Table of Contents
What is Diffraction?
Diffraction is the bending of waves around obstacles or through openings, resulting in characteristic patterns of constructive and destructive interference. When light passes through a narrow slit comparable in size to its wavelength, it spreads out and creates a pattern of bright and dark fringes on a screen. This phenomenon provides powerful evidence for the wave nature of light and is fundamental to understanding optical instruments.
Diffraction limits the resolution of all optical instruments including microscopes, telescopes, and cameras. The Rayleigh criterion states that two point sources are just resolvable when the central maximum of one coincides with the first minimum of the other. This fundamental limit drives the design of advanced optical systems and motivates the use of shorter wavelengths for higher resolution imaging.
Diffraction Formulas
Where a is the slit width, d is the slit separation, θ is the diffraction angle, m is the order number, and λ is the wavelength. Single-slit formula gives minima positions; double-slit formula gives maxima positions.
Types of Diffraction
- Fraunhofer: Far-field diffraction with parallel rays (most common calculations)
- Fresnel: Near-field diffraction with curved wavefronts
- Single slit: Produces a central maximum with diminishing side lobes
- Double slit: Young's experiment showing interference fringes modulated by single-slit envelope
- Diffraction grating: Multiple slits producing sharp, bright maxima for spectroscopy
Example Angular Positions (632 nm laser)
| Slit Width | 1st Minimum | 2nd Minimum |
|---|---|---|
| 5 μm | 7.26° | 14.6° |
| 10 μm | 3.62° | 7.26° |
| 50 μm | 0.72° | 1.45° |
| 100 μm | 0.36° | 0.72° |
Frequently Asked Questions
Why does narrower slit produce wider pattern?
This is a consequence of wave mechanics. A narrower slit constrains the wave more tightly, causing it to spread out more on the other side (similar to the Heisenberg uncertainty principle). The angular width of the central maximum is approximately 2λ/a, so halving the slit width doubles the pattern width. This inverse relationship is fundamental to diffraction.
What determines the resolution of a telescope?
The angular resolution of a circular aperture is given by the Rayleigh criterion: θ = 1.22λ/D, where D is the aperture diameter. Larger telescopes have better resolution because the diffraction limit decreases with aperture size. This is why astronomers build ever-larger telescopes and why space-based telescopes avoid atmospheric turbulence that further degrades resolution.
How are diffraction gratings used in spectroscopy?
Diffraction gratings contain thousands of parallel slits per millimeter. They separate light into its component wavelengths with high precision, allowing measurement of atomic emission and absorption spectra. The resolving power equals m*N, where m is the order and N is the total number of slits illuminated.