How this instrument works
A human hair is far too thin for calipers or a ruler, but light does not care how you'd measure it by hand. Babinet's principle says a thin opaque obstacle and a slit of the identical width throw the same diffraction pattern everywhere except along the beam's original direction — so a strand of hair blocking a laser beam spreads light into exactly the pattern a single narrow slit of the same width would produce. Measure that pattern and you have measured the hair.
The dark fringes on the screen arise because light diffracting past the two edges of the hair interferes destructively at specific angles. For a single-slit obstacle the first minimum sits at sin θ ≈ λ ⁄ d; the small-angle approximation replaces sin θ with x ⁄ L, the ratio of fringe offset to screen distance, and rearranging gives d ≈ λL ⁄ x. The hair's width falls out of the relationship between how far light bends and how narrow the obstruction was, with no contact and no micrometer screw.
The formula only holds while the small-angle approximation holds, which in practice means keeping the screen many hundred hair-widths away — a metre or two is comfortable for a strand around 50 to 100 micrometres across. Push the screen too close, or shine light whose wavelength approaches the hair's own diameter, and true sin θ departs enough from x ⁄ L that the reading drifts. Astronomers hit the same ceiling estimating asteroid or star diameters from occultation diffraction, and the fix is identical: more distance, or a full-angle formula in place of the small-angle shortcut.
- Enter the Laser wavelength — 650 nm is typical for a common red laser pointer; a green pointer runs nearer 532 nm, so use the figure printed on your own unit if you have it.
- Enter the Screen distance, measured straight back from the hair to the screen where the pattern lands; 1 to 3 metres works well on a tabletop or across a room.
- Tape the hair across the beam, dim the room, and measure the Distance to first dark fringe from the bright centre out to the first dark band, not the first bright fringe beside it.
- Read the Hair diameter in micrometres; switch its unit to millimetres if you'd rather compare the figure against a printed spec sheet.
Worked example — measuring a strand with a 650 nm pointer
Shine a 650 nm red laser pointer through a single strand of hair taped across the beam, and let the diffracted light fall on a screen 2 m away — a comfortable tabletop distance. Dim the room, find the bright central band, and measure out to the first dark fringe: 15 mm from centre. Feeding those three numbers into d ≈ λL ⁄ x gives d = (6.5 × 10⁻⁷ m × 2 m) ⁄ 0.015 m = 8.66667 × 10⁻⁵ m, which is 86.67 µm — squarely inside the 50 to 100 µm range typical of human hair.
That range check is not incidental: optical and electron microscopy on comparable strands routinely land in the same band, which is exactly why this classroom demonstration is trusted as a teaching tool rather than dismissed as a curiosity. Move the screen to 1 m instead of 2 m while the fringe stays at the same 15 mm, and the arithmetic returns 43.33 µm instead — a reminder that the screen distance carries as much weight in the result as the fringe measurement itself.
Questions
Why does a thin hair produce a diffraction pattern instead of just a shadow?
Light doesn't travel in a perfectly straight line past a sharp edge — it bends slightly, a wave effect called diffraction. Babinet's principle is the shortcut used here: a thin opaque strand and a narrow slit of the same width produce identical diffraction patterns away from the direct beam, because the diffracted field depends only on what light is blocked, not on which side of the obstruction the missing light would have gone. A hair a fraction of a millimetre wide sits at exactly the right scale to show this clearly with visible light.
What counts as the first dark fringe?
It's the first point going outward from the bright central band where the light nearly vanishes, just before the next, dimmer bright band appears. Measure from the centre of the bright spot straight out to that first dark gap, not to the next bright fringe beside it — picking the wrong band scales the implied hair diameter up or down by roughly the ratio between the two positions.
Does the laser's wavelength change the answer much?
Yes, proportionally — d scales directly with λ, so an error in wavelength carries straight through to the diameter. A common red pointer sits near 650 nm, but cheap units vary by tens of nanometres, and a green pointer runs closer to 532 nm. If the pointer's datasheet lists an exact wavelength, use that instead of a nominal 650 nm; even a 20 nm difference shifts the computed diameter by about 3 percent.
Why does moving the screen closer change the computed diameter?
Because fringe spacing is itself proportional to the screen distance L — halve L and the same physical hair produces fringes at half the offset from the centre. If you measure a 15 mm fringe at half the intended distance without noticing the screen moved, the formula reads a hair half as wide as it actually is. Screen distance and fringe position must come from the same trial, never mixed from two different setups.
How accurate is this compared to a micrometer or microscope?
In a careful classroom setup, diffraction measurements typically land within a few percent of micrometer or microscope readings on the same strand — easily good enough to place a hair correctly within its usual 50 to 100 micrometre range. The main error sources are the fringe measurement itself, since a ruler held against a screen carries maybe half a millimetre of reading uncertainty, and any mismatch between the assumed and actual laser wavelength.
Can this same setup measure other thin objects, like a wire or a fibre?
Yes — any object narrow enough to sit within a few hundred micrometres, and thin compared with the screen distance, diffracts by the same physics, whether it is a hair, a fine wire, or a synthetic fibre. Neither the formula nor Babinet's principle cares about the material; both only see an opaque strip of a certain width blocking part of a coherent beam.