Hair diffraction calculator
A 500 nm laser, a screen 2 m away and dark fringes 10 mm apart give a hair diameter of 0.0001 m, or 100 micrometres. It turns the classic laser-pointer optics lab into a measurement you can check at once. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Wavelength
- 0.0000005
- Screen distance
- 2
- Fringe spacing
- 0.01
- Hair diameter
- 0.0001
A human hair is a thin opaque obstacle. When a collimated laser beam strikes it, Babinet's principle says the far-field diffraction envelope matches that of a slit of the same width, so a distant screen shows a bright central band flanked by regularly spaced dark minima. Under the small-angle approximation used in teaching labs, the spacing between adjacent minima is wavelength times screen distance divided by hair diameter: fringe spacing equals lambda L over d. This hair diffraction calculator inverts that identity. Given the laser wavelength, the distance from the hair to the screen, and the measured fringe spacing, it returns the hair diameter d equals lambda L over delta y. A zero or negative fringe spacing is rejected because the formula would divide by zero.
How a laser fringe pattern becomes a hair diameter
A thin hair is an opaque obstacle, not an opening, but Babinet's complementarity principle says the far-field diffraction envelope of an obstacle matches that of an aperture of the same outline. In a teaching laboratory a collimated laser therefore produces a bright central band on a distant screen, flanked by dark minima whose spacing encodes the hair diameter.
Under the small-angle approximation used in every introductory write-up, the path difference across the hair grows linearly with the screen coordinate, so the distance between adjacent minima is wavelength times screen distance divided by diameter: delta y equals lambda L over d. Rearrangement is a single division: the hair diameter d equals lambda times L divided by the measured fringe spacing.
Wavelength, screen distance, and fringe spacing must share one length unit so the ratio is a length; metres for all three is the SI choice, but millimetres work equally well if you stay consistent end to end. A zero or negative fringe spacing is not a physical pattern period and is rejected rather than producing a division by zero or a negative diameter. Wavelength and screen distance must also be strictly positive: a non-positive laser wavelength or a non-positive bench length is not a laboratory geometry.
Where a hair-diffraction calculator earns its keep
Secondary-school and college optics courses assign the classic experiment of measuring a hair with a laser pointer or a helium-neon source: students record fringe spacing on a wall or a metre stick, then invert delta y equals lambda L over d for the diameter. A single trusted oracle that returns metres from the three laboratory numbers speeds grading, demo setup, and write-up checks without a full wave-optics solver.
Teaching labs that compare several hairs, nylon fibres, or drawn wires need the same Babinet inversion used in the experiment handout, so predicted diameters can be checked before a micrometer reading is treated as ground truth. Quality and materials notebooks that log fibre diameter from an optical bench, rather than from contact gauges, can call the same closed form from a script. Failed validation does not consume balance.
Keep requests in matching length units end to end, convert nanometre wavelengths and millimetre fringe spacings to one shared unit before calling, and pin the diameter value in tests so homework checks, LMS plugins, and edge workers stay reproducible. Circular apertures, double-slit fringe spacing, and ruled diffraction gratings remain separate search intents; treat this page as the hair-diameter inversion rather than a general interferometer.
What you can do with it
Hair-and-laser teaching labs
Invert measured fringe spacing, laser wavelength, and screen distance to a hair diameter so lab groups share one ground truth before they write up Babinet's principle.
Homework and auto-grading
Compute d = λL/Δy from textbook SI lengths so teachers and LMS plugins mark the same millimetre-scale fibre without a wave-optics library.
Fibre and wire optical checks
Estimate the diameter of a thin fibre or drawn wire from a laser fringe pattern when a contact micrometer is inconvenient or would deform the sample.
FAQ
What formula does this hair diffraction calculator use?
The small-angle Babinet / single-slit inversion d = λL/Δy. Wavelength, screen distance, and fringe spacing must use the same length unit; the returned hair diameter is in that unit.
What happens if fringe spacing is zero or negative?
Fringe spacing that is not positive would make the formula divide by zero, so it is rejected with a clear validation error and is not charged.
Do wavelength, screen distance, and fringe spacing have to use the same unit?
Yes. The ratio λL/Δy is a length only when all three inputs share one unit. Enter metres for all three, or millimetres for all three; mixed units produce a wrong diameter.
Why does a hair diffract like a slit?
Babinet's principle: the far-field diffraction envelope of an opaque obstacle matches that of an aperture of the same outline. A hair of diameter d is treated as a slit of width d, then inverted for d from the measured fringe spacing.
What does the hair diffraction calculator cost?
The browser tool is free and runs locally.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/phys/hair-diffraction \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"wavelength":5e-7,"screen_distance":2,"fringe_spacing":0.01}'const res = await fetch("https://api.kit.forhosting.com/phys/hair-diffraction", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"wavelength": 5e-7,
"screen_distance": 2,
"fringe_spacing": 0.01
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/hair-diffraction",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"wavelength": 5e-7,
"screen_distance": 2,
"fringe_spacing": 0.01
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/hair-diffraction", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"wavelength":5e-7,"screen_distance":2,"fringe_spacing":0.01}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"wavelength":5e-7,"screen_distance":2,"fringe_spacing":0.01}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/hair-diffraction", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"wavelength": 5e-7,
"screen_distance": 2,
"fringe_spacing": 0.01
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.hair_diffraction",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How a laser fringe pattern becomes a hair diameter
The implementation is pure floating-point arithmetic with no network, no random seeds, and no wall-clock timestamps, so the same three numbers always yield the same JSON object. This page does not fit Airy disks, ruled gratings, or Young's two-slit fringe formula as a different experiment; those remain separate search intents served by other calculators.
Input contract, response shape, and error behaviour
Wavelength must be strictly positive. Screen distance must be strictly positive. Fringe spacing must be strictly greater than zero: both a zero period and a negative period fail with a message that fringe spacing is not positive, matching the product promise that a one-over-delta-y singularity never masquerades as a finite diameter. POST a JSON body with three required finite numbers: wavelength, the laser λ in any length unit; screen_distance, the hair-to-screen length L in that same unit; and fringe_spacing, the measured period Δy between adjacent dark or bright fringes, again in that unit. Each field may arrive as a JSON number or as a numeric string. Aliases lambda, laser_wavelength, wl and wave_length for the wavelength, L, distance, D and screenDistance for the bench length, and delta_y, spacing, dy, fringeSpacing and pattern_width for the fringe period are accepted so notebooks written against textbook notation do not need a rename layer. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. On success the body echoes the cleaned wavelength, screen_distance, and fringe_spacing, reports hair_diameter in the same length unit, and includes the formula string d equals lambda L over delta y for display next to a lab sketch. Pair the response with your own unit conversion if you next need micrometres for a lab notebook; this endpoint does not invent a unit system and does not emit plots or intensity envelopes. Successful API calls are billed at the published $0.002 per item; validation failures do not consume prepaid balance.
Where a hair-diffraction calculator earns its keep
Because this capability is a pure parse engine, every successful call costs the published $0.002 base price with no model tokens and no outbound network.