Interference Fringe Calculator
Compute the fringe spacing in a Young's double-slit or similar two-beam interference experiment. Useful for optics labs, physics coursework, and verifying experimental setups.
About this calculator
When two coherent light waves overlap, they produce an alternating pattern of bright and dark bands called interference fringes. In Young's double-slit experiment, bright fringes appear where path differences are whole-number multiples of the wavelength, and dark fringes where they are half-integer multiples. The fringe spacing (Δy) — the distance between adjacent bright bands on the screen — is given by: Δy = (λ · L) / d, where λ is the wavelength of light, L is the distance from the slits to the screen, and d is the separation between the two slits. All three variables must be in consistent units. A longer wavelength, a more distant screen, or a narrower slit separation all produce wider, easier-to-measure fringes. This formula assumes the small-angle approximation (L >> d), which holds well for typical lab setups where the screen is at least several centimeters away.
How to use
Consider a double-slit experiment using a green laser (λ = 550 nm = 0.00055 mm), slit separation d = 0.25 mm, and a screen distance L = 1500 mm. Apply the formula: Δy = (λ · L) / d = (0.00055 × 1500) / 0.25. Numerator: 0.00055 × 1500 = 0.825 mm·nm... let's keep consistent units — using mm throughout: λ = 5.5 × 10⁻⁴ mm. Δy = (5.5 × 10⁻⁴ × 1500) / 0.25 = 0.825 / 0.25 = 3.3 mm. Bright fringes on the screen are spaced 3.3 mm apart, which is easily measurable with a ruler.
Frequently asked questions
How does slit separation affect fringe spacing in a double-slit experiment?
Fringe spacing and slit separation are inversely proportional: halving the slit separation doubles the fringe spacing, making the bands wider and easier to resolve. Conversely, increasing the slit separation squeezes the fringes closer together until they become too fine to distinguish with the naked eye. This inverse relationship is a direct consequence of the geometry of path differences — a narrower gap between slits means a given angular separation corresponds to a larger physical distance on the screen. In laboratory practice, slit separations between 0.1 mm and 1 mm are typical for producing clearly visible fringes with visible light.
What wavelengths of light produce the widest interference fringes?
Since fringe spacing Δy = λL/d is directly proportional to wavelength, longer wavelengths produce wider, more spread-out fringes. Red light (around 700 nm) creates noticeably wider fringes than violet light (around 400 nm) under identical conditions. This is why red lasers are often preferred in introductory optics labs — the fringe pattern is larger and simpler to measure. In white light experiments, each wavelength produces its own fringe pattern at a slightly different spacing, creating colorful overlapping bands with white at the center and a rainbow-like spread on each side.
Why must light be coherent for interference fringes to be visible?
Interference fringes are only visible when the two interfering beams maintain a constant phase relationship over time — a property called temporal coherence. Ordinary white light sources emit random, uncorrelated wave packets from millions of atoms, so the phase difference between the two slits fluctuates too rapidly for a stable fringe pattern to form. Lasers and filtered monochromatic sources have long coherence lengths, producing sharp, high-contrast fringes. In Young's original 1801 experiment, he used a single pinhole to create a spatially coherent source from sunlight, which is why a sunlit room and a pin were sufficient to demonstrate the wave nature of light.