Diffraction Calculator

Calculate diffraction patterns for single-slit, double-slit, diffraction grating, and circular apertures

Single-Slit Parameters

Enter parameters for single-slit diffraction

nm
μm
m
Central Maximum Width
20.0 mm
Width of central bright fringe
Minima Position (y)
10.0 mm
Position of selected minima
Angular Position (θ)
0.286°
Angle of selected minima
Minima Condition
a sinθ = mλ
Condition for minima
Double-Slit Parameters

Enter parameters for double-slit diffraction

nm
mm
μm
m
Fringe Spacing (Δy)
1.896 mm
Distance between bright fringes
Central Maximum Width
19.0 mm
Width of central envelope
Number of Fringes
10
Fringes in central envelope
Minima Position
9.48 mm
Position of first minima
Diffraction Grating Parameters

Enter parameters for diffraction grating

nm
lines/mm
m
Grating Spacing (d)
2000 nm
Distance between lines
Angular Position (θ)
16.0°
Angle of selected order
Position on Screen (y)
0.574 m
Position of selected order
Resolving Power
1000
Ability to distinguish wavelengths
Circular Aperture Parameters

Enter parameters for circular aperture diffraction

nm
mm
m
Airy Disk Radius
1.61 mm
Radius to first minimum
Angular Resolution (θ)
0.00069 rad
Minimum resolvable angle
Resolution Limit
1.38 mm
Minimum resolvable distance
F-Number
2.0
Focal ratio
Understanding Diffraction

Diffraction is the bending of waves around obstacles or through openings. It occurs when waves encounter an obstacle or aperture that is comparable in size to their wavelength.

  • Single-slit diffraction: Produces a central maximum with diminishing side maxima
  • Double-slit diffraction: Combines interference and diffraction patterns
  • Diffraction grating: Creates sharp, well-defined maxima at specific angles
  • Circular aperture: Produces concentric rings with an Airy disk at center
  • Rayleigh criterion: Defines resolution limit for optical systems
Diffraction Formulas
θ = mλ / a (minima)
Where:
θ = Angular position
λ = Wavelength
a = Slit width
d = Slit separation
D = Aperture diameter
m = Order
Δy = Fringe spacing
L = Distance to screen
Diffraction Examples
Scenario Wavelength Aperture Result Application
Single-slit 500 nm 0.1 mm slit Central width: 20mm Optical experiments
Double-slit 632 nm 0.5mm separation Fringe spacing: 1.9mm Wave nature demonstration
Diffraction grating 550 nm 500 lines/mm θ=16.0° for m=1 Spectroscopy
Circular aperture 550 nm 1mm diameter Airy radius: 1.61mm Telescope resolution
Human eye 550 nm 2mm pupil Resolution: 0.00034 rad Visual acuity

Understanding Diffraction

Diffraction is the bending of waves around obstacles or through openings. It occurs when a wave encounters an obstacle or slit that is comparable in size to its wavelength.

1

Huygens' Principle: Every point on a wavefront acts as a source of secondary wavelets

Explains how waves spread out after passing through an aperture

2

Fraunhofer vs Fresnel Diffraction:

Fraunhofer: Far-field diffraction (parallel rays)

Fresnel: Near-field diffraction (curved wavefronts)

3

Diffraction Limit: Minimum resolvable detail

θ = 1.22 × λ / D (Rayleigh criterion)

4

Applications: Spectroscopy, optical instruments, CD/DVD reading, astronomy

Key Concepts

Airy Disk
d = 2.44λf/D
Central spot in circular diffraction
Fresnel Number
N = a²/(λL)
Distinguishes near/far-field diffraction
Resolving Power
R = λ/Δλ
Ability to distinguish wavelengths
Diffraction Limit
θ = 1.22λ/D
Minimum resolvable angle

Diffraction Types

Single-Slit

Central maximum with decreasing intensity minima

Circular Aperture

Airy pattern with concentric rings

Diffraction Grating

Sharp maxima with angular separation

Fresnel Diffraction

Near-field pattern with complex wavefronts

Diffraction:

  • Bending of waves around obstacles
  • Occurs with single wavefront
  • Produces patterns with central maximum
  • Examples: Single-slit, circular aperture

Interference:

  • Superposition of waves from different sources
  • Requires coherent sources
  • Produces distinct bright and dark fringes
  • Examples: Double-slit, thin-film interference

In practice, diffraction and interference often occur together.

The Rayleigh criterion defines the minimum angular separation at which two point sources can be resolved:

θ = 1.22 × λ / D

Where:

  • θ = Minimum resolvable angle (radians)
  • λ = Wavelength of light
  • D = Diameter of aperture or lens

Two sources are considered resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other.

Applications:

  • Determining telescope resolution
  • Microscope resolving power
  • Camera lens performance
  • Optical system design

The Airy pattern is the diffraction pattern produced by a circular aperture:

  • Central bright disk (Airy disk)
  • Surrounded by concentric rings of decreasing intensity
  • First minimum at angle θ = 1.22λ/D
  • 84% of light energy in central disk

Mathematically described by:

I(θ) = I₀ [2J₁(kD sinθ/2) / (kD sinθ/2)]²

Where:

  • I₀ = Intensity at center
  • J₁ = First-order Bessel function
  • k = 2π/λ (wave number)
  • D = Aperture diameter
  • θ = Angle from center

The Airy pattern sets the fundamental limit for resolution in optical systems.

Fresnel zones are concentric circular regions used to analyze diffraction patterns:

  • Each zone boundary is λ/2 farther from observation point
  • Odd-numbered zones contribute constructively
  • Even-numbered zones contribute destructively
  • Zone plate uses alternating opaque zones to focus light

Radius of nth Fresnel zone:

rₙ = √(nλL)

Where:

  • n = Zone number
  • λ = Wavelength
  • L = Distance to observation point

Applications:

  • Zone plate lenses
  • Antenna design
  • Acoustics
  • Seismic wave analysis