Projects In Optics Workbook - Novel Device Lab

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ProjectslnOpticsApplicationsWorkbookCreatedby the technical staff of Newport Corporationwith the assistanceof Dr. Donald C. O'Sheaof the School of Physicsat the GeorgiaInstitute of Technology.We gratefully acknowledge J. Wiley and Sons, publishers ofTbe Eements of Modern Optical Design by Donald C. O'Sheafor use of copyrighted material in the Optics Primer section.

Table of ContentsPagePrefaceAn opricsp't*"''.::::::::::::::::::::::::.i.B0.1 GeometricalOptics.3.60.2 Thin LensEquation.0.3 Diffraction.9. 130.4 Interference.160.5 ComponentAssemblies.220 .6 La se rs.300.7 The Abbe Theory of Imaging0.8 References.36Component AssembliesProjects Section.45451.0 Project 1: The Laws of GeometricalOptics.5l2.0 Project 2: The Thin Lens Equation3.0 Project 3: ExpandingLaserBeams.55.4.0 Project 4: Diffractionof CircularApertures595.0 Proiect 5: SingleSlit Diffraction and Double Slit Interference. 63.676.0 Proiect 6: The MichelsonInterferometer.7l7.0 Project 7: Lasersand Coherence.758.0 Project 8: Polarizationof Light.".9.0 Project 9: Birefringenceof Materials.7910.0 Project l0: The Abbe Theory of Imaging.82

Projects In OpticsPrefaceThe Projects in Optics Kit is a set of laboratory equipment containing all of the optics and optomechanicalcomponents needed to complete a series of experiments that will provide students with a basic background in optics and practical hands-on experience inlaboratory techniques. The projects cover a wide rangeof topics from basic lens theory through interferometryand the theory of imaging. The Project in OpticsHandbook has been developed by the technical staff ofNewport Corporation and Prof. D. C. O'Shea,in order toprovide educators with a convenient means of stimulating their students' interest and creativity.This handbook begins with a description of severalmechanical assemblies that will be used in variouscombinations for each experiment. In addition, thesecomponents can be assembled in many other configurations that will allow more complex experiments to bedesigned and executed. One of the benefits fromconstructing these experiments using an optical bench(sometimes called an optical breadboard) plus standard components, is that the student can see that thecomponents are used in a variety of different circumstances to solve the particular experimental problem,rather than being presented with an item that willperform only one task in one way.A short Optics Primer relates a number of opticalphenomena to the ten projects in this handbook. Eachproject description contains a statement of purposethat outlines the phenomena to be measured, theoptical principle is being studied, a brief look at therelevant equations governing the experiment or references to the appropriate section of the Primer, a list ofall necessary equipment, and a complete stepby-stepinstruction set which will to guide the student throughthe laboratory exercise. After the detailed experimentdescription is a list of somewhat more elaborateexperiments that will extend the basic conceptsexplored in the experiment. The ease with which theseadditional experiments can be done will depend bothon the resources at hand and the inventiveness of theinstructor and the student.The equipment list for the individual experiments isgiven in terms of the components assemblies,plusitems that are part of the project kits. There are acertain number of required items that are to be supplied by the instructor. Items such as metersticks andtape measures are easily obtainable. Others. for the

I(((elaborate experiments, may be somewhat more difficult, but many are found in most undergraduateprograms. Note that along with lasers and adjustablemirror mounts, index cards and tape is used to acquirethe data. The student should understand that thepurpose of the equipment is get reliable data, usingwhatever is required. The student should be allowedsome ingenuity in solving some of the problems, but ifhis or her choices will materially affect their data aninstructor should be prepared to intervene.These experiments are intended to be used by instructors at the sophomore/junior level for college engineering and physical science students or in an advancedhigh school physics laboratory course. The projectsfollow the general study outline found in most opticaltext books, although some of the material on lasers andimaging departs from the standard curriculum at thepresent time. They should find their greatest applicability as instructional aids to reinforcing the conceptstaught in these texts.Acknowledgement: A large part of the text and many ofthe figures of "An Optics primer" are based on ChapterOne of Elements of Modem Optical Designby Donald C.O'Shea,published by J. Wiley and Sons, Inc., New york01985. They are reprinted with permission of JohnWiley & Sons, Inc.(((II!IIIIIITITIITTIT!!TIITt

