What this calculator does
Diffraction Grating works out angle at which a given order of light diffracts off a grating of known line spacing. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulam·λ = d·(sinθi + sinθm)
The inputs explained
| Field | What to enter |
|---|---|
| Diffraction order (m) | A number. Starts at 2. |
| Wavelength (λ) (nm) | A number, measured in nm. Starts at 560. |
| Grating line density (lines/mm) | A number, measured in lines/mm. Starts at 1000. |
| Incident angle (θi) (°) | A number, measured in °. Starts at 30. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with diffraction order (m)
Every other input is held at the calculator’s starting values while diffraction order (m) varies. Select any row to load that scenario into the calculator.
How the answer changes with diffraction order (m)
| Diffraction order (m) | Diffraction angle (θm) | Grating spacing (d) | Grating line density used |
|---|---|---|---|
| 1 | 3.44 ° | 1000.0 nm | 1,000 lines/mm |
| 1.5 | 19.88 ° | 1000.0 nm | 1,000 lines/mm |
| 2 | 38.32 ° | 1000.0 nm | 1,000 lines/mm |
| 3 | No solution, this order does not exist at this angle and spacing | 1000.0 nm | 1.180 |
| 4 | No solution, this order does not exist at this angle and spacing | 1000.0 nm | 1.740 |
| 6 | No solution, this order does not exist at this angle and spacing | 1000.0 nm | 2.860 |