Demonstration pubs.acs.org/jchemeduc
Teaching the Operating Principles of a Diffraction Grating Using a 3D-Printable Demonstration Kit Paul A. E. Piunno* Department of Chemical and Physical Sciences, University of Toronto Mississauga, Mississauga, Ontario L5L 1C6, Canada S Supporting Information *
ABSTRACT: The principles which a diffraction grating provides for the dispersion of optical radiation, as employed in most monochromators, are often not easily embraced by analytical chemistry students. To this end, a 3D-printable demonstration kit has been created with the aim to more clearly demonstrate the concepts of diffraction and interference based wavelength selection. The kit consists of 3Dprintable sinusoidal waves of various wavelengths and a platform on which angles at which constructive interference occurs may be recorded. The conceptual demonstration of diffraction grating operation is complemented by a real experiment done on the same platform, using a section of a DVD as a dispersive element and laser pointer light sources. Given the widespread availability of 3D-printers and use of low cost components, this demonstration is not limited to instructors, but can also be printed and used by the students themselves. KEYWORDS: Second-Year Undergraduate, Analytical Chemistry, Demonstrations, Hands-On Learning/Manipulatives, Instrumental Methods, Spectroscopy
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INTRODUCTION Diffraction gratings are perhaps the most commonly employed component for wavelength dispersion in optical spectroscopy instrumentation and in the tuning of dye lasers. As such, developing an understanding of the operating principles of this core instrument component may be considered fundamental to a well-grounded education in analytical chemistry. This notion has been evidenced by the inclusion of this topic in popular (if not all) introductory analytical chemistry textbooks,1−3 and via various educational articles aimed at improving the teaching of how diffraction gratings function.4−8 With the recent advent and widespread availability of 3D-printing technology, a new paradigm has manifested for educators to develop and share designs for demonstrations and other educational materials.9−23 To this end, a 3D-printable demonstration kit has been developed to facilitate the teaching of the concepts of diffraction and interference based wavelength selection afforded by grating based monochromators.
emission wavelength ranges in cases where emission spectroscopy is done. Monochromators typically comprise an entrance slit, an exit slit, optics for focusing and collimating the radiation traversing the device, and, at its heart, a dispersive element. A diffraction grating is used as the dispersive element in most modern monochromators. Two commonly employed monochromator designs, namely, the Czerny−Turner and the Fastie−Ebert, are shown in Figure 1. Wavelength selection is achieved by impinging collimated source radiation onto the grating surface, which in turn has been rotated on a pivot mount within the monochromator so that the desired wavelength band can be made to traverse the exit slit. Gratings are optical components with either flat (as shown in Figure 1) or curved surfaces onto which a series of parallel grooves have been milled or etched, as illustrated in Figure 2.24 These features, known as blazings for the case where they were prepared by milling, are quite small with respect to both the width of the grooves and the intergroove spacing. The groove spacing is typically in the range of 400−3300 nm for UV−vis experiments.24 While the grating substrate is typically made of glass (and operation in a transmission mode can be done), gratings employed in monochromators have their grooved surfaces coated with a thin film of metal so as to
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MONOCHROMATORS AND GRATING BASED WAVELENGTH SELECTION Contained within most optical spectroscopy instruments is one or more monochromator(s). These are components of the ensemble instrument used for selection of a narrow range of wavelengths (typically from a polychromatic emitter) that is to be delivered to or from a sample. The selected radiation can be used for excitation of a sample (as done in both absorption and emission based measurements), and/or to identify sample © XXXX American Chemical Society and Division of Chemical Education, Inc.
Received: November 22, 2016 Revised: February 22, 2017
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DOI: 10.1021/acs.jchemed.6b00906 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Figure 1. (a) Czerny−Turner monochromator design. Optical radiation focused through the entrance slit is directed to a first concave mirror, which produces a collimated beam on reflection that is directed to the diffraction grating. The diffracted radiation striking the second concave mirror is focused through the exit slit of the monochromator. (b) Fastie−Ebert monochromator design. A single concave mirror is used for collimation of the light beam entering the monochromator via the entrance slit onto the grating and also for focus of the diffracted light of desired wavelength through the exit slit. In both designs, rotation of the grating is done to achieve wavelength selection.24
Figure 2. Schematic illustration of a blazed reflection grating, with blaze spacing d. Collimated polychromatic incident radiation, at angle α with respect to the normal of the grating surface, is diffracted in all directions from each blaze feature. Each blazing can therefore be considered as radial source of electromagnetic radiation. At a given angle of observation, β, light of a specific wavelength will undergo constructive interference.
