Diffraction grating calculator

When the requested order is physically unreachable—because the absolute value of m lambda over d exceeds one—the API returns a clear invalid_input error naming the maximum order instead of inventing an imaginary angle.

How to call the API and what comes back

Spacing and wavelength must be finite positive numbers within the published absolute limits; order must be an integer that may be negative for the opposite side of the zero-order beam. Send a JSON body with three required fields: spacing (aliases d, grating_spacing, slit_spacing, line_spacing), wavelength (aliases lambda, wl, wave_length), and order (aliases m, diffraction_order, n). Absolute values stay within the published ceilings so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded spacing, d, wavelength, lambda, order, and m; sets sin_theta to the clamped ratio m lambda over d; angle_rad and theta_rad to arcsin of that ratio in radians; angle_deg and theta_deg to the same angle in degrees; max_order_abs to the largest absolute integer order still allowed; side to zero_order, positive, or negative; formula to the string d · sin(θ) = m · λ; message to a short English summary; and steps to an ordered array of substitution lines. Failed validation—missing fields, non-finite or non-positive lengths, non-integer order, values outside absolute limits, or an unreachable order where absolute m lambda over d exceeds one—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.

Practical tips, limits, and related searches

Convert ruled density into spacing before you call: if a grating is specified as N lines per millimetre, then d equals one over N in millimetres, or convert consistently into metres for SI reports. Prefer nanometres for visible laser lines only when spacing is also expressed in nanometres; otherwise convert both to metres so lab partners share one convention. Near-grazing orders where absolute sine is extremely close to one are accepted and reported near plus or minus ninety degrees after fixed rounding, matching the physical limit rather than rejecting float noise. Prefer this capability when you already have d, λ, and m and only need θ or a reachability check. Check max_order_abs first when scanning many orders in a script, and only request m values from negative max through positive max inclusive of zero. When teaching, pair examples: a five-hundred-nanometre line on a six-hundred-lines-per-millimetre grating with m equals one yields a clean mid-range angle; the same grating with a deliberately large m demonstrates the unreachable-order invalid_input path; and m equals zero always returns zero degrees. This landing targets people searching for a diffraction grating calculator, grating angle from spacing and wavelength, or order cutoff online; it is not a full spectrometer ray-tracer, not a multi-wavelength blaze-efficiency model, and not a tool that converts lines per millimetre for you without you computing d. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately request oversize orders. Round-trip checks are easy: recompute m times lambda over d by hand, confirm it equals published sin_theta within twelve-decimal rounding, and confirm that arcsin of that value matches angle_rad.