Diffraction Grating Calculator

The grating equation is d·sin(θ) = mλ, where d is the grating spacing (distance between slits), θ is the diffraction angle, m is the order (integer), and λ is the wavelength. It predicts the angles at which constructive interference occurs.

Since sin(θ) cannot exceed 1, the maximum order is m_max = floor(d/λ). Higher orders require larger grating spacing relative to the wavelength. For visible light (~550 nm) with 600 lines/mm (d ≈ 1.67 μm), the max order is about 3.

Angular dispersion (dθ/dλ) describes how much the diffraction angle changes per unit wavelength. It equals m/(d·cos θ). Higher orders and finer gratings give greater dispersion, allowing better separation of closely spaced wavelengths.