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
Order 2
Order 3
Grating Spacing
Maximum 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
Common Wavelengths
Common Gratings
Key Concepts
Wavelength
Distance between wave peaks
Grating Spacing
Distance between grating lines
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.