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Young's Double-Slit Equation

In the famous double-slit experiment, light passes through two narrow slits and forms a pattern of bright and dark bands on a screen. This equation gives the position of the bright bands (fringes) based on the wavelength of light, the distance between the slits, and the distance to the screen. It was one of the first experiments to prove that light behaves as a wave. It is still used today in optics labs and in understanding interference in thin films and coatings.

Written by the Vorzep Team

Optics Wave Optics Interference

Young's Double‑Slit Calculator y = m λ L / d

y = m · λ · L / d
y = fringe position  ·  m = order number  ·  λ = wavelength  ·  L = screen distance  ·  d = slit separation
⟹ Solve ⟷ y, m, λ, L, d
m
(integer)
m
m
m
Please fix the errors above.
Solve for:
Presets:
Fringe Position —
—
y: — m: — λ: — L: — d: —
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Fringe Position (y) —
Small (< 2 mm) Medium (2–8 mm) Large (> 8 mm)
y = m λ L / d  ·  All lengths in metres (m). Order m is an integer (0, 1, 2, ...).

Variables

Symbol Quantity Unit
y Fringe position m
m Fringe order
λ Wavelength m
L Screen distance m
d Slit separation m

What it means

This formula gives the position of bright fringes (constructive interference) in Young’s double-slit experiment. It is a classic demonstration of the wave nature of light. The spacing between fringes is Δy = λL/d. This experiment is used to measure the wavelength of light, to demonstrate interference, and to illustrate wave‑particle duality. It is also used in optical testing and in coherence measurements. The equation is derived from the path difference between the two slits. Understanding this is fundamental for wave optics and for interpreting interference patterns.

Worked example

Young's Double‑Slit – Two Detailed Examples

Real‑World
Scenario: In a double‑slit experiment, light of wavelength 500 nm illuminates slits separated by d = 0.20 mm. The interference pattern is observed on a screen L = 1.0 m away. The student wants to calculate the position y of the first‑order bright fringe (m = 1). Using y = mλL/d, they compute y = 1 × 500×10⁻⁹ × 1.0 / (0.20×10⁻³) = 2.50×10⁻³ m = 2.50 mm. This predicts where the bright spot will appear, validating the wave nature of light.
ParameterValue
m1
λ (nm)500
L (m)1.0
d (mm)0.20
1y = 1 × 500e-9 × 1.0 / (0.20e-3) = 2.50e-3 m = 2.50 mm
Result 2.50 mm ✓ Fringe position
Scenario: A researcher uses slits with d = 0.25 mm and a screen distance L = 1.2 m. They observe the second‑order bright fringe (m = 2) at a position y = 5.76 mm. They want to determine the wavelength of the light. Rearranging y = mλL/d gives λ = y d / (m L) = 5.76e-3 × 0.25e-3 / (2 × 1.2) = 1.44e-6 / 2.4 = 6.0e-7 m = 600 nm. This confirms that the light source is in the orange‑yellow region, matching the expected spectral line.
ParameterValue
m2
y (mm)5.76
L (m)1.2
d (mm)0.25
1λ = y d / (m L) = 5.76e-3 × 0.25e-3 / (2 × 1.2) = 1.44e-6 / 2.4 = 6.0e-7 m = 600 nm
Result 600 nm ✓ Wavelength deduced
Insight: Young's double‑slit experiment demonstrates the wave nature of light. The fringe spacing is proportional to wavelength and screen distance, and inversely proportional to slit separation. This formula is foundational in optics.

Common mistakes

  • Double‑slit interference: y = mλL/d – the position of the m‑th bright fringe on a screen.
  • m: Order number (0, ±1, ±2, …) – m=0 is the central maximum.
  • L: Distance from the slits to the screen – must be much larger than d for the small‑angle approximation.
  • d: Slit separation – in the same units as λ.
  • Units: y, L, d in metres, λ in metres – y in the same unit as L.
  • Assumption: Small angles (sinθ ≈ tanθ ≈ θ) – for large angles, use the exact formula y = L·tanθ.

Applications

Young's double‑slit equation, y = mλL/d, gives the positions (y) of bright fringes on a screen placed at distance L from two slits separated by distance d, for wavelength λ and order m. This classic experiment demonstrates the wave nature of light and is fundamental to wave optics. Engineers use it to measure the wavelength of light, to design interference filters, and to study the coherence of light sources. It also has applications in optical metrology and in testing optical systems. By analysing fringe patterns, professionals can determine the characteristics of light sources and optical components. This equation is a cornerstone of optics education and research.

  • Measurement of light wavelength using interference patterns
  • Optical metrology for surface flatness and displacement
  • Design of interferometers for precision measurements
  • Testing optical components and systems
  • Educational demonstration of wave interference

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  • Published July 8, 2026
  • Last updated September 18, 2026