Interference Fringe Spacing Calculator
Young's double-slit experiment produces alternating bright and dark fringes on a screen when coherent light passes through two closely spaced slits. The fringe spacing (distance between adjacent bright fringes) is delta y = lambda L / d, where lambda is the wavelength, L is the screen distance, and d is the slit separation. This calculator also finds the position of the m-th order fringe y_m = m lambda L / d and shows the angular fringe spacing. The formula assumes the far-field (Fraunhofer) approximation: L >> d and L >> lambda. For a typical classroom setup with d = 0.25 mm slits, L = 1 m screen distance, and 550 nm green light, fringe spacing is 2.2 mm.
Fringe spacing formula
delta y = lambda L / d
ym = m lambda L / d (position of m-th fringe)
Angular spacing: theta = lambda / d (radians)
Where lambda is wavelength, L is the slit-to-screen distance, d is the slit separation, and m is the fringe order (0, 1, 2, ...). All distances must be in consistent units.
Double-slit interference conditions
- Bright fringe (constructive): path difference = m lambda, where m is an integer.
- Dark fringe (destructive): path difference = (m + 0.5) lambda.
- The formula assumes L much larger than d: the angles are small so sin(theta) approximately theta.
- Fringe visibility decreases with slit width (single-slit envelope modulates the pattern) and with source coherence length.
- For a typical setup: 550 nm, d = 0.25 mm, L = 1 m gives 2.2 mm fringe spacing, which is easy to observe and measure.
Interference fringes: frequently asked questions
What is the interference fringe spacing formula?
For Young's double-slit experiment, the fringe spacing (distance between adjacent bright fringes) is delta y = lambda L / d, where lambda is the wavelength, L is the distance from the slits to the screen, and d is the slit separation. This formula applies when L >> d (far-field or Fraunhofer regime).
What is Young's double-slit experiment?
Young's double-slit experiment (1801) demonstrates the wave nature of light. Light from a single source passes through two closely spaced slits, and the two beams interfere to create alternating bright and dark fringes on a screen. The bright fringes occur where path length differences equal integer multiples of the wavelength.
What causes the bright and dark fringes?
Bright fringes (constructive interference) occur when path length difference = m lambda (m = 0, 1, 2, ...). Dark fringes (destructive interference) occur when path length difference = (m + 1/2) lambda. The central maximum (m=0) is directly between the two slits. Fringe positions: y_m = m lambda L / d.
How does slit separation affect fringe spacing?
Fringe spacing is inversely proportional to slit separation d. Closer slits (smaller d) produce wider fringes (larger delta y), making them easier to see. Wider slits (larger d) produce narrower fringes that may require a magnifier to observe.
Does this formula work for sources other than visible light?
Yes. The same formula applies to any wave undergoing two-slit interference: microwaves, sound waves, water waves, and even electron beams (demonstrating quantum wave behavior). For electrons, use the de Broglie wavelength lambda = h/(mv) in the formula.
Official sources
- OpenStax University Physics Volume 3, Chapter 3: Interference. openstax.org.
- NIST, Physical Measurement Laboratory. physics.nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.