provide operation in a reflection mode (and are called reflection gratings). Optical dispersion (i.e., separation of the various wavelengths of light from a polychromatic source) is achieved through the processes of diffraction and interference. Diffraction occurs when a propagating wave interacts with a feature of a size scale that is similar to the wavelength of the incident wave. The feature will serve to redistribute the waves in all directions from the feature such that each feature can be considered as a radial source of radiation. The phase of the radiation waves emanating from the feature is conserved with respect to that of the incident wave. In the case of a grating, which contains many such features, electromagnetic radiation diffracted from the grooves or blazings may then interact with the radiation emanating from neighboring grooves or blazings and undergo constructive or destructive interference. The relationship between the angle of incidence of the source radiation (with respect to the grating normal), α, the blazing separation distance, d, and the angle, β, at which diffracted beams of a desired wavelength, λ, undergo constructive interference is provided in eq 1, below.
d(sin α + sin β) = nλ
(1)
The term n in eq 1 is an integer value and represents the order of diffraction. In most applications, only the first order is considered as the spectral range of the source often does not provide for significant higher order contributions over the working wavelength range of the monochromator.
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DEMONSTRATION MATERIALS AND DESIGN An easily fabricated and low cost demonstration kit has been created with the aim to more clearly demonstrate the concepts of diffraction and interference based wavelength selection. The kit consists of 3D-printable components, including a combined platform and storage box (Figure 3a), sinusoidal wave support pegs (Figure 3b), slotted support peg (Figure 3c), sinusoidal waves of various wavelengths and colors and associated indicator pegs (Figure 3d), in addition to three laser pointers (405, 532, and 635 nm output), and a section of a DVD (∼1 cm × 3 cm, excised from a whole DVD such that the tracks of the DVD will be parallel to the short axis of the DVD piece and oriented vertically when placed on the platform). The individual 3D-printable component drawings have been B
DOI: 10.1021/acs.jchemed.6b00906 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Figure 3. Components used in the demonstration: (a) combined platform and storage box, (b) long and short support posts used to secure the colored sinusoidal waves to the platform, (c) DVD section attached to a support peg, and (d) sinusoidal waves of various wavelengths and colors and associated indicator pegs, which are used to record the positions where constructive interference is observed to occur.
size scale similar to the wavelength of the radiation. The result is the dispersion of light in all directions from the feature, where the feature can then be thought of as a new, radial source of radiation, as per the wave model originally proposed by Huygens.25 This radial source functionality can be demonstrated by installing a support peg in the centrally situated hole near the base of the platform, mounting the ring of one of the sinusoidal waves on the support post and rotating it in all directions about the platform.
provided in the Supporting Information in stereolithographic (.STL) format. At the scale provided, the largest component (the platform) is 22 cm at its widest; however, as these are vector based drawings, the size of the objects can be scaled up or down as desired or to otherwise fit the build platform of the available 3D-printer. The demonstration has been designed so that it may be projected to the class via an overhead camera, or for use by the students themselves.
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PROVIDING THE DEMONSTRATION
Dispersion by Diffraction
Constructive and Destructive Interference of Various Wavelengths
The first concept to communicate to the students is that of the dispersion of light by diffraction. This phenomenon occurs when the electromagnetic radiation interacts with a feature of a
When electromagnetic radiation is incident at normal incidence on two small features, each will in turn act as a radial source of radiation, with the phase of the light emanating from the C
DOI: 10.1021/acs.jchemed.6b00906 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Figure 4. Demonstrating diffraction based wavelength selection. (a) Two support posts (one long, one short) have been installed into the outermost holes near the base of the platform, onto which the shortest sinusoidal wave set (blue) has been fitted onto the support posts. (b) The waves may be rotated about their support posts and locations at which constructive interference occurs may be noted and (c) marked by placement of an appropriately colored peg in the closest of the radially situated holes on the platform. The locations of constructive interference for the case when sinusoidal waves of increasingly longer wavelength (i.e., (d) green and (e) red) can be similarly marked on the demonstration platform.
radiation, the DVD segment can be mounted on a slotted support peg and installed in the centrally situated mounting hole (Figure 5) for use as a dispersive element. DVDs and CDs are suitable for use in this demonstration as surrogates for a grating owing to the fact that the tracks of these optical discs consist of effectively parallel embossments that are spaced 740 and 1600 nm apart, respectively.26 Laser pointers of various wavelengths can be seated in the cylindrical depression within the 3D-printed platform, with the output of the laser directed at the DVD piece. It should be noted that class 3R laser pointers, of 1−5 mW power output, should be used in order to prevent inadvertent eye damage. The diffracted components of the beam undergoing constructive interference are clearly visualized on the raised rim of the platform, and similarly colored indicator pegs can be installed to record where these events occurred for each wavelength of light used, as illustrated in Figure 5. The similarity in results obtained between the conceptual experiment using the sinusoidal 3D-printed waves and the real experiment with laser radiation helps to solidify the linkage between the visualized concept and the physically observable phenomenon of diffraction and interference based wavelength selection.
