Diffraction Grating Calculator Formula
Understand the math behind the diffraction grating calculator. Each variable explained with a worked example.
Formulas Used
Diffraction Angle
angle = asin(order * wavelength / slit_spacing) * 180 / piVariables
| Variable | Description | Default |
|---|---|---|
slit_spacing | Slit Spacing (d)(nm) | 1667 |
order | Diffraction Order (m) | 1 |
wavelength | Wavelength(nm) | 550 |
How It Works
Diffraction Grating
A diffraction grating splits light into its component wavelengths at specific angles.
Formula
d * sin(theta) = m * lambda
where d is the slit spacing, m is the diffraction order (1, 2, 3, ...), and lambda is the wavelength. The slit spacing d = 1/(lines per unit length).
Worked Example
First-order diffraction of 550 nm light through a 600 lines/mm grating (d = 1667 nm).
slit_spacing = 1667order = 1wavelength = 550
- 01d * sin(theta) = m * lambda
- 021667 * sin(theta) = 1 * 550
- 03sin(theta) = 550/1667 = 0.3299
- 04theta = 19.26°
Ready to run the numbers?
Open Diffraction Grating Calculator