Single-slit diffraction minima angle

The angular position of those minima follows the sine relation slit width times sine of theta equals order times wavelength: a sin θ equals m λ, so θ equals arcsin of m λ over a. This capability takes the integer order, the wavelength, and the slit width in matching length units and returns that angle in degrees and radians. Non-positive aperture or wavelength, zero or fractional order, and orders whose sine argument exceeds one are rejected with invalid_input rather than a silent empty success. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.

The sine condition for single-slit diffraction minima

This endpoint evaluates only that closed-form angular condition. It does not integrate the full single-slit intensity envelope sin beta over beta squared, does not treat circular apertures or Airy disks, and does not compute double-slit fringe spacing or grating resolving power. The pipeline is pure floating-point arithmetic with no network calls, no random seeds, and no wall-clock timestamps, so identical order, wavelength, and slit width always produce identical JSON.

Request fields, response shape, and validation failures

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. POST a JSON object with three required fields: order, the nonzero integer m of the minimum; wavelength, lambda in the same length unit as the aperture; and slit_width, the aperture width a. Aliases such as m, n, or min_order for the order, lambda, wave_length, or wl for the wavelength, and a, width, slit, or slitWidth for the aperture are accepted so scripts written in 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 order, wavelength, and slit_width, returns angle_degrees and angle_radians for display and further trigonometry, includes sin_theta equal to m lambda over a for intermediate checks, reports max_order as the largest positive integer order that still has a real angle for the given a over lambda, and adds formula and unit strings. Classic checks include order one with a equals one times ten to the minus four metres and lambda equals five times ten to the minus seven metres, which yields a small angle near zero point two nine degrees; the same geometry with order zero as the explicit central-maximum error path; and a zero slit width as the mandatory invalid_input path for division by zero. Successful API calls use prepaid KIT balance at the published base of $0.002 per item.

Where a minima-angle calculator earns its keep

Because this capability is a pure parse engine, every successful call costs the published base of $0.002 with no model tokens and no outbound network, and failed validation does not consume balance.