Hair Diffraction Calculator

Tape a hair strand across the front of a laser pointer (perpendicular to the beam), aim it at a white wall/screen 2–4 meters away in a dark room, measure the hair-to-screen distance (L) and the distance from the central bright spot to the first dark fringe (y, order m=1). Enter the laser wavelength (e.g. 650 nm for a red laser), L, and y into this calculator to get the hair diameter a = m·λ·L/y.

Because of Babinet’s principle: the diffraction pattern of a thin obstacle (like a hair) is identical to that of a slit of equal width. So the single-slit formula a·sin θ = m·λ applies directly, with a being the hair diameter.

The base formula is a·sin θ = m·λ, where a is the hair diameter, θ is the angle of the m-th dark minimum, m is the diffraction order (1, 2, 3, ...), and λ is the laser wavelength. With the small-angle approximation sin θ ≈ tan θ = y/L, the formula becomes a = m·λ·L/y. The calculator also shows the exact correction without approximation for transparency.

The small-angle approximation replaces sin θ with tan θ = y/L, which is valid when the angle is small (y much smaller than L). At a y/L ratio of 0.1 the error is only ~0.5%; in a typical experiment (y/L ≈ 0.01) it is below 0.01% — far smaller than your ruler measurement error. The calculator shows this validity status automatically.

A red laser pointer (around 650 nm) or green (around 532 nm) — what matters is that the wavelength is known and the light is monochromatic (single color). Do not use a flashlight or ordinary lamp because the light is not coherent, so no diffraction pattern forms.

Do not measure a single fringe: measure the total distance from the order −N dark fringe to the order +N dark fringe (pattern width W), then divide by 2N to get the average y. This significantly reduces ruler reading error. The calculator provides a pattern-width input mode for this.

Human hair is typically 50–100 micrometers in diameter (0.05–0.10 mm). If your result is far outside this range (e.g. 10 µm or 500 µm), double-check your input units — the most common mistake is mixing up cm and mm for the fringe distance.

Usually from measuring y (the fringe distance, only a few cm, so ruler error is relatively large) and L (the hair-to-screen distance). The laser wavelength is generally known accurately enough (±1 nm is fine). The calculator computes a worst-case error estimate from the uncertainty of each quantity you enter.

The first-order minimum (m=1) is the brightest and easiest to identify — it is the first dark line on either side of the central bright spot. Higher orders (m=2, 3) are dimmer and farther away, so their angular error grows. The formula still holds for any order as long as the minimum is clearly measurable.

Never stare directly into the laser beam or its reflection — point the laser away from eyes and other people, and work in a dark room so the pattern is clearly visible without needing a high-power laser. A standard laser pointer under 5 mW is enough for this experiment.