Diffraction and interference are basic phenomena of waves. They are treated in wave optics extensively, because experimental setups are easy to built, diffraction patterns are visible and because of their importance for further

subjects at school and university (diffraction of X-rays, cristallography, Fourier-Transformation, . . . ). Unfortunately, in many cases the experiments are demonstration experiments with a few diffracting objects and not enough possibilities for the students to participate. Therefore we developed a very flexible Remotely Controlled Laboratory (RCL) about diffraction and interference—a real experiment, which can be performed over the internet. The user can choose from among 5 different wavelengths, about 150 diffracting objects and 3 different techniques of qualitative and quantitative measurement. In this contribution we describe the experimental setup, give an overview about experimental results and end with the added value of the experiment

Gröber, S.

Jodl, H.-J.

Vetter, M.

English

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2010-10625-xColloquia: MPTL14IL NUOVO CIMENTO Vol. 33 C, N. 3 Maggio-Giugno 2010Experimenting from a distance in case of diffractionand interferenceS. Gro¨ber(∗), M. Vetter and H.-J. JodlDepartment of Physics, University of Technology KaiserslauternErwin-Schro¨dinger-Straße, 67663 Kaiserslautern, Germany(ricevuto il 30 Novembre 2009; pubblicato online il 26 Luglio 2010)Summary. — Diffraction and interference are basic phenomena of waves. Theyare treated in wave optics extensively, because experimental setups are easy tobuilt, diffraction patterns are visible and because of their importance for furthersubjects at school and university (diffraction of X-rays, cristallography, Fourier-Transformation, . . . ). Unfortunately, in many cases the experiments are demonstra-tion experiments with a few diffracting objects and not enough possibilities for thestudents to participate. Therefore we developed a very flexible Remotely ControlledLaboratory (RCL) about diffraction and interference—a real experiment, which canbe performed over the internet. The user can choose from among 5 different wave-lengths, about 150 diffracting objects and 3 different techniques of qualitative andquantitative measurement. In this contribution we describe the experimental setup,give an overview about experimental results and end with the added value of theexperiment.PACS 01.50.-i – Educational aids.PACS 01.50.F- – Audio and visual aids.1. – IntroductionDiffraction and interference are phenomena, which play a significant role not onlyin pure physics (wave optics, optical spectroscopy), but also in technical applicationse.g. coating of eyeglasses or resolution of microscopes. In addition we know of manyinterference phenomena in nature such as the colour of butterfly wings or aureoles aroundthe sun or the moon. Diffraction as well as interference can be nicely modelled in waveoptics (intensity distribution on a screen due to diffraction of light by objects, opticalpath difference, etc.). Consequently all theoretical results (intensity function of singleslit and grating, calculation via Fourier-Transformation) can be checked by the results(∗) E-mail: groeber@rhrk.uni-kl.dec© Societa` Italiana di Fisica 211212 S. GRO¨BER, M. VETTER and H.-J. JODLof quantitative measurements, in principle. Therefore this subject is intensively taughtat school and university level in lectures as well as in student labs.The experimental setup is comparatively simple and is mostly used in teaching in aqualitative manner: e.g. transition of the intensity distribution caused by a single slit,double slit, multiple slits and gratings, which students are watching on a wall in a class.Unfortunately these experimental setups do not incorporate all necessary technical pa-rameters from theory such as different wavelengths for a deeper comparison of theoreticaland experimental results. In general there is not available a complete set of diffractingobjects of industrial grade to systematically investigate theoretical dependence on slitwidth, slit distance and number of slits. The laser granulation in the central