Light and Electromagnetic Waves Teaching in Engineering Education
aa r X i v : . [ phy s i c s . e d - ph ] N ov Light and Electromagnetic Waves Teaching in Engineering Education
Roman Ya. Kezerashvili
Physics Department, New York City College of Technology,The City University of New York300 Jay Street, Brooklyn, NY 10201 and
Suggestion of physics laboratory exercises and discussion of the physics laboratory curricula forengineering majors where the properties of light and electromagnetic waves are studied in parallel. Itis shown that one of the important educational advantages of an experimental study of the propertiesof microwaves as an example of electromagnetic waves simultaneously with the properties of lightare, on one hand, visualization of the properties of microwaves, and on the other hand, provideevidences that light is an electromagnetic wave.
I. INTRODUCTION
Engineering is the application of mathematics andscience to develop useful products or technologies. Inother words, engineering is turning ideas into reality.Physics is the study of the physical world and physics isan indispensable component in engineering curricula be-cause technology is based on our knowledge of physicallaws. Physics remains the leader of the modern naturalsciences, the theoretical basis of modern engineering andas no any other science, promotes the development ofcreative and critical thinking in future engineers. Goodtraining in physics also provides a solid base for lifelonglearning.Research in education in different countries showsthat students at the college and even university levelscontinue to hold fundamental misunderstandings of theworld around them. Science learning remains within theclassroom context and just a small percentage of studentsare able to use the knowledge gained at school for solvingvarious problems of the larger physical world .In most of the courses students hear lectures with-out strong connections to their everyday experiences.Students usually do not have the opportunity to formtheir own ideas, they rarely get a chance to work in away where they are engaged in discovery and buildingand testing models to explain the world around them,like the scientists do.In the last four years I started to include some‘simple’ conceptual questions in the exams of the physicscourses I taught. The results were at first quite surpris-ing: Most students performed very poorly on the concep-tual questions which most physics would consider as tobe almost ‘too easy’, while they sometimes solved ‘dif-ficult’ multiple-step quantitative problems better. Someof the ‘top’ students with high scores on the quantitativeproblems had very low scores on the conceptual part .One of the questions which I asked is “What are the sim-ilarities and differences between electromagnetic wavesand light? The best short answer I had was “Light is anelectromagnetic wave” without any deeper explanation ofthe properties and phenomena. I had a lot of speculationsabout light but only a few students mentioned that light is the part of the electromagnetic spectrum the humaneye can detect and they listed the main properties of elec-tromagnetic waves. This motivated me to revise physicslaboratory curricula and develop physics laboratory ex-ercises where the properties of light and electromagneticwaves are studied in parallel. Indeed, one of the placeswhere active and collaborative learning can be realizedis the physics laboratory, where students become activeparticipants of the learning process .When Maxwell showed that electric and magneticfields can propagate through space according to the clas-sical wave equation and found the equation for the speedof propagation of electromagnetic field to be c = 1 √ ε µ , (1)where ε and µ are electric permittivity and magneticpermeability of free space, he evaluated the numericalvalue for the speed of these electromagnetic waves bysubstituting the numerical values for ε and µ and ob-tained the remarkable result: m/s . Maxwell recognizedthat this result is very close to the experimentally mea-sured speed of light and made a great conceptual conclu-sion that light is electromagnetic waves. Of course, thisconclusion does not surprise physicists today. Equation(1) is one of the great equations in physics stemming as itdoes from Maxwell’s electromagnetic theory. This equa-tion unifies three seemingly disparate fields of physics:electricity, magnetism and optics.Since electromagnetic wave concepts are usuallyunfamiliar, abstract, and difficult to visualize, conceptualanalogies from familiar light phenomena are invaluablefor teaching. Such analogies emphasize the understand-ing of continuity of electromagnetic waves and supportthe spiral development of student understanding. Wefound that the approach of teaching the topics of elec-tromagnetic waves and optics in parallel in the physicslaboratory is very helpful and useful.The following experiments can be easily designedand they provide a methodical introduction to electro-magnetic theory using microwave radiation and light: thestudy of the inverse square law of the dependence of theintensity of radiation (microwave and light) on the dis-tance, the law of reflection and refraction, investigationof the phenomenon of polarization and how a polarizercan be used to alter the polarization of microwave ra-diation and light, studying interference by performingthe double-slit experiment for microwave radiation andlight. Finally students measure the wavelength of laserlight and microwave radiation using the correspondingversions of the Michelson’s interferometer, and recognizethat these two forms of radiations differ only by the