How to use it
- Choose what to find: the fringe spacing, or the wavelength from a measured spacing.
- Enter the wavelength in nanometres (or the measured spacing in millimetres).
- Enter the slit separation d in millimetres (centre to centre) and the screen distance L in metres.
- Choose the fringe order m: 0 is the central bright fringe, 1 the first on either side, and so on.
Formulas
- Bright fringes: d × sin θ = m × λ
- Dark fringes: d × sin θ = (m + ½) × λ
- Position on the screen: y = L × tan θ
- Small-angle approximation: y ≈ m × λ × L ÷ d, so neighbouring bright fringes are Δy = λ × L ÷ d apart
- Wavelength from a measurement: λ = Δy × d ÷ L
The exact positions use sin and tan, so they stay right at large angles where the simple formula fails.
Worked example
A green laser (532 nm) shines on two slits 0.25 mm apart; the screen is 1 m away.
- Δy = 532 × 10⁻⁹ × 1 ÷ 0.25 × 10⁻³ = 2.128 mm
- First bright fringe: sin θ = 0.002128, θ = 0.1219°, y = 2.128 mm from the centre
- The dark fringe after it is at 3.192 mm
- Highest possible order: 469
Tips
- Measure across many fringes. Ten spacings measured at once are ten times more precise than one.
- Slit separation is centre to centre, not the width of each slit. The width sets the envelope that dims the outer fringes.
- Shorter wavelength, tighter fringes: blue light gives narrower spacing than red with the same slits.