Hair Diffraction Calculator

A human hair can be measured without touching it by observing how coherent laser light diffracts around the strand. Although the hair is an opaque obstacle rather than an open slit, Babinet's principle says its far-field diffraction pattern has the same fringe spacing as a slit of equal width. A bright-and-dark pattern spreads across a distant screen, and that spacing contains enough information to estimate the hair's diameter. For small angles, adjacent-fringe spacing equals laser wavelength multiplied by hair-to-screen distance and divided by hair diameter. Rearranging gives diameter equal to wavelength times distance divided by fringe spacing. This calculator accepts wavelength in nanometers, screen distance in meters, and fringe spacing in millimeters. The unit conversions simplify neatly so the numerical result is returned in micrometers: wavelength in nanometers times distance in meters divided by spacing in millimeters. A typical visible laser has a wavelength between about 400 and 700 nanometers, while human hair commonly ranges from roughly 17 to 180 micrometers in diameter. For example, a 650-nanometer red laser, a two-meter screen distance, and 20-millimeter fringe spacing indicate a 65-micrometer hair. Thicker hairs make fringes closer together, while a longer screen distance or wavelength spreads the pattern farther apart. Measurement technique strongly affects accuracy. Secure one hair vertically across the beam, keep the screen perpendicular to the beam, and measure the distance from the hair to the screen. Rather than measuring a single small interval, measure across several adjacent fringe spacings and divide by the number of intervals. This reduces ruler-reading error. Work in a dim room so the pattern is clear, and do not confuse the broad central region with one ordinary adjacent-fringe interval. The equation uses the small-angle approximation, which works well when screen distance is much larger than fringe spacing and hair diameter. For unusually wide patterns, an exact angular treatment may be preferable. Hair is not always circular or uniform, so rotating the strand can produce a different apparent diameter. Most importantly, never look into a laser beam or aim it toward another person, reflective surface, vehicle, or aircraft. Use a low-power classroom laser, control reflections, and follow its safety instructions.