wave-length or frequency.To perform the above mentioned experiments weare using a regular light source or He-Ne laser for op-tics, and microwaves transmitter and receiver for mi-crowave electromagnetic radiation experiments. Todayfor experiments with microwaves PASCO , as well asDAEDALON provide excellent sets. In our laboratorywe are using PASCO equipment. We are using the samedesign for light and microwave experiments to demon-strate the similarity of measurements and the only dif-ference is that in the case of light experiments studentscan see the phenomena and measure its physical proper-ties and in the case of the microwaves they can observethe same phenomena through the meters reading of theintensity of the microwave radiation.The purpose of the present paper is to introducelaboratory curricula for the study of the properties oflight and microwaves in parallel in the general physicslaboratory course for engineering majors, especially forelectrical engineering and telecommunication students.The article is organized as follows: Sec. II introducesthe experiments for the inverse square law of the depen-dence of the intensity of light and microwave radiation onthe distance from a source of electromagnetic waves, inSec. III we analyze and discuss the reflection and refrac-tion experiments for microwaves and light, the double-slitinterference and polarization experiments for light andmicrowaves are discussed in Sec. IV and Sec. V, re-spectively. Interferometer measurements for wavelengthof light and microwaves are presented in Sec. VI, andconclusions follow in Sec. VII. II. INVERSE SQUARE LAW FOR LIGHT ANDMICROWAVE RADIATION
The intensity received from the pointlike sourceof an electromagnetic wave is inversely proportional tothe square of the distance from the wave source and aninverse square law can be written in the form I = L πr , (2)where L is the luminosity of the source. To observethis phenomenon we designed the experiment where thephotoelectric photometer has been used to measure theintensity of light in increments of distances from the light Inverse square of the distance, , m -2 R e l a t i v e i n t en s i t y , I/I (a) I/I = 0.0151 x , x = 1/ r , R = 0.998 Inverse square of the distance, , m -2 R e l a t i v e i n t en s i t y , I/I (b) I/I =0.1564 x + 0.06145, x =1 /r , R =1 FIG. 1: Inverse square law for light (a) and microwaves (b). source. In the case when the students perform the mea-surements for the intensity of electromagnetic waves byusing the microwave transmitter and receiver they grad-ually increase the distance between the transmitter andreceiver by moving the receiver. Students represent theresults of the measurements for the dependence of inten-sity on the distance for light as well as for microwavesin graphical form by plotting the relative intensity ver-sus the inverse square of the distance as shown in Figs.1a and 1b. The analysis of these graphs shows that in-tensities of visible light as well as invisible microwavesdecrease inversely proportional to the square of the dis-tance from the source.
III. REFLECTION AND REFRACTION OFLIGHT AND MICROWAVES.
There are two fundamental laws of geometric op-tics: the law of reflection and Snell’s law – the law of re-fraction. Today’s laboratory class technology allows stu-dents to verify these laws using a beam of light as well asa beam of monochromatic laser light. Students can per-form experiments for the reflection and refraction of lightgradually changing the angle of incidence and measuringthe angle of reflection or the angle of refraction and atthe same time visually observing the propagation of theincident ray and reflected or refracted rays for each of theincident angles. By plotting the graph of dependence ofthe angle of reflection versus the angle of incidence theycan find that the slope of this graph is unity and there-fore, conclude that the angle of incidence equals the an-gle of reflection. In the same way by plotting the graphof the sine of the angle of incidence versus the sine ofthe angle of refraction students see that there is a lineardependence and from the slope of the graph determinethe index of refraction for the given medium. Fig. 2arepresents an example of such dependence for refractionof light in glass. We are suggesting studying reflectionand refraction of microwaves in parallel with these op-tics experiments. The difference of the setting for theseexperiments is that in the case of light students actuallysee the reflected and the refracted rays, but in the caseof microwaves the reflected and refracted electromagneticwaves are invisible and students determine the angle ofrefraction as well as the angle of refraction of microwavesby finding the maximum intensity for the reflected or re-fracted microwave radiation. Using a transmitter andreceiver of microwaves and a metallic reflected plate andgradually increasing the angle of incidence, students canfind the angle of refraction which corresponds to the max-imum intensity of reflecting microwaves. In the case ofrefraction the incident microwaves are refracted on theprism mold filled with styrene pellets. The angle of therefracted microwaves can be found by the maximum in-tensity meter reading of the refracted waves. Plottingthe same graphs as in the case of light experiments forthe angle of incidence versus the angle of reflection andfor the sine of the angle of incidence versus sine of theangle of refraction, students can verify the laws of reflec-tion and refraction for the microwaves and justify thatthese are the same as for light. Fig. 2b presents theresults for these kinds of measurements for reflection ofthe microwaves.
