Double-Slit Interference Calculator (Young's Experiment)
Fringe spacing, the angle of the first bright fringe and the brightness anywhere on the screen, with the whole interference pattern drawn.
Results
The dashed line marks the value you entered.
What this tool does
Thomas Young's two-slit experiment, first presented in 1803, was the evidence that light is a wave: two slits make a row of bright and dark stripes λL/d apart. The width of each slit lays a second, wider pattern over it — the single-slit envelope, dashed on the chart — so the stripes fade out and some vanish exactly where the envelope goes dark. With a green laser pointer, slits a quarter of a millimetre apart and a wall two metres away, the stripes are about 4 mm apart, easy to see by eye. The spacing uses the small-angle approximation; the brightness uses the exact angle.
Formula
Δy = λ L ÷ d · I(θ) = I₀ cos²(π d sinθ ÷ λ) × (sin β ÷ β)², β = π a sinθ ÷ λ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
wl | Wavelength | nm |
d | Distance between the slits d | mm |
a | Width of each slit a | mm |
l | Distance to the screen L | m |
y | Position on the screen (from the centre) | mm |
DY | Fringe spacing | mm |
TH | Angle of the first bright fringe | ° |
CW | Width of the central diffraction band | mm |
NF | Bright fringes inside the central band | — |
IY | Brightness there (centre = 100 %) | % |
Worked example
- Wavelength532 nm
- Distance between the slits d0.25 mm
- Width of each slit a0.05 mm
- Distance to the screen L2 m
- Position on the screen (from the centre)2 mm
- Fringe spacing4.256 mm
- Angle of the first bright fringe0.1219 °
- Width of the central diffraction band42.56 mm
- Bright fringes inside the central band9
- Brightness there (centre = 100 %)0.86 %
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.