features being conserved with respect to that of the incident beam. The electromagnetic radiation propagating from the small features may then interact with the radiation propagating from neighboring features and undergo constructive or destructive interference as a function of the angle of observation. This interference phenomenon can be demonstrated by installing two support pegs (a long and a short support post) in the holes situated near the storage box side of the platform and sinusoidal waves of the same wavelength on each of the two posts, as illustrated in Figure 4a. The sinusoidal waves can be rotated about the posts and angles at which constructive interference occurs (Figure 4b) and can be marked by placement of a similarly colored marker peg in the appropriate hole situated near the perimeter of the platform, as shown in Figure 4c. The process can be repeated for the other sinusoidal waves so as to demonstrate how the wavelength of light affects where constructive interference will occur, as shown in Figure 4d,e. The purpose of the longer support post is to maintain the sinusoidal waves at different heights above the build platform so that they may be made to overlap one another. This vertical offset is necessary for the case where constructive interference of the longer wavelengths is required, as illustrated in Figure 4e. From this visual demonstration, the reason why “rainbows” of light can be observed from objects comprised of regularly spaced, small features, such as diffraction gratings, CDs, or DVDs, can be explained to the class.
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CONCLUDING REMARKS This demonstration was designed as a visual teaching tool that provides a straightforward means for students to appreciate the key concepts and mechanism by which wavelength dispersion of optical radiation is achieved by use of a diffraction grating. Owing to the dropping costs and increased availability of 3Dprinters and 3D-printing services, coupled with the low cost of laser pointers and DVD media, this kit may also serve as a hands-on manipulative that students can readily print, assemble,
Constructive and Destructive Interference of Laser Light Emanating from a DVD
To tie this conceptual demonstration of interference based wavelength dispersion to an actual experiment using optical D
DOI: 10.1021/acs.jchemed.6b00906 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Figure 5. Demonstrating diffraction of laser light from a DVD section. The DVD section has been installed into the slot of a support post, which in turn has been mounted in the central hole near the base of the platform. A laser pointer has been placed in the cylindrical depression in the platform and illuminated. Locations at which constructive interference of diffracted light from the various laser pointers are observed may be recorded using appropriately colored pegs.
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ACKNOWLEDGMENTS The thoughtful feedback received from analytical chemistry students at the University of Toronto Mississauga regarding the design and effectiveness of this demonstration is gratefully acknowledged. Prof. Marc Laflamme is gratefully acknowledged for his assistance in photographing the demonstration kit.
and use themselves. With the basic concepts of dispersion by diffraction at normal incidence and the fundamental operating principles of a grating grasped, students may then better appreciate the diffraction equations and the finer details underlying the design and operation of grating based monochromators. For example, it is anticipated that, after the experience of this demonstration, the effects of illumination under non-normal incidence and the significance of blazing spacing will be more easily comprehended.
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(1) Skoog, D. A.; West, D. M.; Holler, F. J.; Crouch, S. R. Fundamentals of Analytical Chemistry, 9th ed.; Brooks/Cole Cengage Learning: Belmont, CA, 2014; pp 690−696. (2) Christian, G. D.; Pernendu, K. D.; Schug, K. A. Analytical Chemistry, 7th ed.; Wiley: Hoboken, NJ, 2014; pp 506−508. (3) Harris, D. C.; Lucy, C. A. Quantitative Chemical Analysis, 9th ed.; W.H. Freeman: New York, NY, 2016; pp 496−499. (4) Glasser, L. Diffraction at Your Finger Tips. J. Chem. Educ. 1988, 65 (8), 707. (5) Tellinghuisen, J.; Salter, C. Exploring the Diffraction Grating Using a He-Ne Laser and a CD-ROM. J. Chem. Educ. 2002, 79 (6), 703−704. (6) Grossman, W. E. L. The Optical Characteristics and Production of Diffraction Gratings. J. Chem. Educ. 1993, 70 (9), 741−748. (7) Samide, M. J. Understanding Diffraction Using Paper and a Protractor. J. Chem. Educ. 2013, 90 (7), 907−909. (8) Hughes, E., Jr.; Holmes, L. H., Jr.; George, A. Using Lasers to Demonstrate Refraction, Diffraction, and Dispersion. J. Chem. Educ. 1997, 74 (3), 298. (9) Griffith, K. M.; de Cataldo, R.; Fogarty, K. H. Do-It-Yourself: 3D Models of Hydrogenic Orbitals through 3D Printing. J. Chem. Educ. 2016, 93 (9), 1586−1590.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.6b00906. Information about filament colors selection, tips for successful printing of the demonstration, and preparation of the DVD section (PDF, DOCX) Stereolithographic files of all of the 3D-printable components (ZIP)
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Paul A. E. Piunno: 0000-0001-6809-2843 Notes
The author declares no competing financial interest. E
DOI: 10.1021/acs.jchemed.6b00906 J. Chem. Educ. XXXX, XXX, XXX−XXX
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