IV. DOUBLE-SLIT INTERFERENCE FORLIGHT AND MICROWAVES
The other experiment in optics which is easy tovisualize is double-slit interference for light. This is thestandard set which is available on the market. Perform-ing this experiment students can see a clear interference
Sine of angle of refraction, sin (cid:84) R S i ne o f ang l e o f i n c i den c e , s i n (cid:84) i (a) sin (cid:84) i =1.53sin (cid:84) R , R = 0.9999 Angle of incidence, (cid:84) i A ng l e o f r e f l e c t i on , (cid:84) r (b) (cid:84) r =1.0034 (cid:84) i , R = 0.999 FIG. 2: (a) Refraction of light in glass. Dependence of the sineof the angle of refraction on the sine of the angle of incidence.(b) Reflection of microwaves. Dependence of the angle ofreflection on the angle of incidence. pattern. Of course, there are many different experiments,which also demonstrate the interference of light and vi-sualize the interference concept for light. We are choos-ing the double-slit interference of light because a some-what similar phenomenon occurs when microwaves passthrough a two-slit aperture and can be easily set andperformed with microwaves. When incident microwavesfrom a transmitter radiate on a double-slit aperture, theintensity of the microwave beyond the aperture will varydepending on the angle of detection by a receiver. Fortwo thin slits separated by a distance d, maxima of the
Angle for the detection M e t e r r ead i ng , a r b i t r a r y un i t s FIG. 3: Interference pattern for microwaves. intensity will be found at such angles that d sin θ = mλ, (3)where θ is the angle of detection, λ is the wavelengthof the incident radiation, and m is any integer. Gradu-ally changing the angle by 5 for the detection positionof the receiver the student measures the intensity of mi-crowaves beyond the double-slit aperture. Fig. 3 presentsan example of such measurements for two different runs.The solid curve represents the measurements when thereceiver is positioned close to the double-slit aperture,while the dotted curve corresponds to the measurementswhen the distance between the receiver and double-slit isincreased. To analyze the results of the experiment stu-dents for the given wavelength of microwave calculate theangles at which they would expect the maxima and min-ima to occur and compare with the locations of observedmaxima and minima. V. POLARIZATION PHENOMENA FOR LIGHTAND MICROWAVES
The other laboratory activities which excite studentsand catch their attention deal with observation of polar-ization of light. Two activities which are the easiest toset in the undergraduate college physics laboratory arepolarization by absorption and polarization by reflection.As it is well known when unpolarized light is incident ona polarizing material, the transmitted light is linearly po-larized in the direction parallel to the transmission axis ofthe polarizer. When two polarizing materials are placed in succession in a beam of light, the first is called the po-larizer and the second - the analyzer, the amount of thelight transmitted by the analyzer depends on the angle θ between its transmission axis and the direction of theaxis of the polarizer. The intensity of light transmittedby both polarizer and analyzer will be given by Malus’slaw I = I cos θ, (4)where I is the intensity of the light incident on theanalyzer. The standard setting for this experiment re-quires the light source (regular light source for qualita-tive observation or laser for a quantitative observation),polarizer and analyzer to be placed in succession in abeam of light and screen or photometer for measurementof the intensity of transmitted light. Students set up apolarizer-analyzer system and the laser light source asshown in Fig. 4 and orient and align their polarizationaxes. Slowly rotate the analyzer in either direction whileobserving the intensities of the light spot on the screen.Their observation shows that intensity of light changes.Afterwards, students attach the analyzer to the specialcomponent carrier of the angular translator connected tothe photometer with the fiber probe and place it insteadof the screen. A student starts at θ = 0 and rotates theanalyzer by increasing the angle in 10 increments up to180 and measures the intensity of transmitted light forthe different angles of polarization. The typical resultsof the measurements are presented in graphical form asshown in Fig.5a. Then students study the polarizationphenomenon for microwave radiation. The microwaveradiation from the transmitter is already linearly polar-ized along the transmitter diode axis. Therefore, as themicrowave propagate through space, its electric field re-mains aligned with the axis of the diode. Thus, if thetransmitter diode was aligned vertically, the electric fieldof the transmitted wave would be vertically polarized.If the detector diode of the receiver is at an angle θ tothe transmitter diode, the receiver would only detect thecomponent of the incident electric field that was alignedalong its axis. Students rotate the initially aligned re-ceiver from 0 to 180 in increments of ten degrees andmeasure the intensities of the microwave. Plotting thegraph for the relative intensities versus the angle stu-dents can observe the similarity with the polarization oflight. By comparing the data in Figs 5a and 5b and plot-ting the graph of the relative intensity versus as shown inFig. 