0.0 An Optics PrimerThe field of optics is a fascinating area of study. In manyareas of science and engineering, the understanding ofthe concepts and effects in that field can be difficultbecause the results are not easy to display. But inoptics, you can see exactly what is happening and youcan vary the conditions and see the results. This primeris intended to provide an introduction to the 10 opticsdemonstrations and projects contained in this Projectsin Optics manual. A list of references that can provideadditional background is given at the end of thisprimer.0.1 Geometrical OpticsThere is no need to convince anyone that light travelsin straight lines. When we see rays of sunlight pouringbetween the leaves of a tree in a light morning fog, wetrust our sight. The idea of light rays traveling instraight lines through space is accurate as long as thewavelength of the radiation is much smaller than thewindows, passages,and holes that can restrict the pathof the light. When this is not true, the phenomenon ofdiffraction must be considered, and its effect upon thedirection and pattern of the radiation must be calculated. However, to a first approximation, when diffraction can be ignored, we can consider that the progressof light through an optical system may be traced byfollowing the straight line paths or rays of light throughthe system. This is the domain of geometrical optics.Part of the beauty of optics, as it is for any good game,is that the rules are so simple, yet the consequences sovaried and, at times, elaborate, that one never tires ofplaying. Geometrical optics can be expressed as a set ofthree laws:l.The Law of Transmission.In a region of constant refractive index, lighttravels in a straight line.2. LawofReflection.Light incident on a plane surface at an angle 0,with respect to the normal to the surface isreflected through an angle Q equal to the incidentangle (Fig.0.l).e eII(0.1)l , n , I .: n,1 :, , ,. :./\.o,,i '.I;-v.-.\I- - - Y - - - - - - - - L . :1,,-L0:i0,t",.lI,' ' IFigure 0. I Reflection and refraction of light at aninterface.

(Iai3. I aw of Refraction (Snell's l aw).Light in a medium of refractive index n. incidenton a plane surface at an angle Q with respect tothe normal is refracted at an angle Q in a mediumof refractive index n, as @g. 0.f),n, sinO n, sin9,(0 2)A corollary to these three rules is that the incident,reflected, and transmitted rays, and the normal to theinterface all lie in the same plane, called the plane ofincidence, which is defined as the plane containing thesurface normal and the direction of the incident ray.Note that the third of these equations is not written as aratio of sines, as you may have seen it from your earlierstudies, but rather as a product of n sin6. This isbecause the equation is unambiguous as to whichrefractive index corresponds to which angle. If youremember it in this form, you will never have anydifficulty trying to determine which index goes where insolving for angles. Project #l will permit you to verifythe laws of reflection and refraction.A special case must be considered if the refractiveindex of the incident medium is greater than that of thetransmitting medium, (n, 'n,).Solving for 0,,we getFigure 0.2. Three rays incident at angles near or at thecritical angle.sin0, (n, /n) sing(G3)In this case, ni /nr, l, and sin0, can range from 0 to l.Thus, for large angles of Q it would seem that we couldhave sing, l. But sinQ must also be less than one, sothereisacriticalangle Q 0,where sin 0 n, ln, andsinO, l. This means the transmitted ray is travelingperpendicular to the normal (i.e., parallel to the interface), as shown by ray #2 in Fig. 0.2. For incidentangles 0, greater than 0" no light is transmitted.Instead the light is totally reflected back into theincident medium (see ray #3, Fig. 0.2). This effect iscalled total intemal reflection and will be used inProject #l to measure the refractive index of a prism.As illustrated in Fig. 0.3, prisms can provide highlyreflecting non-absorbing mirrors by exploiting totatinternal reflection.Figure 0.3. Total intemal neflection fuom piruaTotal internal reflection is the basis for the transmission of light through many optical fibers. We do notcover the design of optical fiber systems in this manualbecause the application has become highly specializedand more closely linked with modern communicationstheory than geometrical optics. A separate manual andseries of experiments on fiber optics is available fromNewport in our Projects in fiber Opdcs.I ./IITIIITTTTITTT,{qqdI.lIdddddddJJ.{J1IIJJ.l

