How this calculator works
By Babinet principle, a narrow opaque hair gives the same far-field minima as a slit of equal width. Measure x from the central bright maximum to the chosen dark minimum, rather than across the full central band. The tool uses sin(theta) = x/sqrt(D^2+x^2), avoiding the small-angle approximation. A far screen, nearly uniform hair width and near-normal illumination are assumed.
Formula
w sin(theta) = m lambda; tan(theta) = x/D. Thus w = m lambda sqrt(D^2+x^2)/x.
Worked example
For a 650 nm laser, D = 2 m and first minimum x = 0.02 m, width is 65.0032499 micrometres. Using the second minimum at the corresponding angle should recover the same width.
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Frequently asked questions
Which dark fringe is order one?
The first dark minimum on either side of the central bright band.
Can I measure the whole central bright band?
Divide its edge-to-edge width by two to obtain the first-minimum distance from the centre.
Why repeat the measurement?
Measuring several orders and both sides helps reveal alignment and fringe-location error.