Diffraction Grating Calculator

Calculate diffraction angles using the grating equation: a × λ = d × (sin θ₀ + sin θₐ)

Calculate Diffraction Patterns

Wavelength of incident light

Number of grating lines per unit length

Angle between incident light and grating normal

Diffraction Results

Diffraction Angles by Order

Order 1
30.00°
Diffraction angle
Order 2
No diffraction at this order
Order 3
No diffraction at this order

Grating Spacing

1.00 μm
Distance between grating lines

Maximum Order

1
Highest observable diffraction order

Grating Equation: a × λ = d × (sin θ₀ + sin θₐ)

Where: a = order, λ = wavelength, d = grating spacing, θ₀ = incident angle, θₐ = diffraction angle

Physics Analysis

📊 Low-order diffraction only - consider higher density grating for more orders.
🔍 High resolution grating - excellent for fine spectral details.

Common Wavelengths

Common Gratings

Key Concepts

λ

Wavelength

Distance between wave peaks

d

Grating Spacing

Distance between grating lines

θ

Diffraction Angle

Direction of diffracted light

Applications

🌈

Spectroscopy and wavelength analysis

💿

CD/DVD optical storage

🔬

Optical instruments

🌟

Holography

🔆

Laser beam shaping

📡

Telecommunications

Understanding Diffraction Gratings

What is Diffraction?

Diffraction is a wave phenomenon that occurs when light encounters an obstacle or aperture comparable in size to its wavelength. The light waves bend around edges and spread out, creating interference patterns that can be observed and measured.

How Gratings Work

  • Multiple parallel slits create coherent interference
  • Constructive interference at specific angles
  • Different wavelengths diffract at different angles
  • Enables wavelength separation and analysis

Grating Equation

a × λ = d × (sin θ₀ + sin θₐ)

  • a: Diffraction order (1, 2, 3, ...)
  • λ: Wavelength of light
  • d: Grating spacing (distance between lines)
  • θ₀: Incident angle
  • θₐ: Diffraction angle

Note: For normal incidence (θ₀ = 0), the equation simplifies to: a × λ = d × sin θₐ

Types of Diffraction Gratings

Transmission Gratings

Light passes through transparent lines or slits. Common in spectroscopy and educational demonstrations. Easy to manufacture and use.

Reflection Gratings

Light reflects off ruled grooves in a mirror surface. Higher efficiency and better for UV/IR applications. Used in professional instruments.

Real-World Examples

CD/DVD Discs

The rainbow patterns you see on CDs are caused by diffraction from the microscopic data tracks acting as a grating.

Spectroscopy

Astronomers use gratings to analyze starlight and determine stellar composition, temperature, and motion.

Holography

Holographic gratings create three-dimensional images and are used in security features on credit cards and currency.