0.1.1.LensesIn most optical designs, the imaging components - thelenses and curved mirrors - are symmetric about aline, called the optical axis. The curved surfaces of alens each have a center of curvature. A line drawnbetween the centers of curvatures of the two surfacesof the Iens establishes the optical axis of the lens, asshown in Fig.0.4. In most cases, it is assumed that theoptical axes of all components are the same. This lineestablishes a reference line for the optical system.R2. uenrerorcurvarureof surface,By drawing rays through a series of lenses, one candetermine how and where images occur. There areconventions for tracing rays; although not universallyaccepted, these conventions have sufficient usage thatit is convenient to adopt them for sketches and calculations.l.An object is placed to the left of the opticalsystem. Light is traced through the system fromleft to right until a reflective component altersthe general direction.*.-'/ l--.-Rl-OpticatAxis\/\/\- .uenrerorcurvarureof surface1/Figure 0.4 Optical axis of a lens.Although one could draw some recognizableobject to be imaged by the system, the simplestobject is a vertical arrow. (Ihe arrow, imaged bythe optical system, indicates if subsequentimages are erect or inverted with respect to theoriginal object and other images.) If we assumelight from the object is sent in all directions, wecan draw a sunburst of rays from any point onthe arrow. An image is formed where all the raysfrom the point, that are redirected by the opticalsystem, again converge to a point.A positive lens is one of the simplest imageforming devices. If the object is placed very faraway ("at infinity" is the usual term), the raysfrom the object are parallel to the optic axis andproduce an image at the focal point of the lens, adistance / from the lens (the distance f is thefocal length of the lens), as shown in Fig. 0.5(a).A negative lens also has a focal point, as shown infig. 0.5(b). However, in this case, the parallelrays do not converge to a point, but insteadappear to diverge from a point a distance f infront of the lens.A light ray parallel to the optic axis of a lens willpass, after refraction, through the focal point, adistance / from the vertex of the lens.3. Light rays which pass through the focal point ofa lens will be refracted parallel to the optic axis.4. A light ray directed through the center of the Iensis undeviated.b.Figure 0.5. Focusing of parallel light by positive andnegative lenses.

-IItFigure 0.6. Imaging of an object point by a positivelens. A real inverted image with respect to the objectis formed by the lens.The formation of an image by a positive lens isshown in Fig. 0.6. Notice that the rays cross at apoint in space. If you were to put a screen at thatpoint you would see the image in focus there.Because the image can be found at an accessibleplane in space, it is called a real image. For anegative lens, the rays from an object do notcross after transmission, as shown in Fig. 0.2, butappear to come from some point behind the lens.This image, which cannot be observed on ascreen at some point in space, is called a virtualimage. Another example of a virtual image is theimage you see in the bathroom mirror in themorning. One can also produce a virtual imagewith a positive lens, if the object is locatedbetween the vertex and focal point. The labels,"real" and "virtual", do not imply that one type ofimage is useful and the other is not. They simplyindicate whether or not the rays redirected bythe optical system actually cross.Most optical systems contain more than one lensor mirror. Combinations of elements are notdifficult to handle according to the following rule:5. The image of the original object produced by thefirst element becomes the object for the secondelement. The object of each additional element isthe image from the previous element.More elaborate systems can be handled in asimilar manner. In many cases the elaboratesystems can be broken down into simplersystems that can be handled separately, at first,then joined together later.0.2 Thin Lens Equationi.-r-f Figure 0.7. Imaging of an object poinr by a negativelens. A virtud erect image with respect to the obieclis formed by the lens.Thus far we have not put any numbers with the examples we have shown. While there are graphicalmethods for assessing an optical system, sketching raysis only used as a design shorthand. It is throughcalculation that we can determine if the system will dowhat we want it to. And it is only through these calculations that we can specify the necessary components,modify the initial values, and understand the limitationsof the design.Rays traced close to the optical axis of a system, thosethat have a small angle with respect to the axis, aremost easily calculated because some simple approximations can be made in this region. This approximation iscalled the paraxial approximation, and the rays arecalled paraxial rays.IItitIItIaatrtjrttUrt!I!U!U!!tJJaJJJJJJJJJJ

