Calculatorism

Young's Double-Slit Calculator

Enter wavelength, slit separation d, screen distance L and order m to compute fringe spacing Δy=λL/d, bright-fringe position y_m=mλL/d and path difference. λ=550 nm, d=0.1 mm, L=2 m → Δy=11 mm.

Input Data

Wavelength λ (m). Red 700 nm; green 550 nm; blue 450 nm.
m
Slit separation d (m). Pinhole 0.1 mm=1e-4; fine slit 0.5 mm=5e-4; grating 1e-5.
m
Screen distance L (m). Lab 1–3; far-field 10.
m
Fringe order m (integer ≥0). Centre 0; first bright 1; second 2.

Results

Spacing between adjacent bright fringes Δy (m).
0.01m
Position of the m-th bright fringe y_m (m).
0.01m
Path difference mλ (m).
0.0000005m

At a glance:Young's double-slit experiment (Thomas Young, 1801, England): light passing through two narrow slits separated by distance d produces alternating bright and dark interference fringes on a distant screen. Bright-fringe condition: path difference Δ=mλ (m integer), at position y_m=mλL/d; dark-fringe condition: Δ=(m+½)λ. Fringe spacing Δy=λL/d. Derivation: the two-slit path difference ≈ d·sinθ ≈ d·y/L (small-angle approximation sinθ≈tanθ=y/L). Constructive interference (bright) occurs when Δ=mλ, giving y_m=mλL/d. Physical meaning: (1) fringe spacing is proportional to wavelength, proving light is a wave; (2) it was key evidence for the wave theory, opposing Newton's corpuscular view; (3) it is the foundational experiment for interference and diffraction. History: Young demonstrated it to the Royal Society in 1801, shaking the corpuscular mainstream; later Maxwell's electromagnetic theory established light as an EM wave. In 1905 Einstein's photoelectric effect revealed wave-particle duality, and the double slit gained deeper meaning in quantum mechanics — single-photon double-slit interference demonstrates quantum superposition. Applications: (1) wavelength measurement (interferometers); (2) holography; (3) quantum double-slit interference; (4) optical testing (surface flatness); (5) electron interference (electron microscopy).

Formula

Fringe spacing: Δy = λL/d

Bright position: y_m = m·λL/d

Path difference: Δ = m·λ (bright)

Bright condition: d·sinθ = m·λ

Small angle: sinθ ≈ tanθ ≈ y/L

$$\Delta y = \frac{\lambda L}{d}, \quad y_m = \frac{m\lambda L}{d}, \quad \Delta = m\lambda, \quad d\sin\theta = m\lambda$$

How to Use

  1. Enter wavelength λ (m; visible 4–7e-7).
  2. Enter slit separation d (m; 0.1 mm = 1e-4).
  3. Enter screen distance L (m; 1–3).
  4. Enter order m (≥0; centre is 0).
  5. The tool computes fringe spacing, bright position and path difference.

Case Studies

Wavelength measurement and interferometry

Green light λ=550 nm, d=0.1 mm, L=2 m.

Δy=λL/d=5.5e-7×2/1e-4=0.011 m=11 mm.

Measuring the fringe spacing lets you infer λ — the principle of interferometers.

Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.

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