Single-slit diffraction calculator
Green light at 500 nm through a 0.1 mm slit puts its first dark fringe at 0.286480091241°. Enter the slit width, wavelength and order to locate any minimum and see the highest order the slit can show. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Slit width
- 0.0001
- Wavelength
- 0.0000005
- Order
- 1
- Angle degrees
- 0.2864800912 degrees
- Angle radians
- 0.0050000208
- Sin theta
- 0.005
- Max order
- 199
A single narrow slit illuminated by monochromatic light produces a diffraction pattern of a bright central maximum and a series of dark minima on either side. The standard condition for those minima is slit width times sine of the angle equals an integer order times the wavelength, written a sine theta equals m lambda, with m equal to plus or minus one, two, three, and so on. This calculator takes the slit width, the wavelength in the same length unit, and the integer order, then returns the angular position of that minimum in degrees and radians. Zero or non-positive slit width is rejected because the formula would divide by zero. Orders whose absolute sine argument exceeds one are also rejected because those minima do not appear for the given aperture.
How single-slit diffraction minima are located
Begin with a long narrow rectangular aperture of width a illuminated by a plane wave of wavelength lambda. In the far field, or equivalently in the focal plane of a collecting lens, every direction theta measured from the optical axis receives a coherent sum of secondary wavelets across the slit. The directions of destructive interference for the single-slit envelope satisfy a times sine of theta equals m times lambda, where m is a nonzero integer.
Solving for the unknown angle yields theta equals the arcsine of m lambda over a. Positive m places a minimum on one side of the central peak; negative m places the symmetric partner on the other side. The central bright fringe is not a minimum: m equals zero is excluded from the dark-fringe formula.
Because sine cannot exceed one in magnitude, only orders with absolute value less than or equal to a over lambda are observable; higher orders simply do not appear. Wider slits or shorter wavelengths pack the minima closer to the axis, while a narrower slit or longer wavelength spreads the pattern. This capability evaluates only that closed-form angular condition for minima.
It does not integrate the full intensity envelope, does not treat circular apertures or Airy disks, and does not compute double-slit fringe spacing or spectral resolving power. Both lengths must be finite and strictly positive and must share one length unit; the order must be a nonzero integer.
Where single-slit diffraction calculators show up in real work
Secondary-school and college optics courses assign endless far-field pattern problems that ask for the angle or screen position of the first dark fringe, the second minimum, or the half-width of the central peak derived from m equals one; a single trusted oracle that returns degrees and radians speeds grading and demo setup. Teaching labs that measure laser wavelength from measured fringe angles need a forward calculator that matches the same a sine theta equals m lambda relation used in the experiment write-up.
Instrument design sketches for monochromators and entrance slits estimate how wide a diffraction envelope will be at a given wavelength before more detailed wave-optics models are run. If you later need double-slit fringe spacing, circular-aperture Airy radii, lens magnification from object and image distances, or Snell's law refraction angles, treat those as separate search intents and landings rather than overloading this single-slit diffraction minimum page.
What you can do with it
Homework and lab answer keys
Compute the angular position of the m-th single-slit minimum from textbook slit width and wavelength so teachers and auto-graders share one ground truth.
Laser wavelength teaching labs
Forward-check measured dark-fringe angles against a·sin(θ)=m·λ for a known slit before solving for λ from the inverse experiment.
Slit and monochromator envelope estimates
Estimate how far the first few diffraction minima sit from the optical axis when sizing entrance slits at a design wavelength.
FAQ
What formula does this single-slit diffraction calculator use?
The standard condition for single-slit minima: a·sin(θ) = m·λ, so θ = arcsin(m·λ/a). Slit width and wavelength must use the same length unit; m is a nonzero integer order.
What happens if the slit width is zero?
Zero (or non-positive) slit width would make the formula divide by zero, so it is rejected with a clear validation error and is not charged.
What if |m·λ/a| is greater than one?
There is no real angle for that order with the given aperture and wavelength.
What does it cost?
The browser tool is free and runs locally.
How many dark fringes can a single slit produce?
Only orders up to the slit width divided by the wavelength exist. A 0.1 mm slit lit with 500 nm light reaches order 199 on each side of the bright centre.
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/optics/single-slit-diffraction \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"slit_width":0.0001,"wavelength":5e-7,"order":1}'const res = await fetch("https://api.kit.forhosting.com/optics/single-slit-diffraction", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"slit_width": 0.0001,
"wavelength": 5e-7,
"order": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/optics/single-slit-diffraction",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"slit_width": 0.0001,
"wavelength": 5e-7,
"order": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/single-slit-diffraction", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"slit_width":0.0001,"wavelength":5e-7,"order":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"slit_width":0.0001,"wavelength":5e-7,"order":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/single-slit-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
{
"slit_width": 0.0001,
"wavelength": 5e-7,
"order": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "optics.single_slit_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 single-slit diffraction minima are located
The pipeline is pure floating-point arithmetic with no network, no random seeds, and no wall-clock timestamps, so identical a, lambda, and m always produce identical JSON.
What you send and what you get back
All three fields are required. Zero slit width is called out explicitly because dividing by a would be undefined. Wire the free browser form for homework and lab demos, then call the identical contract from scripts when you need bulk answer keys. Send three numbers under the fields slit_width, wavelength, and order. slit_width is the aperture width a, wavelength is lambda in the same unit as a, and order is the integer m of the minimum you want. Aliases such as a, width, or slit for the aperture, lambda, wave_length, or wl for the wavelength, and m, n, or min_order for the order are accepted so scripts written against common textbook notation do not need a rename layer. Missing fields, non-numeric strings, NaN, Infinity, non-positive slit width, non-positive wavelength, zero or non-integer order, and orders with absolute m lambda over a greater than one fail with invalid_input and are not charged. On success the response echoes cleaned slit_width, wavelength, and order, returns angle_degrees and angle_radians, includes sin_theta equal to m lambda over a for intermediate checks, reports max_order as the largest positive integer order with a real angle for the given a over lambda, and adds formula and unit strings for display. Classic checks include a equals one times ten to the minus four metres, lambda equals five times ten to the minus seven metres, m equals one giving a small angle near zero point two nine degrees; the same geometry with m equals zero as the explicit error path for the central maximum; and a zero slit width as the mandatory invalid_input path. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where single-slit diffraction calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Technical questions
Why is order m = 0 rejected?
m = 0 corresponds to the central maximum of the single-slit pattern, not a dark minimum. Only m = ±1, ±2, … label minima under the standard condition.