tItItItItItItttttrtItItItttrtttDrtBefore proceeding, a set of sign conventions should beset down for the thin lens calculations to be considerednext. The conventions used here are those used in mosthigh school and college physics texts. They are not theconventions used by most optical engineers. This isunfortunate, but it is one of the difficulties that is foundin many fields of technology. We use a standard righthanded coordinate system with light propagatinggenerally along the z-axis.l.Light initially travels from left to right in apositive direction.2. Focal lengths of converging elements are positive;diverging elements have negative focal lengths.3. Object distances are positive if the object islocated to the left of a lens and negative if locatedto the right of a lens.4. Image distances are positive if the image is foundto the right of a lens and negative if located to theleft of a lens.We can derive the object-image relationship for a lens.With reference to Fig. 0.8 let us use two rays from anoff-axis object point, one parallel to the axis, and onethrough the front focal point. When the rays are traced,they form a set of similar triangles ABC and BCD.lnABC,-h . - h , h ,s o f(04a)and in BCDho h, hos,f(04b)Adding these two equations and dividing through byho h. we obtain the thin lens equationlllfJ-t.s.-o.s(0-5)Solving equations 04a and 04b for ho * h, , you canshow that the hnsverse magnification or lateralmagnification, M, of a thin lens, the ratio of the imageheight h, to the object height hn,is simply the ratio ofthe image distance over the object distance:M-L--s'hoso(0-6)With the inclusion of the negative sign in the equation,not only does this ratio give the size of the final image,its sign also indicates the orientation of the imageFigure 0.8. Geometry for a derivation of the thin lensequation.

I:.II(relative to the object. A negative signindicates thatthe image is inverted with respect tthe object. Theaxial or longitudinal magnification,the magnification ofa distance between two points on theaxis, can beshown to be the square of the lateralor transversemagnification.Mt M2I{I(IIII(o 7)In referring to transverse magnification,an unsubscripted Mwill be used.rmageonScreenFigure 0.9 Determination of the focallength of anegative rens with the use of a positivere"nsof knownfocal length.The relationship of an image to an objectfor a positivefocal length lens is the same for all lenses.If we startwith an object at infinity we find fromEq. 0 5that for apositive lens a real image is locatedat the focal point ofthe lens ( l/s" 6, therefore s, f), andas the objectapproaches the lens the image distanceincreases untilit reaches a point 2/on the other sideof the lens. At thispoint the object and images arethe same size and thesame distance from the lens. As the objectis movedfrom 2f to f the image moves from2f to infinity. Anobject placed between a positive lensand its focal pointforms a virtual, magnified image thatdecreases inmagnification as the object approachesthe lens. For anegative lens, the situation is simpler:starting with anobject at infinity, a virtual image, demagnified,appearsto be at the focal point on the same sideof the lens asthe object. As the object moves closerto the lens sodoes the image, until the image and objectare equal insize at the lens. These relationshipswiit be explored indetail in Project #2.t(t{ItIItIaaaaaThe calculation for a combination of lensesis not muchharder than that for a single lens. As indicatedearlierwith ray sketching, the image of the precedinglensbecomes the object of the succeedinglens.One particular situation that is analyzed projectin#2 isdetermining the focal length of a nelativelens. The ideais to refocus the virtual image creatidby the negativelens with a positive lens to create a realimage. In Fig.0.9 a virtual image created by a negativelens of unknown focal length is reimaged bV positivea{lens of*n:yl tocat tength fr. The power of the positivelens issultlctent to create a real image at a distances, from it.By determining what the object distances" should befor this focal length and image distance,th'e location ofthe image distance for the negative lenscan be foundbased upon rule 5 in Sec. 0. l: ihe imageof one lenss-eryesas the object for a succeeding lens.The imagedistance s, for the negative lens is th-eseparationbetween-lense-sf, minus the object distances, of thepositive lens. Since the original objectdistance soandthe image distance s, have been found,the focal lengthtaaaaJaJJJJJJJJ-J

of the negative lens can be found from the thin lensequation.In many optical designs several lenses are used together to produce an improved image. The effectivefocal length of the combination of lenses can be calculated by ray tracing methods. In the case of two thinlenses in contact, the effective focal length of thecombination is given by1 - 1 - 1f f,f,(0-8)F.a'','0.3 DiffractionAlthough the previous two sections treated light as rayspropagating in straight lines, this picture d

optics, you can see exactly what is happening and you can vary the conditions and see the results. This primer is intended to provide an introduction to the 10 optics demonstrations and projects contained in this Projects in Optics manual. A list of references that can provide additional background is given at the end of this primer. 0.1 .

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