maximumand the relative poor quality of photographically produced objects (like contrast ratio) donot always allow quantitative measurements (e.g. subsidary maxima for n ≥ 3, intensityratio between main maxima).2. – RCL variantTherefore we developed, set up and tested a technically very comprehensive experi-ment for diffraction and interference in an RCL variant. An RCL experiment (RemotelyControlled Laboratory) is a real experiment at location A which can be controlled by auser from his computer via the internet at location B. The interested reader may have alook at our two basic papers describing the technical solution, the programming, concept,aims and experiences as well as didactical approach [1,2]. Our portal [3] now offers about20 RCL experiments such as “Speed of Light” or “Photoelectrical Effect”.Figure 1 shows the experimental setup, which is a standard setup with light source,diffracting object and screen in Fraunhofer diffraction manner. As light sources we offer5 different laser diodes with wavelengths λ = 532 nm, 635 nm, 670 nm, 780 nm, 850 nmand power P ≈ 3mW. On top of the laser diode λ = 670 nm we placed a second laserdiode λ = 635 nm for studying the resolution of a grating.157 diffracting objects are arranged on a plate of glass (size 5 cm×5 cm), which can bemoved horizontally and vertically via stepper motors to select an individual diffractingobject. Instead of diffracting objects produced by photo lithography [4] our diffractingobjects were produced by electron lithography from an institute at the Technical Univer-sity of Kaiserslautern [5]. The advantages are much better resolving power and bettercontrast. The use of a lens is not necessary, because of the small size of the diffractingobjects. Table I shows the geometry (slit number N , slit width b, slit distance d) ofthe diffracting objects, which we selected such that investigations cover all theoreticalpredictions. They are divided into 3 groups: 134 standard objects, 6 different pairsof objects to study the resolving power of a grating and 7 special objects like a wire,an asymmetric double slit and 5 unknown objects to determine their geometry. Thediffraction pattern on screen and its intensity distribution can be investigated with threetechniques of measurement:– qualitative observation by eye via webcam-1 and taking a screenshot for furtheranalysis– observation by eye via webcam-1 and use of an illuminated ruler for direct quanti-tative reading and measuring– quantitative measurement of intensity by a light sensor behind a little hole in thescreen.EXPERIMENTING FROM A DISTANCE IN CASE OF DIFFRACTION AND INTERFERENCE 213Fig. 1. – a) Sketch from top view of experimental setup. b) Pictures and components of leftand right part of experimental setup: 5 laser diodes 532 nm–870 nm (1), laser diode 635 nm (2),quadratic diaphragm (3), object holder with diffracting objects (4), webcam-1 (5), screen withlight sensor and illuminated ruler (6), webcam-2 (7) and interface (8).Table I. – Geometry of standard, resolving power (r) and special (s) diffracting objects.Slit number N Slit width b in μm Slit distance d in μm1 1, 5, 10, 15, 20, 25, 30, 60, 90, 800 –21 6010, 15 20, 30, 40, 60, 9020, 25 30, 40, 60, 9030 40, 60, 903, 4, 5, 610, 15 20, 30, 40, 60, 9020, 25 30, 40, 60, 9030 40, 60, 90105 10, 20, 30, 40, 50, 60, 8010 20, 30, 40, 50, 60, 8020 30, 40, 50, 60, 804, 5, 6, 8, 10, 12 (r) 5 601 wire (s) 90 –2 (s) 15 and 20 605 unknown objects (s)214 S. GRO¨BER, M. VETTER and H.-J. JODLFig. 2. – From the RCL website, menu item “Laboratory”: RCL menu (left), view of webcams(middle) and control panel to vary technical parameters (right).To study the resolving power of a grating two laser beams from laser diodes with wave-lengths 635 nm and 670 nm irradiate the same diffracting object and the diffraction pat-terns are superimposed on one another on the screen.3. – Experimenting and resultsFigure 2 shows the laboratory website of this RCL. With the control panel on theright the user can perform the experiment. First, selection of desired wavelength: Inthe picture of the lower webcam-2 one can observe the horizontal adjustment of thelaser diode and how the laser