About the Double Slit Experiment Calculator
This double slit calculator handles Young's interference experiment. Enter the light's wavelength, the distance between the two slits and the distance to the screen, and it returns the spacing between bright fringes, the angle and exact position of any bright fringe order you choose, the position of the matching dark fringe, and the highest order that can appear. Add the width of each slit to see how many bright fringes fit inside the central diffraction envelope, and which orders go missing.
It is built for physics students analysing a lab or homework problem, teachers setting up a laser demonstration, and anyone who wants to measure the wavelength of a laser pointer at home: switch the mode, enter the fringe spacing you measured on the wall, and the calculator works backwards to the wavelength. The chart shows the predicted intensity pattern on the screen.
The fringe-spacing formula Δy = λL/d uses the small-angle approximation, which is excellent when the screen is far away compared with the slit separation. Fringe positions are also computed exactly from sin θ = mλ/d, so you can see when the approximation starts to drift.
How to use the double slit experiment calculator
- 1Choose whether you know the wavelength or measured the fringe spacing.
- 2Enter the wavelength in nm (or the measured spacing in mm).
- 3Enter the slit separation in mm and the screen distance in metres.
- 4Pick a fringe order and, optionally, the width of each slit.
- 5Read the spacing or wavelength, fringe positions and the intensity chart.
Formula and method
Light from two narrow slits a distance d apart reaches each point on the screen by two paths. Where the path difference d·sin θ is a whole number of wavelengths the waves arrive in step and give a bright fringe; where it is an odd number of half-wavelengths they cancel and give a dark fringe. For small angles sin θ ≈ tan θ = y/L, so bright fringes are equally spaced by Δy = λL/d. Rearranging, a measured spacing gives the wavelength λ = Δy·d/L.
Each slit also has a finite width a, which produces a single-slit diffraction envelope with its first zeros at a·sin θ = ±λ. The intensity plotted is I ∝ cos²(πd·sin θ/λ) × sinc²(πa·sin θ/λ). The number of bright fringes inside the central peak is about 2d/a − 1 when d/a is a whole number (those orders are suppressed), otherwise 2⌊d/a⌋ + 1.
- Δy
- Spacing between adjacent bright fringes
- λ
- Wavelength of the light
- L
- Distance from slits to screen
- d
- Slit separation (centre to centre)
- a
- Width of each slit
- m
- Fringe order (0, 1, 2…)
Worked examples
Red laser, 0.25 mm slits, screen at 1.5 m
Δy = 650 × 10⁻⁹ × 1.5 ÷ 0.25 × 10⁻³ = 3.9 mm. The first bright fringe is at 0.149° and the first dark fringe halfway, at 1.95 mm. With 0.05 mm slits d/a = 5, so 9 bright fringes fit in the central diffraction peak (orders ±5 are missing).
Green laser, 0.1 mm slits, screen at 2 m, 3rd order
Δy = 532 × 10⁻⁹ × 2 ÷ 10⁻⁴ = 10.64 mm. The third bright fringe sits at sin θ = 3 × 532 × 10⁻⁹ ÷ 10⁻⁴, θ = 0.914°, y = 2 × tan 0.914° = 31.92 mm — almost exactly 3 × 10.64 mm.
Measuring a laser’s wavelength
Fringes 2.4 mm apart on a wall 1.2 m from slits 0.3 mm apart give λ = 2.4 × 10⁻³ × 0.3 × 10⁻³ ÷ 1.2 = 6.0 × 10⁻⁷ m = 600 nm, orange light.
Frequently asked questions
What is the formula for fringe spacing in the double slit experiment?+
Fringe spacing Δy = λL/d, where λ is the wavelength, L the slit-to-screen distance and d the slit separation. It assumes the screen is far away compared with d, so the angles are small.
How does slit separation affect the fringes?+
Fringe spacing is inversely proportional to the slit separation. Moving the slits closer together spreads the fringes out; doubling d halves the spacing. A longer screen distance or longer wavelength also widens the fringes.
Why are some bright fringes missing?+
Each slit’s own diffraction pattern has dark zeros at a·sin θ = λ, 2λ… If one of these coincides with a bright interference order (when d/a is a whole number), that order is suppressed and appears missing.
How can I measure the wavelength of a laser pointer?+
Shine the laser through a double slit (or a pair of scratches on a blackened slide), measure the distance across several fringes on a far wall, divide to get Δy, and use λ = Δy·d/L.
What did the double slit experiment prove?+
Thomas Young’s experiment, first presented in the early 1800s (1801–1803), showed light behaves as a wave, because only waves produce interference fringes. Later versions with single electrons and atoms showed that matter also has wave properties, a cornerstone of quantum mechanics.