Diffraction Grating & Double-Slit Calculator

Diffraction Guide

What do I need to know about Diffraction Grating Equation?

d sin θ = nλ. Where d = grating spacing (distance between slits), n = order number (1, 2, 3...), λ = wavelength, θ = angle of nth order maximum. Grating spacing: d = 1/(lines per mm) in mm. 600 lines/mm: d = 1/600 mm = 1,667 nm. For sodium yellow light (λ = 589nm), first order: sin θ = 1 × 589/1667 = 0.353. θ = arcsin(0.353) = 20.7°. Maximum order: n_max = d/λ (sin θ cannot exceed 1). At d=1667nm, λ=589nm: n_max = 1667/589 = 2.83 → maximum order = 2.

What should I know about Young's Double Slit?

Fringe spacing: Δy = λD/d. Where λ = wavelength, D = slit-to-screen distance, d = slit separation. Example: red light λ=650nm, d=0.5mm, D=1.5m. Δy = 650×10⁻⁹ × 1.5 / (0.5×10⁻³) = 1.95×10⁻³ m = 1.95mm. Increasing D: wider fringe spacing. Increasing d: narrower fringe spacing. Shorter wavelength: narrower fringes. Young's experiment (1801): the first demonstration of the wave nature of light — producing an interference pattern that cannot be explained by particles alone.

What should I know about Single Slit Diffraction?

Single slit: minima at a sin θ = mλ. Where a = slit width, m = integer (1, 2, 3...). Note: minima (dark bands), not maxima — opposite to the grating equation. Central maximum: between first minima at ±arcsin(λ/a). Angular width of central maximum = 2λ/a (for small angles). Single slit envelopes the double slit pattern — the double slit produces fine fringes within the broad single-slit diffraction envelope. Smaller slit width: wider diffraction pattern. This is why telescopes need a large aperture — a bigger opening reduces diffraction spreading and allows finer detail to be resolved.

What should I know about Diffraction and Resolution?

Rayleigh criterion: two point sources are just resolved when the central maximum of one coincides with the first minimum of the other. Minimum resolvable angle: θ_min = 1.22λ/D. Where D = lens or mirror diameter. Human eye (D=3mm, λ=550nm): θ_min = 1.22×550×10⁻⁹/(3×10⁻³) = 2.24×10⁻⁴ rad = 0.77 arcminutes. This sets the maximum visual acuity of the eye (~1 arcminute in practice due to other factors). Hubble Space Telescope (D=2.4m): θ_min = 2.8×10⁻⁸ rad = 5.8×10⁻³ arcseconds. This explains why large telescope mirrors, like those on the James Webb Space Telescope, are built as big as engineering and cost allow — resolution improves directly with aperture size.