointers also know as laser penlights, have becoe very afforable recently ue to new evelopents in laser technology. They are wiely available at electronic stores, novelty shops, through ail orer catalogs an by nuerous other sources. They are in the price range fro $1 to $30 as other electronic toys an are being treate as such by any parents an chilren. Pointers are use for other purposes such as the aligning of other lasers, laying pipes in construction, an as aiing evices for firears. aser pointer can be use to observe the interference, iffraction an polarization of light in college physics laboratory. aser pointers can be use to prouce hologras [1-]. It been opinions it couln't be one because of the short coherence of the bea an that laser pointer s bea was not polarize. But it was practically prove that a laser pointer coul be use not only to observe a hologra but to prouce a high quality transission an reflection isplay hologra [1-3]. We suggeste a series of classic experients with a laser pointer as a light source, an using etersticks as an optical branch an the screen to easure the interference an iffraction patterns. The etail proceures of suggeste experients are given in Ref. 4.. Deterination of wavelength of laser ight A wave phenoenon, which occurs when two or ore waves overlap in the sae region of space at the sae tie an for an interference pattern, is known as the interference of waves. When two waves of the sae frequency but of ifferent phases cobine, the resultant wave is a wave of the sae frequency, the aplitue of which epens on the phase ifference. If the phase ifference is 0 or an θ D θ D 1 y P integer ties π, the waves are in phase an interfere constructively. For the constructive interference, the resultant aplitue equals the su of the iniviual aplitues, an the intensity has a axiu. If the phase ifference is π or any o integer ties π, the waves are out of phase an interfere estructively. For estructive interference the resultant aplitue is the ifference between the 1 Fig.1. Two slits act as coherent sources of light for the observation of interference. Because the screen is very far away copare with the slit separation, the rays fro the slits to the point P on the screen are consiere approxiately parallel an the path ifference between the two rays is sinθ.

2 iniviual aplitues, an the intensity has a iniu. If the two sources have the sae aplitue, aser Pointer y Diffraction Grating y Top view screen aser pointer Diffraction Graing the estructive interference results in the zero net aplitue. The phase ifference between two waves is often the result of ifference in path length travele by the two waves. If waves fro two sources with the sae wavelength arrive at the sae point together with exactly the sae phase, then the conition for axiu constructive interference is that the path length of two waves ust be ientical or else iffer by an integer ultiple of the wavelength, that is D D = λ, 0,1,, 3,... (constructive interference), (1) 1 = Fig.. Interference. Setup for easureent of the wavelength of a laser light. where D 1 an D are the path lengths of the waves fro their source to the point P (Fig. 1). If the istances D 1 an D are quite large copare to the separation between the sources, we can write the conitions for the constructive an estructive interferences in ters of the angle θ an the istance of separation. When the istance between the light sources an the plane containing the observation point is uch greater than, two paths D 1 an D are nearly parallel an the path ifference is approxiately sinθ, as shown in Fig.1. This result gives equation for eterining the constructive interference of the resultant wave at point P: sin θ = λ, = 0,1,, 3,... (constructive interference), () As it is shown in Fig. 1, the istance y easure along the screen fro the central bright point to the th bright fringe is relate to the angle θ by sinθ = y + y (3) Substituting this into equation () we obtain y + y = λ. (4)

3 Solving equation (4) for wavelength we get y λ =, = 1,, 3,... (constructive interference). (5) + y Thus, for the known istance of separation, by easuring the istance y along the screen fro the central bright point to each of the th bright fringe an the istance fro the slit to the screen, we can eterine the wavelength of the onochroatic light. We eterine the wavelength of the laser light using iffraction grating. In the first part of this experiental activity we will be using a onochroatic laser bea, which is incient norally on a transission iffraction grating. By observing the interference pattern an easuring the istances y between the central bright axiu an each of the th bright fringe an the istance fro the iffraction grating to the screen, we will eterine the wavelength of the laser light fro equation (5). 3. Deterination of the grating raial spacing of the CD By solving equation (5) for the istance of separation we obtain + y = λ, = 1,, 3,... (constructive interference). (6) y Equation (6) allows us to eterine the istance of separation between the light sources. That eans we can fin a grating spacing by using a light source of a known wavelength an easuring the aser Pointer y screen with hole Top view y CD CD aser pointer Fig.. Interference. Setup for easureent a grating space of a CD. istance y along the screen fro the central bright point to each of the th bright fringe an the istance fro the slit to the screen. The rainbow-colore reflections that you can see fro the surface of a CD are the reflection grating effects. The grooves are tiny pits 0.1 µ eep on the surface of the isc, with the unifor raial spacing of =1.6 µ. The reflection grating aspect of the CD is erely an aesthetic sie benefit. The interference pattern prouce on the screen on a large istance fro the grating is ue to a large nuber of equally space light sources. The interference axia are at the angle θ given by equation 3

