Wavelength from double-slit fringes calculator

Enter the spacing between adjacent bright fringes, the centre-to-centre separation of the slits, and the perpendicular distance from the slits to the screen, all in metres. The calculator applies the standard small-angle relation and reports the result in metres, nanometres, and micrometres. It is designed for laboratory checks, classroom experiments, and quick analysis of a clean, regularly spaced fringe pattern.

Measure the three distances consistently

The calculation needs three positive lengths: fringe spacing, slit separation, and screen distance. Fringe spacing is the centre-to-centre distance between two adjacent bright bands, not the width of one bright patch at an arbitrary threshold. For a more reliable measurement, measure across several fringe intervals and divide by the number of intervals. Slit separation means the distance between the centres of the two openings, while screen distance is measured perpendicular to the slit plane. Enter every value in metres. For example, convert 0.25 millimetres to 0.00025 metres before submitting it. Keeping one unit system prevents scale errors that can shift the answer by factors of one thousand or more. The pattern should be formed by essentially monochromatic, coherent light, and the slits and screen should be aligned well enough that adjacent central fringes have nearly uniform spacing. If the spacing changes sharply across the region you measured, record a central interval or use a model beyond the paraxial approximation.

Understand the equation and approximation

For a double slit, bright fringes occur when the path difference is an integer number of wavelengths. Near the centre of a distant screen, the small-angle approximation makes the spacing between adjacent bright fringes equal to wavelength multiplied by screen distance and divided by slit separation. Rearranging gives wavelength = fringe spacing × slit separation ÷ screen distance. The calculator evaluates that expression deterministically and returns the wavelength in metres, nanometres, and micrometres. The relation assumes the screen distance is large compared with both the slit separation and the measured displacement from the central axis, so that sine, tangent, and the angle in radians are approximately equal. It also assumes adjacent fringes are being compared. If you measure from the central maximum to a fringe several orders away, divide that total displacement by the number of fringe intervals first. The result is an experimental estimate: it inherits uncertainty from every ruler reading, slit specification, alignment error, and decision about each fringe centre.

Interpret and check the wavelength result

Use the nanometre output for a quick comparison with visible light, but retain the metre result for further equations and uncertainty calculations. A plausible-looking value does not by itself prove the measurements are correct. Repeat the fringe-spacing measurement at several locations near the centre, average the values, and confirm that increasing the screen distance produces proportionally wider fringes. Likewise, a larger slit separation should produce narrower fringes when wavelength and distance remain fixed. These proportional checks are excellent at exposing a mistaken unit conversion or the use of slit width instead of slit separation. If the calculated wavelength differs from the source specification, inspect alignment, ambient light, the sharpness of the fringe centres, and whether the screen is truly perpendicular to the optical axis. The calculator does not fit an image, identify colors, or propagate measurement uncertainty automatically. It provides the ideal paraxial wavelength estimate for the three distances supplied. Browser calculation is free, while an automated API request uses the published base price of $0.002.