6 student can conclude that the intensity of polar-ized light as well as polarized microwaves follows Malus’slaw.To better understand the mechanism of polarizationfor the experiment with microwaves, student places agrid of parallel conducting strips under different anglesbetween the transmitter and aligned receiver and againmeasures the intensities for the different angular posi-tions of the grid. Linearly polarized microwaves are sentthrough a grid of parallel conducting strips. We choose Angle, (cid:84) , degrees R e l a t i v e I n t en s i t y , I/I (a) I/I = cos (cid:84) Angle, (cid:84) , degrees R e l a t i v e i n t en s i t y , I/I (b) I/I = cos (cid:84) FIG. 4: Dependence of the relative intensity of the polarizedlight (a) and microwaves (b) on the polarization angle. the two perpendicular directions used to represent thelinearly polarized incident beam to be parallel and per-pendicular to the metallic strips. The polarized waveswith electric field vector parallel to the conducting stripsare absorbed by the strips. The oscillatory field paral-lel to the strips transfers energy to the electrons thatcan move along the strips; it is the polarization directionperpendicular to the strips that is transmitted. So themetallic strip grid acts as a polarizer, a device for produc-ing polarized microwaves. The axis of a polarizer is thedirection parallel and antiparallel to the plane of polar-ization of the transmitted waves. The axis of a polarizeris not a unique line but simply a direction or a wholecollection of lines oriented parallel to each other. There- cos (cid:84) R e l a t i v e i n t en s i t y , I/I Average of all data
FIG. 5: Relative intensity for polarized light and microwavesversus cos θ . Triangles represent experimental data for lightand circles — for microwaves. fore, for the metallic strip grid polarizer of microwaves,the axis of the polarizer is a direction in the plane ofthe polarizer perpendicular to the direction of the strips.Thus, the experiments of polarization of light and mi-crowaves are complementary which helps to understandand visualize the phenomenon and mechanism of polar-ization.Hence, on one hand students visualize the phenomenonof polarization by observing the polarization of light.They can observe that by changing the angle betweenthe polarizer and analyzer the brightness of the spot oflight changes from maximum bright to dark when theangle is changing from 0 to 90 . On the other hand,polarization of microwaves helps to visualize the mecha-nism of polarization by observing that intensity changesdepending on the angular position of the grid. VI. INTERFEROMETER MEASUREMENTSFOR WAVELENGTH OF LIGHT ANDMICROWAVES
In the interferometry technique we superpose (in-terfere) two or more electromagnetic waves, which createsan output wave different from the input waves. Becauseinterference is a very general phenomenon with waves,interferometry can be applied to a wide variety of elec-tromagnetic waves, including optical spectrum and mi-crowave, and can be used for measurements of wavelengthof light as well as microwaves. The Michelson interferom-eter is the most common configuration for optical inter-ferometry and can be very easily adapted for microwaveinterferometry. In many scientific and industrial uses ofinterferometers, a light source of a known wavelength isused to measure incredibly small displacements - about10 -6 meters. However, if you know the distance of mir-ror movement, you can use the interferometer to measurethe wavelength of a light source as well as a source ofother electromagnetic waves. The aim of this experimentis to make the students familiar with the simplest typeof interferometers and use the interferometer to measurethe wavelength of a helium-neon laser light source anda microwave source. The first part of the experiment iscentered at giving the students a ”feeling” for the sen-sitivity of a Michelson interferometer and the differenttypes of interference patterns which can be observed vi-sually with the laser source. The Michelson interferom-eter produces interference fringes by splitting a beam ofmonochromatic laser light by a partially transparent re-flector so that one beam strikes a fixed mirror and theother a movable mirror. When the reflected beams arebrought back together, an interference pattern results.By measuring the distance d m , that