4 (3). In this part of the experient the onochroatic laser bea will incient norally on a reflection iffraction grating. We will be using a CD as the reflection iffraction grating. By easuring the istances y between the central bright axiu an each of the th bright fringe, the istance fro the CD to the screen an using the wavelength of the laser light foun previously, we will eterine the grating raial spacing of the CD fro equation (6). 4. Diffraction on a wire In this experient a narrow slit or a thin wire is inserte in the path of a laser pointer bea an aser Pointer θ θ 1 1 Top view Slit/Wire aser pointer Slit/Wire iffracte spots are projecte on a eterstick-screen as it is shown in Fig. 4. The laser bea is assue to be very parallel rays of light, which eans that the waves are plane light waves, passes though a slit. Plane waves are iffracte by the slit an light rays fall on the screen, which is very far away, so the rays heaing for any point are very nearly parallel before they eet at the screen. This approxiates the conitions for Fraunhofer iffraction. At the screen a central bright region is fore an a series of syetrical ark an bright fringes can be observe. A general conition for a ark frige of the iffraction pattern is asin θ = λ, = ± 1, ±, ± 3,..., (Dark Fringe) (7) where a is the with of a slit an θ is the angle between the position of the ark fringe of orer an central bright fringe. The central bright fringe occurring at θ=0 an is the brightest, seconary an so on bright fringes occurring on both sie of the central axiu. However, the intensity of those axia iinish ore rapily. Fro the Fig. 4 we see that for the sall angle θ we can replace sinθ by the expression Fig. 4. Diffraction fro a slit or on a wire sin θ, = 1,, 3,..., (8) where is the istance between two syetrical ark fringes of the sae orer, an is a istance between the wire an the screen. Substitution of equation (8) into equation (7) gives the with of the slit as 4

5 λ a =, = 1,, 3,4,..., (9) Therefore, we can fin the with of very narrow slit by easuring the istances between two syetrical ark fringes of the sae orer, an the istance. Fig. 5 (a) Intensity of the iffraction pattern of a single slit as a function of sinθ. are the istances between two ark fringes of the sae orer. (b) Intensity of the iffraction pattern on a wire as a function of sinθ. are the istances between two bright fringes of the sae orer. 3 1 Intensity (a) sinθ 1 Intensity (b) sinθ Now let us consier the iffraction on an obstacle. Replace the narrow slit slie by a wire holing slie. You can observe the iffraction pattern. The central bright fringe occurring at θ=0 an is the brightest, seconary an so on bright fringes occurring on both sie of the central axiu. A general conition for a bright frige of the iffraction pattern is asin θ = λ, = ± 1, ±, ± 3,..., (Bright Fringe) (10) where a is the iaeter of a wire an θ is the angle between the position of the bright fringe of orer an central bright fringe. We can eterine the iaeter of the wire using equation (10) an as a result it will be yiel to equation (9) only now istance is the istance between two syetrical bright fringes of the sae orer. Thus, we can fin the iaeter of the thin wire by easuring the istances between two syetrical bright fringes of the sae orer, an the istance. In this experient using a laser pointer you can observe the sharp iffraction pattern for the wire of the gages fro 34 to 48 ( ). 5. Observation of a Polarization of ight Polarizer Axis of Polarizer Analyzer Fig. 6. Unpolarize light becoes polarize after passing through the first Polaroi (polarizer). The plane of polarization is change an the intensity is reuce by factor cos θ as the light passes the secon Polaroi (analyzer) oriente at angle θ relative to the first. θ Axis of Analyzer 5 If an unpolarize light is incient on a polarizing aterial, the transitte light is linearly polarize in the irection parallel to the transission axis of the polarizer, as in Fig.6. The polarizer transits half of an intensity of the incient light, while the other half is absorbe by the polarizer. This fact is known as the one-half rule. We can use this rule only when the light reaching the polarizer is unpolarize. If the light is linearly polarize when it is incient on the secon polarizer, as in Fig.6, then the secon polarizer exaines or analyzes the incoing light an can tell us soething about the nature of this polarize light. The secon polarizing aterial thus calle an analyzer. In other wors, when two polarizing aterials are place in succession in a bea of light as on Fig.6, the first is calle the polarizer an the secon - the

6 analyzer. The aount of the light transitte by the analyzer epens on the angle θ between its transission axis an the irection of the axis of the polarizer. The observations show that the aplitue of the electric fiel of the light is reuce by the secon polarizer (analyzer) by factor cos θ. Since the intensity of the light, which is the energy transitte per unit tie an area, is proportional to the aplitue square, the intensity of the light transitte by both polarizer an analyzer will be given by I = I 0 cos θ. (11) In equation (11) I 0 is the intensity of the light incient on the analyzer ( I 0 is the axiu intensity of the light transitte at θ=0), an I is the intensity of the light transitte by both polarizer an analyzer. If the transission axis of the polarizer an analyzer are perpenicular to each other, no light aser pointer Polarizer Analyzer gets through. Equation (11) is known as Malus s law. This law applies to any two polarizing eleents, transission axes of which ake an angle θ with each other. 6. Observation of a Hologra Fig. 7. Setup for observation of the polarization of light One of the ost failiar applications of laser is a process for proucing three-iensional iages. aser Pointer Iage Hologra Top View aser pointer Diverging ens Diverging lens Hologra Eye Fig. 8. Setup for observation of the hologra To prouce a holographic iage, the laser bea fro the laser pointer passes through the center of the iverging lens (fro -6 to -5 focal length, ouble concave lens) an as a result spreas the 6

7 bea to uniforly illuinate the transparent hologra.the basic setup for a single bea transission hologra is shown in Fig. 8. The istance between the iverging lens an the hologra holer is approxiatel (the istance epens on the focal length of the iverging lens) to get unifor illuination. References 1. Stephen W. Michael, Three Diensional Iagery s. Frank DeFreitas, aser Pointer/ Seiconuctor aser Holography, 3. Frank Defreitas, Alan Rhoy, Stephen W. Michael Shoebox Holography: A Step-By-Step Guie To Making Hologras Using Inexpensive Seiconuctor Dioe asers, Ross Books, Berkeley CA 4. Roan Ya. Kezerashvili, College Physics aboratory Experients: Electricity, Magnetis, Optics. Gurai Publishing, New York, 003 7