spot irradiates the quadratic diaphragm in front of thediffracting objects. Second, choice of diffracting object among the three groups (table I):In the lower webcam-2 picture one can watch the object holder moving in vertical andhorizontal directions to find the chosen diffracting object. Simultaneously the diffractionpatterns of all the diffracting objects illuminated during the movement appear in theupper webcam-1 picture. Third, choice of technique of measurement: One can switchon or off the illuminated ruler, take a screenshot of the diffraction pattern or choose astep size for a measurement with the light sensor. In the last case a white LED marksthe horizontal position of the light sensor during its motion over the diffraction pattern.The intensity distribution is automatically displayed in a diagram and one can downloadthe measured data as a text file. In the RCL we can only work with small diffractionangles α < |αmax| = 4.5◦ because the distance e between screen and diffracting objectsEXPERIMENTING FROM A DISTANCE IN CASE OF DIFFRACTION AND INTERFERENCE 215Fig. 3. – N = 1, λ = 532 nm. Diffraction patterns for increasing slit width b.is 1.005m and the horizontal width of the diffraction pattern, which can be viewed viawebcam-1, is about 16 cm.On the far left one can see the RCL menu (Introduction, Setup, Theory, Tasks,Laboratory, Analysis, Discussion, Material, Support), which is identical in all RCLsand contains all necessary information to perform the experiment autonomously. Thefollowing subsections demonstrate how– one can check all kinds of theoretical predictions for a slit or grating– one can use the different techniques of measurement– accurate measured data for further analysis are– flexible and comprehensive one can set up a measuring program– quickly one can collect sufficient data for measuring series.3.1. Investigations with single slit . – In fig. 3 we deal with the diffraction pattern ofa single slit. Qualitatively with increasing slit width b all maxima and minima of ordern are moving closer to the central maximum (n = 0). Moreover the intensity of themaxima of order n is increasing. One can assume for the limiting case b → 0 (b  λ)that the intensity distribution becomes a constant and zero. For the limiting case b λ(b→∞ makes no sense) we get the intensity distribution of a geometrical shadow.To investigate the first observation quantitatively we measured with the ruler thedistance a1 between the minimum of order n = 1 and the central maximum of order n = 0(fig. 4a). The experimental data fit very well to the theoretically derived dependencesinα1 =λb≈ tanα1 = a1e⇔ a1(b) = eλb.(1)216 S. GRO¨BER, M. VETTER and H.-J. JODLFig. 4. – a) N = 1, λ = 532 nm. Distance a1 between minimum of order n = 1 and centralmaximum versus slit width b. Comparison between measured (squares) and theoretical data(line). b) N = 1, λ = 532 nm. Intensity I0 of central maximum versus slit width b. Proof ofI0 ∼ b2 for measured data (squares) and regression line.To investigate the second observation quantitatively we measured with the light sensorthe intensity I0 of the central maximum for different slit width b (fig. 4b). The measureddata and the regression line show that I0 ∼ b2, which confirms the theoretical predictionfor a rectangular diaphragm with area A = cb and constant height c that I0 ∼ A2 =(cb)2 ∼ b2 [6].3.2. Structure of intensity distribution of a grating . – The final step in our considera-tions here will be the quantitatively measured intensity distribution of a grating. In fig. 5awe compare a typical intensity distribution with the well known theoretical predictiondescribed byI(α) = I0 ·(sin(πbλ sinα)πbλ sinα)2·(sin(N πdλ sinα)sin(πdλ sinα))2(2)and tanα = x/e. Measured data and theoretical line fit very well.To qualitatively develop step by step the intensity distribution of a grating we startwith a double slit (N = 2), because subsidiary maxima are missing. We took a sequenceof screenshots of a double slit for constant slit distance d and different slit width b (fig. 5b,upper pictures) and compare those to screenshots of a single slit with the same slit widthb (fig. 5b, lower picture). We can recognize