PhysicsCalcs
Optics

Diffraction Grating Calculator

Calculate diffraction angles, wavelengths, grating spacing, resolving power, angular dispersion, and screen positions using d·sinθ = mλ.

Interactive calculator

Diffraction Grating Calculator

Calculate diffraction angles, wavelengths, grating spacing, resolving power, angular dispersion, and screen positions using the grating equation d·sinθ = mλ.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose a mode: find angle, wavelength, spacing, lines/mm, resolving power, dispersion, or screen position.
  • Enter known values. Use presets for common laser/grating combinations.
  • Click Calculate to see results with step-by-step explanation.

Table of Contents

Key Takeaways

  • The grating equation d·sinθ = mλ governs diffraction from periodic structures.
  • Higher orders (m = 2, 3, …) produce wider angles but may exceed sinθ = 1 and become unobservable.
  • Resolving power R = mN determines the minimum wavelength difference the grating can separate.
  • Angular dispersion D = m/(d·cosθ) increases with order and decreases with spacing.
  • More lines (higher N) and finer spacing produce sharper spectral resolution.

What Is a Diffraction Grating?

A diffraction grating is an optical component with a periodic structure that splits light into its component wavelengths. When monochromatic light hits the grating, it produces bright maxima at specific angles where constructive interference occurs. Polychromatic (white) light is separated into a spectrum, much like a prism but with higher resolution.

Gratings are used in spectrometers, monochromators, laser tuning, telecommunications wavelength-division multiplexing, and scientific research from astronomy to chemistry.

The Grating Equation

dsin⁡θ=mλd \sin\theta = m\lambda

Where d is the slit spacing, θ is the diffraction angle, m is the order (positive integer), and λ is the wavelength. The zeroth order (m = 0) passes straight through at θ = 0°.

Resolving Power

R=mN=λΔλR = mN = \frac{\lambda}{\Delta\lambda}

The resolving power R equals the diffraction order m times the total number of illuminated slits N. It determines the smallest wavelength difference Δλ the grating can distinguish at wavelength λ.

How to Use

  1. Select a mode: find angle, wavelength, spacing, lines/mm, resolving power, angular dispersion, or screen position.
  2. Enter your known values. Use presets for common setups.
  3. Click Calculate. Results include all derived quantities.

Examples

HeNe laser (632.8 nm) through 600 l/mm grating

d = 1/600 mm = 1.667 μm; θ = arcsin(632.8 nm / 1667 nm) ≈ 22.3° (1st order)

Resolving sodium doublet (589.0 & 589.6 nm)

R = λ/Δλ = 589.3/0.6 ≈ 982. With m=1, need N ≥ 982 slits. A 600 l/mm grating 2 mm wide has 1200 slits — sufficient.

FAQ

What is a diffraction grating?›

A diffraction grating is an optical element with many parallel, equally spaced slits or grooves. When light passes through (transmission grating) or reflects off (reflection grating), each slit acts as a source of wavelets that interfere constructively at specific angles determined by the grating equation.

What does grating spacing mean?›

Grating spacing (d) is the distance between adjacent slits or grooves. It is the reciprocal of the line density: d = 1/N, where N is lines per unit length. A 600 lines/mm grating has d = 1/600 mm ≈ 1.667 μm.

Why can't some orders be observed?›

The grating equation requires sinθ ≤ 1. If mλ/d > 1, no real angle satisfies the equation and that order is physically impossible — the diffracted beam would need to travel backward.

How does resolving power work?›

Resolving power R = mN (order × total slits) determines the minimum resolvable wavelength difference: Δλ = λ/R. A grating with 15,000 slits in first order gives R = 15,000, resolving wavelengths 0.04 nm apart at 600 nm.

What is angular dispersion?›

Angular dispersion D = dθ/dλ = m/(d·cosθ) measures how much the diffraction angle changes per unit wavelength change. Higher dispersion means better wavelength separation on a detector.

Sources

  1. Hecht – Optics (6th ed.) — Diffraction Gratings
  2. HyperPhysics – Diffraction Grating
  3. Newport – Diffraction Grating Handbook
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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