The Classical Double Slit Interference Experiment: A New Geometrical Approach

Joseph Ivin Thomas

doi:doi:10.11648/j.ajop.20190701.11

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The Classical Double Slit Interference Experiment: A New Geometrical Approach

Joseph Ivin Thomas

Published in American Journal of Optics and Photonics (Volume 7, Issue 1)

Received: 2 March 2019 Accepted: 9 April 2019 Published: 7 May 2019

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Abstract

The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.

Published in	American Journal of Optics and Photonics (Volume 7, Issue 1)
DOI	10.11648/j.ajop.20190701.11
Page(s)	1-9
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Interference, Fringe, Hyperbola, Wavefront, Locus

References

[1]	Young, T. (1804). I. The Bakerian Lecture. Experiments and calculations relative to physical optics. Philosophical transactions of the Royal Society of London, 94, 1-16.
[2]	Young, T. (1807). A Course of Lectures on Natural Philosophy and the Mechanical Arts, Vol. 1 (William Savage, Bedford Bury, London), pp. 463-465.
[3]	Halliday, Resnick and Walker, Fundamentals of Physics, 6th Edition (John Wiley and Sons, Inc., New York, 2003) pp. 866-870.
[4]	Giancoli, Physics for Scientists & Engineers, 4th Edition (Pearson- Prentice Hall, New Jersey, 2008) pp. 903-909.
[5]	Young and Freedman, Sears and Zemansky’s University Physics, 13th Edition (Peason Education publishing as Addison-Wesley, San Francisco CA, 2012) pp. 1164-1170.
[6]	Born and Wolf. Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, 4th Edition (Elsevier, 2013) pp. 256-260.
[7]	Sobel, Michael I. "Algebraic Treatment of Two-Slit Interference." The Physics Teacher 40, no. 7 (2002): 402-404.
[8]	Poon, Dick CH. "How Good Is the Approximation “Path Difference≈ d sin θ”?." The Physics Teacher 40, no. 8 (2002): 460-462.
[9]	Hopper, Seth, and John Howell. "An exact algebraic evaluation of path-length difference for two-source interference." The Physics Teacher 44, no. 8 (2006): 516-520.
[10]	Hughes, Joe, and Frederic Liebrand. "Conic Sections in the Double-Slit Experiment."
[11]	Thomas, J. "A Mathematical Treatise on Polychronous Wavefront Computation and its Application into Modeling Neurosensory Systems. Research Gate; 2014." Unpublished.
[12]	Meyer, Daniel Z. "A Student-Centered, Inquiry-Based Approach to Young’s Double-Slit Experiment (and Other Investigations of Light’s Wave Character)." The Physics Teacher 55, no. 3 (2017): 159-163.
[13]	de Broglie, Louis. "Wave mechanics and the atomic structure of matter and radiation." Le Journal de Physique et le Radium8 (1927): 225.
[14]	Böhm, David. "A Suggested Interpretation of the Quantum Theory in Terms of" Hidden" Variables. I." Physical Review 85, no. 2 (1952): 166-179.
[15]	Böhm, David. "A Suggested Interpretation of the Quantum Theory in Terms of" Hidden" Variables. II." Physical Review 85, no. 2 (1952): 180-193.

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Joseph Ivin Thomas. (2019). The Classical Double Slit Interference Experiment: A New Geometrical Approach. American Journal of Optics and Photonics, 7(1), 1-9. https://doi.org/10.11648/j.ajop.20190701.11

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Joseph Ivin Thomas. The Classical Double Slit Interference Experiment: A New Geometrical Approach. Am. J. Opt. Photonics 2019, 7(1), 1-9. doi: 10.11648/j.ajop.20190701.11

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Joseph Ivin Thomas. The Classical Double Slit Interference Experiment: A New Geometrical Approach. Am J Opt Photonics. 2019;7(1):1-9. doi: 10.11648/j.ajop.20190701.11

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@article{10.11648/j.ajop.20190701.11,
  author = {Joseph Ivin Thomas},
  title = {The Classical Double Slit Interference Experiment: A New Geometrical Approach},
  journal = {American Journal of Optics and Photonics},
  volume = {7},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ajop.20190701.11},
  url = {https://doi.org/10.11648/j.ajop.20190701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajop.20190701.11},
  abstract = {The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.},
 year = {2019}
}

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TY  - JOUR
T1  - The Classical Double Slit Interference Experiment: A New Geometrical Approach
AU  - Joseph Ivin Thomas
Y1  - 2019/05/07
PY  - 2019
N1  - https://doi.org/10.11648/j.ajop.20190701.11
DO  - 10.11648/j.ajop.20190701.11
T2  - American Journal of Optics and Photonics
JF  - American Journal of Optics and Photonics
JO  - American Journal of Optics and Photonics
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SN  - 2330-8494
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AB  - The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.
VL  - 7
IS  - 1
ER  -

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Author Information

Joseph Ivin Thomas

School of Natural Sciences & Engineering, National Institute of Advanced Studies, IISc Campus, Bangalore, India

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Joseph Ivin Thomas. (2019). The Classical Double Slit Interference Experiment: A New Geometrical Approach. American Journal of Optics and Photonics, 7(1), 1-9. https://doi.org/10.11648/j.ajop.20190701.11

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ACS Style

Joseph Ivin Thomas. The Classical Double Slit Interference Experiment: A New Geometrical Approach. Am. J. Opt. Photonics 2019, 7(1), 1-9. doi: 10.11648/j.ajop.20190701.11

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AMA Style

Joseph Ivin Thomas. The Classical Double Slit Interference Experiment: A New Geometrical Approach. Am J Opt Photonics. 2019;7(1):1-9. doi: 10.11648/j.ajop.20190701.11

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@article{10.11648/j.ajop.20190701.11,
  author = {Joseph Ivin Thomas},
  title = {The Classical Double Slit Interference Experiment: A New Geometrical Approach},
  journal = {American Journal of Optics and Photonics},
  volume = {7},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ajop.20190701.11},
  url = {https://doi.org/10.11648/j.ajop.20190701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajop.20190701.11},
  abstract = {The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - The Classical Double Slit Interference Experiment: A New Geometrical Approach
AU  - Joseph Ivin Thomas
Y1  - 2019/05/07
PY  - 2019
N1  - https://doi.org/10.11648/j.ajop.20190701.11
DO  - 10.11648/j.ajop.20190701.11
T2  - American Journal of Optics and Photonics
JF  - American Journal of Optics and Photonics
JO  - American Journal of Optics and Photonics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2330-8494
UR  - https://doi.org/10.11648/j.ajop.20190701.11
AB  - The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.
VL  - 7
IS  - 1
ER  -

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