that the diffraction pattern of the single slitis modulating the ideal intensity distribution of the double slit. In fig. 5c we keep theslit width b constant and vary the slit distance d. Now the fine structure in the intensitydistribution is determined by the property of the double slit. If d is small the spacingbetween maxima is high and if d is large the spacing is small.3.3. Transition between real and ideal grating . – Half-quantitatively, we study in fig. 6the transition between a real and an ideal grating (N → ∞ and b → 0). As a first stepwe increase in fig. 6a the slit number N for constant slit width b: one can see, that thenumber of subsidary maxima is increasing and their relative intensity is decreasing. Asa second step we decrease in fig. 6b the slit width b: due to the expanding intensityEXPERIMENTING FROM A DISTANCE IN CASE OF DIFFRACTION AND INTERFERENCE 217Fig. 5. – a) λ = 532 nm, N = 5, b = 10μm, d = 20μm. Comparison of measured (black points)and theoretical intensity distribution of grating with slit function (grey lines). I(0) of theoreticalintensity distribution adapted to measured intensity distribution. b) λ = 532 nm. Comparisonbetween diffraction pattern of double slits with constant slit distance d = 60μm and single slitsof same slit width b for increasing b. c) λ = 532 nm. Comparison of diffraction pattern of doubleslits with constant slit width b = 10μm for increasing slit distance d (single slit with the sameslit width).distribution of the single slit envelope the relative intensity of main maxima n = 0 isincreasing and the first missing main maximum is shifted to greater distance |x|. For thelimiting case of an ideal grating we get a diffraction pattern, which consists of equidistant“points” with intensity zero, whereas the mathematical representation of the intensitypattern is a function with equidistant delta-type maxima.3.4. Further investigations with the intensity distribution of a grating . – As a first seriesof studies we want to investigate the influence of parameter wavelength λ on diffraction.As an example we measured the distance a6 of the maximum n = 6 from the centralmaximum (fig. 7a). Measured data fit very well the theoretical prediction a6(λ) = 6eλ/d.As a second series of studies we want to investigate the property of central maximum.From formula 2 we expect that the intensity I(0) varies with the slit number N likeI(0) ∼ N2, which is well documented by fig. 7b. From theory we expect also that the218 S. GRO¨BER, M. VETTER and H.-J. JODLFig. 6. – a) λ = 532 nm, b = 20μm, d = 30μm. Change of relative intensity distribution I/I(0)and diffraction pattern for increasing slit number N . b) λ = 532 nm, N = 10, d = 30μm. Changeof relative intensity distribution I/I(0) and diffraction pattern for decreasing slit width b.width B of the central maximum vary with the slit number N like B ∼ 1/N , again thisis well confirmed in fig. 7c.The three experimental results are fundamental to understanding the use and actionof a grating in spectroscopy (resolution of light into different wavelengths and separationof two different wavelengths).Fig. 7. – a) N = 10, b = 20μm, d = 80μm. Distance a6 between maximum of order n = 6 andcentral maximum versus wavelength λ. Comparison between measured (squares) and theoreticaldata (line). b) λ = 532 nm, b = 20μm, d = 80μm. Intensity I(0) of central maximum versus slitnumber N . Proof of I(0) ∼ N2 for measured data (squares) and regression line. c) λ = 532 nm,b = 10μm, d = 20μm. Width B of central maximum versus slit number N . Proof of B ∼ 1/Nfor measured data (squares) and regression line.EXPERIMENTING FROM A DISTANCE IN CASE OF DIFFRACTION AND INTERFERENCE 219a) b)Fig. 8. – a) λ1 = 635 nm, λ2 = 670 nm, b = 5μm, d = 60μm. Intensity I versus sensor position x(diagrams from laboratory website) for increasing slit number N = 4 to N = 8. Decreasing ordernmin (arrows) for resolved wavelengths. b) Comparison between measured intensity distributionof a slit (grey) and a wire (black) with the same width b = 90μm (height of central maximumis not shown).3.5. Resolving power of a grating and Babinet’s principle. – In fig. 8a we deal with theresolving power