Light interference pattern measurements from automated low-cost Young’s double-slit experiments

Young’s double-slit experiment is commonly used in undergraduate physics laboratory to show the wave nature of light. As an alternative to expensive commercial kits, here we present an automated, low–cost light intensity measurement setup that allows real-time visualization of the interference pattern. The light intensity is measured by a light dependent resistor placed on the head of a dot matrix printer. The head motion is controlled by an Arduino which also collects the data and send them to a computer. The interference pattern obtained by the setup is in agreement with a model that includes the degree of the coherence of the light source and the effective size related to the light collecting area of the resistor. The apparatus allows quantitative data analysis from the measured light patterns and is suitable to be used in undergraduate physics laboratories.

Keywords
double slit; light waves; Arduino; low cost; light interference

Authorship

C. G. de Oliveira Jr

Universidade Estadual de Campinas, Faculdade de Tecnologia, 13484-332, Limeira, SP, BrasilUniversidade Estadual de CampinasBrasilLimeira, SP, BrasilUniversidade Estadual de Campinas, Faculdade de Tecnologia, 13484-332, Limeira, SP, Brasil

M. R. Gumiero

V. R. Coluci ^**Correspondence email address: vitor@ft.unicamp.br.

https://orcid.org/0000-0001-5179-6182

*Correspondence email address: vitor@ft.unicamp.br.

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Figures | Formulas

Figures (5)
Formulas (5)

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Figure 1
Interference of two light beams R₁ and R₂ on a screen in the double-slit experiment.

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Figure 2
(a) Schematic representation of the three main parts of the apparatus. The LDR and the resistor R₀ (=10 kΩ) are in series. (b) Photographs of the apparatus showing (bottom) the laser beam reaching the slits, (middle) the wood base for the printer carriage, the LDR, and the stepper motor, and (top) an example of an obtained intensity pattern. A scanning electron microscopy image of the double-slit used in this work is also shown in the inset. The diagram of the circuit involving the Arduino, the Easy driver, and the stepper motor was built with Fritzing [²⁴24 A. Knörig, R. Wettach and J. Cohen, in Proceedings of the 3rd International Conference on Tangible and Embedded Interaction, Cambridge, 2009, edited by A. Knorig, R. Wettach and J. Cohen (Association for Computing Machinery, New York, 2009), p. 351.].

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Figure 3
Raw voltage data from the uncovered (black) and partially covered (blue) LDR by a black tape for L=208±1 cm. The minima exhibit a non-zero intensity because neither the LDR data were averaged, to take into account the LDR lateral size, neither scaled, to take into account the nonlinear dependence of the LDR resistance with the illuminance. The LDR size after covered with the tape was about 2 mm which yields to a effective size of about 1 mm.

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Figure 4
Locations of the interference maxima measured from the apparatus (circles). The fitting with Eq. (2)x_n^max (in cm)= (0.02 ± 0.02) + (1.195 ± 0.005)n is also shown.

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Figure 5
Comparison between the interference pattern obtained with the apparatus (circles) with the predicted one (lines) by Eq. (3) ((a) and (b)) and Eq. (4) (c). The parameters used for all curves were a=38 µm, d=274 µm, L=625 cm, and λ=532 nm.

(1)

(2)

(3)

(4)

(5)

Figure 1 Interference of two light beams R₁ and R₂ on a screen in the double-slit experiment.

Figure 2 (a) Schematic representation of the three main parts of the apparatus. The LDR and the resistor R₀ (=10 kΩ) are in series. (b) Photographs of the apparatus showing (bottom) the laser beam reaching the slits, (middle) the wood base for the printer carriage, the LDR, and the stepper motor, and (top) an example of an obtained intensity pattern. A scanning electron microscopy image of the double-slit used in this work is also shown in the inset. The diagram of the circuit involving the Arduino, the Easy driver, and the stepper motor was built with Fritzing [²⁴24 A. Knörig, R. Wettach and J. Cohen, in Proceedings of the 3rd International Conference on Tangible and Embedded Interaction, Cambridge, 2009, edited by A. Knorig, R. Wettach and J. Cohen (Association for Computing Machinery, New York, 2009), p. 351.].

Figure 3 Raw voltage data from the uncovered (black) and partially covered (blue) LDR by a black tape for L=208±1 cm. The minima exhibit a non-zero intensity because neither the LDR data were averaged, to take into account the LDR lateral size, neither scaled, to take into account the nonlinear dependence of the LDR resistance with the illuminance. The LDR size after covered with the tape was about 2 mm which yields to a effective size of about 1 mm.

Figure 4 Locations of the interference maxima measured from the apparatus (circles). The fitting with Eq. (2)x_n^max (in cm)= (0.02 ± 0.02) + (1.195 ± 0.005)n is also shown.

Figure 5 Comparison between the interference pattern obtained with the apparatus (circles) with the predicted one (lines) by Eq. (3) ((a) and (b)) and Eq. (4) (c). The parameters used for all curves were a=38 µm, d=274 µm, L=625 cm, and λ=532 nm.

(1)

I (θ) = I_{0} {sinc}^{2} (\frac{k a \sin θ}{2}) \cos^{2} (\frac{k d \sin θ}{2}),

(2)

x_{n}^{\max} = \frac{λ L}{d} n, n = 0, 1, 2, . . . . .

(3)

I (x) = \frac{I_{0}}{2} {sinc}^{2} (\frac{k a}{2 L} x) [1 + V \cos (\frac{k d}{L} x + δ)],

(4)

\frac{I (x)}{I_{0}} = {[(\frac{V_{T}}{V_{LRD} (x)} - 1)]}^{- \frac{1}{b}}

(5)

Ĩ (x_{i}) = \frac{1}{n_{j} (l)} Σ_{j = 1}^{n_{j} (l)} I (x_{j})

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Light interference pattern measurements from automated low-cost Young’s double-slit experiments

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[1] *Correspondence email address: vitor@ft.unicamp.br.