Diffraction Simulation
Interactive visualization of single-slit and circular aperture diffraction. Watch waves spread through an aperture and observe the far-field diffraction pattern on a screen.
- Aperture Width (a): Width of the slit or diameter of the circular aperture. Narrower aperture = wider diffraction pattern
- Wavelength (λ): Light wavelength (380–700 nm visible). Longer wavelength = wider diffraction pattern
- Screen Distance (L): Distance from aperture to detection screen. Farther = wider pattern on screen
- Huygens Wavelets: Toggle to see secondary wavelets emanating from the aperture
- Circular Aperture: Switch to see the Airy disk pattern produced by a round opening
- Animation: Click Start to see wavefronts propagate through the aperture
📚 Physics Background
🌊 What Is Diffraction?
Diffraction is the bending and spreading of waves as they pass through an aperture or around an obstacle. It occurs when the aperture size is comparable to the wavelength of the wave. This phenomenon demonstrates the wave nature of light and cannot be explained by geometric optics alone.
According to Huygens' Principle, every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront is the envelope of all these wavelets. When a wave passes through a narrow aperture, only a few wavelets contribute, causing the wave to spread out.
📐 Single-Slit Diffraction
For a single slit of width a, the intensity pattern on a distant screen is given by:
I(θ) = I₀ [sin(β) / β]²
β = (π a sin θ) / λ
Minima (dark fringes) occur when:
a sin(θ) = mλ (m = ±1, ±2, ±3, ...)
Where:
- a is the slit width
- λ is the wavelength of light
- θ is the angle from the central axis
- m is the order of the minimum
⭕ Circular Aperture & Airy Disk
For a circular aperture of diameter D, the far-field diffraction pattern is the Airy pattern:
I(θ) = I₀ [2 J₁(x) / x]²
x = (π D sin θ) / λ
Here J₁ is the first-order Bessel function. The central bright disk is the Airy disk. The first dark ring occurs at:
sin(θ) ≈ 1.22 λ / D
The Airy disk determines the angular resolution of telescopes, microscopes, and cameras—this is the Rayleigh criterion.
🌊 Huygens' Principle
Secondary Wavelets
Concept: Every point on a wavefront is a source of spherical secondary wavelets.
The envelope of these wavelets at a later time gives the new position of the wavefront. In the aperture, the limited number of wavelet sources causes the wave to spread out, producing the diffraction pattern.
Fraunhofer vs Fresnel Diffraction
Fraunhofer (far-field): Source and screen are effectively at infinity (plane waves). This is the regime shown in this simulation.
Fresnel (near-field): Source or screen is close to the aperture, requiring more complex calculations with curved wavefronts.
🔬 Applications
- Telescope Resolution: The Airy disk limits the angular resolution of optical instruments (Rayleigh criterion)
- X-ray Crystallography: Diffraction of X-rays by crystal lattices reveals atomic structure
- Spectroscopy: Diffraction gratings split light into component wavelengths
- Optical Disc Reading: CD/DVD/Blu-ray players use diffraction to read data
- Waveguides & Fiber Optics: Diffraction effects govern mode propagation in optical fibers