Wave Diffraction
Wave diffraction is the bending and spreading of waves around obstacles or through openings, occurring most prominently when the wavelength of the wave is comparable in size to the obstacle or aperture. The phenomenon is a direct consequence of Huygens's principle, which states that every point on a wavefront acts as a source of secondary wavelets. Diffraction is exploited in X-ray crystallography to determine molecular structures, in radio communication to allow signals to travel around hills, and in optical instruments to understand resolution limits.
Key Formula
sin(θ) ≈ λ / d
LaTeX: \sin\theta \approx \frac{\lambda}{d}
| Symbol | Meaning | Unit |
|---|---|---|
| \theta | Angle of the first diffraction minimum | degrees or radians |
| \lambda | Wavelength of the wave | m |
| d | Width of the slit or aperture | m |
Worked Example
Problem
Sound of wavelength 0.5 m passes through a doorway 1.0 m wide. At what angle does the first diffraction minimum occur?
Solution
Step 1: Use the single-slit diffraction formula for the first minimum: sin(θ) = λ / d. Step 2: sin(θ) = 0.5 / 1.0 = 0.5. Step 3: θ = arcsin(0.5) = 30°.
Answer
First diffraction minimum occurs at θ = 30°
Diffraction in Different Wave Types
| Wave Type | Wavelength Range | Typical Aperture | Diffraction Visible? | Application |
|---|---|---|---|---|
| Sound | 0.017 m – 17 m | Doorways, rooms | Yes | Acoustics, sonar |
| Visible light | 400 – 700 nm | Diffraction gratings | Yes (special setup) | Spectroscopy |
| X-rays | 0.01 – 10 nm | Crystal lattice (~0.1 nm) | Yes | X-ray crystallography |
| Radio waves | 1 mm – 100 km | Hills, buildings | Yes | Radio communication |
| Water waves | cm to m | Harbour gaps | Yes (visible) | Coastal engineering |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Constructive Interference
Constructive interference occurs when two or more waves overlap in such a way that their displacements add together, producing a resultant wave with greater amplitude than either individual wave. This phenomenon arises when the waves are in phase — that is, their crests and troughs align — leading to a net increase in energy at that point. It is fundamental to technologies such as noise-cancelling headphones (in reverse), optical coatings, and phased-array antennas.
Destructive Interference
Destructive interference occurs when two waves overlap out of phase — with the crest of one aligning with the trough of the other — causing their displacements to cancel partially or completely, reducing the resultant amplitude. When two waves of equal amplitude are exactly 180° out of phase, the resultant amplitude is zero, meaning complete cancellation. This principle underlies active noise cancellation in headphones, anti-reflective optical coatings, and acoustic dead spots in concert halls.
Doppler Effect
The Doppler effect is the apparent change in frequency (and thus pitch or colour) of a wave perceived by an observer when the source of the wave and the observer are moving relative to each other. When a source approaches, the observed frequency increases; when it recedes, the frequency decreases. The effect is named after Austrian physicist Christian Doppler (1842) and applies to all wave types including sound, light, and radar, with applications in medical ultrasound, police speed guns, weather radar, and astronomical redshift measurements.
From Latin "diffractus", past participle of "diffringere" (to break apart), from "dis-" (apart) + "frangere" (to break). First described mathematically by Francesco Maria Grimaldi around 1660.