A of N slits. Due to the selected pair of laser diodes (λ1 = 635 nm, λ2 =670 nm) we find a theoretical and constant resolution Atheo = λ/Δλ = 635 nm/35 nm ≈19, which is equal to the product nminN (nmin is minimal order to resolve the mainmaxima of two wavelengths). Therefore, if we increase the slit number N , the minimalorder nmin decreases. The experimentally determined resolving power is Aexp = 5·4 = 20for N = 4 and Aexp = 3 · 8 = 24 for N = 8.In fig. 8b we compare the intensity distribution of a single slit and a wire of the samewidth b. One can see that Babinets principle is confirmed, because the maxima andminima of slit and wire coincide.4. – Concluding remarksWe designed this and all other RCLs such that the user can vary technical parameters(wavelength, diffracting object, detection type) like in a real experiment and that froma distance the user can follow in real time via webcams—as authentic as possible—how he or she is experimenting. The added value of this experiment “Diffraction andInterference” as an RCL experiment is the following:– Due to the fact of 157 diffracting objects many different measurements and inves-tigations on different research levels are possible.– Electron lithographically produced diffracting objects achieve a contrast rich inten-sity pattern and allow one to consider limiting cases like an ideal grating.220 S. GRO¨BER, M. VETTER and H.-J. JODL– One can collect pretty good experimental data in a relatively short time for furtherexperimental analysis and for theoretical modelling.– The user can choose from among different techniques of measurement the best onefor a given problem.– In the experiment a nearly continuous transition between qualitative, half quanti-tative and quantitative consideration of diffraction is possible.The user can exercise experimental skills, formulate hypotheses and plan a researchmeasuring program besides dealing with pure physics.– An individual user or a group of students can establish their own research questionsand organize their own measuring program.In addition we offer in the RCL menu item “Theory” a very comprehensive introductioninto waves and superposition of waves. For different levels of teaching and learning wetabulate formulas for single, double and multiple slit and derive the formula for a multipleslit with and without using Fourier-Transformation. In the menu item “Material” theinterested teacher will find a link to an extensive teaching sequence and additional mate-rials (in German). We consider this RCL as well suited to catalyze a more autonomouslearning in upper secondary school, to support experimental self study by students andto improve demonstration of diffraction in lectures at university.∗ ∗ ∗We thank Mr. Lu¨tkefedder, who performed this experiment as an RCL during histhesis to become a physics teacher. We thank Ms. Wolff and Mr. La¨gel for produc-ing the diffracting objects for us by electron lithography and Schule Schloss Salem forhosting this RCL. We are grateful to our sponsors (Eberhard-von-Kuehnheim foundationof BMW AG—Ms. Grammes, German employers’ association—Mr. Gollub, Intel c©Education—Mr. Ensle, Schulen ans Netz e. V.—Mr. Heinen) who have been financingthe RCL project for many years.REFERENCES[1] Gro¨ber S, Vetter M, Eckert B and Jodl H-J 2007 Experimenting from a distance - remotelycontrolled laboratory (RCL) Eur. J. Phys. 28 S127-S41.[2] Gro¨ber S, Vetter M, Eckert B and Jodl H-J 2008 Remotely controlled laboratories: aims,examples, and experience Am. J. Phys. 76 374-8.[3] http://rcl.physik.uni-kl.de.[4] Koppelmann G and Rudolph M 1977 Photographische Beugungsobjekte fu¨r den Unterricht- Herstellung und Eigenschaften PhuD 3 220-9.[5] Zentrum fu¨r Nanostrukturtechnologie und Molekularbiologische Technologie, University ofTechnology Kaiserslautern http://www.nbc.uni-kl.de.[6] Hecht E and Zajak A 1974 Optics 349.

Experimenting from a distance in case of diffraction and interference

http://eprints.bice.rm.cnr.it/16896/1/ncc9629.pdf

Experimenting from a distance in case of diffraction and interference

Abstract

Similar works

Full text

Available Versions

Scientific Open-access Literature Archive and Repository