Grating Equation Solver

Solve diffraction grating geometries, list all propagating orders, Littrow configurations, and calculate angular and linear dispersion.

Grating Setup

Vacuum Wavelength (λ, nm)

Groove Density (lines/mm)

Diffraction Order (m)

Incident Angle (θ_i, degrees)

Illuminated Grating Width (W, mm)

Focal Length (f, mm)

Presets

Result Precision

Diffraction Ray Geometry

Angle Sign Convention: positive = same side as incident beam relative to normal

Diffracted Outputs

Diffracted Angle (θ_d)7.9553°

Groove Spacing (d)0.83333 µm

Littrow Angle18.615°

Angular Dispersion0.069423 deg/nm

Recip. Linear Dispersion4.1266 nm/mm

Theoretical Resolving Power60000

Free Spectral Range532 nm

Grooves Illuminated60000

Propagating Diffraction Orders Summary

For the given wavelength of 532 nm and incident angle of 30°, these are all integer orders $m$ that have physically real solutions (non-evanescent):

Order (m)	Diffracted Angle (θ_d, deg)	Status
0	-30.000°	Propagating
1	7.955°	Active Selected
2	50.969°	Propagating

Grating Diffractions & Dispersion Theory

Standard Grating Equation

n_d \sin\theta_d + n_i \sin\theta_i = m \frac{\lambda_0}{d}

Relates incident and diffracted angles. Here, $d$ is the groove spacing ( $d = 1 / N$ ).

Angular Dispersion

\frac{d\theta_d}{d\lambda} = \frac{m}{n_d d \cos\theta_d}

Measures the angular split per unit wavelength. Large angles and high groove densities increase dispersion.

Reciprocal Linear Dispersion

\frac{d\lambda}{dx} = \frac{n_d d \cos\theta_d}{f \cdot m}

Specifies spectral bandwidth spread per millimeter on a focal plane (e.g. CCD sensor width).

Theoretical Resolving Power

R = \frac{\lambda}{\Delta\lambda} = m N_{\mathrm{grooves}} = m \cdot N \cdot W

Specifies the maximum limit to resolve adjacent spectral peaks, proportional to total grooves illuminated.