the movable mirrormoved toward the beam-splitter and the correspondingnumber of fringes m , students are able to determine withhigh precision the wavelength of the laser light as λ = 2 d m m (5)The advantage of this part of the experiment is thatthe students visually see the interference pattern. Thispresents a way of direct understanding of important con-cepts in wave optics. In the second part of this exper-iment students use the Michelson interferometer that issetup with a microwave transmitter, partial reflector, twometallic reflectors and receiver. Microwaves travel fromthe transmitter to the receiver over two different paths.In one path, the microwave passes directly through thepartial reflector, reflects back to the first reflector, andthen is reflected from the partial reflector into the re-ceiver. In the other path, the microwave reflects fromthe partial reflector into the second reflector, and thenback through the partial reflector into the receiver. If inthe optical part of this experiment student can visuallyobserve these pathways, for microwaves the paths are in-visible. Now by moving one of the reflectors the studentchanges the path length of one wave, thereby changingits phase at the receiver. While watching the meter, andslowly moving the reflector, students can observe rela-tive maxima and minima of the meter deflections. Bymeasuring the reflector’s displacement distances and cor-responding numbers of maximum relative intensity thewavelength of microwave radiation can be determined us-ing the same Eq. (3) as for visible laser light.The other advantage of this experiment is thatstudents learn and understand why Michelson’s interfer-ometer has become a widely used instrument for measur-ing extremely small distances by using the wavelength ofa known light source. Based on this experiment students understand that resolution for measurement of distancesdepends on the wavelength of electromagnetic radiationand why an optical interferometer (an interferometer us-ing visible light rather than microwaves) provides betterresolution when measuring distance than a microwave in-terferometer.The detailed procedures of some experiments dis-cussed in this article are presented in Refs.[11] and [12].Some of the experiments are computer-based and someare performed in the traditional way. Because not ev-ery lab has computer access, computer-assisted exper-iments serve as supplements to the traditional experi-ments. This allows instructors to find the appropriatebalance between traditional and computer-based exper-iments for teaching topics of light and electromagneticwaves in the physics laboratory. VII. CONCLUSION
Our ultimate goal is to improve engineering major stu-dents’ learning and motivation in physics courses by pre-senting the abstract material in the traditional curricu-lum through real-time experiments in a laboratory ses-sion. This approach assumes the experimental study ofthe properties of light and microwaves in parallel. Oneof the important educational advantages of the simul-taneous study of electromagnetic waves and light is toshow that light and electromagnetic radiation have thesame properties so that the students can visualize theproperties of the electromagnetic radiation through ob-servation of light propagation. In other words, the ab-stract invisible properties of microwaves are visualizedvia observing visible properties of light. On the otherhand, the observation of the polarization of microwaveshelps to visualize and understand the mechanism of thepolarization of light. It is important to underline thatall this is real-time visualization but not computer-basedanimations, simulations or interactive multimedia designcases. In our approach we suggested studying the proper-ties of electromagnetic microwave radiation and light inparallel by performing the same laboratory experimentsfor light and microwaves to show that these two phenom-ena demonstrate the same properties and follow the samelaws. By performing these experiments students becomeactive participants of the learning process.The other advantage in teaching light and mi-crowaves in parallel is that students realize that formeasuring the same properties of electromagnetic wavesof different range of the electromagnetic spectrum youshould use different equipment and different precision ofmeasurements. In our approach by analyzing data forthe same phenomenon through two different methods ofmeasurements, students gain a greater understanding ofthe concepts behind the experiments.The visualization of complex phenomena does notby itself reach our goal. We put this visualization into acontext of the same invisible phenomena and created aseries of parallel activities that involve questions to moti-vate the students and investigations of practical devices.
Acknowledgments
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