Light Diffraction
Light diffraction is the bending and spreading of light waves around obstacles or through narrow openings, occurring when the size of the aperture or obstacle is comparable to the wavelength of light. It is a consequence of the wave nature of light and produces characteristic interference patterns of alternating bright and dark fringes. Diffraction is fundamental to technologies such as diffraction gratings, X-ray crystallography, CD/DVD data storage, and optical microscopy resolution limits.
Key Formula
d × sin(θ) = m × λ
LaTeX: d \sin\theta = m\lambda
| Symbol | Meaning | Unit |
|---|---|---|
| d | Slit separation or grating spacing | m |
| θ | Angle of diffraction maximum | degrees or radians |
| m | Order of diffraction (integer: 0, ±1, ±2, ...) | dimensionless |
| λ | Wavelength of light | m |
Worked Example
Problem
Monochromatic light of wavelength 600 nm passes through a double slit with slit separation d = 0.3 mm. Find the angle of the second-order (m = 2) diffraction maximum.
Solution
Step 1: Write the diffraction grating equation. d × sin(θ) = m × λ Step 2: Substitute values. Convert units: λ = 600 nm = 600 × 10⁻⁹ m; d = 0.3 mm = 3 × 10⁻⁴ m; m = 2. sin(θ) = (m × λ) / d sin(θ) = (2 × 600 × 10⁻⁹) / (3 × 10⁻⁴) sin(θ) = 1.2 × 10⁻⁶ / 3 × 10⁻⁴ = 0.004 Step 3: Solve for θ. θ = arcsin(0.004) ≈ 0.229°
Answer
θ ≈ 0.23° (second-order maximum)
Comparison of Single-Slit and Double-Slit Diffraction
| Feature | Single Slit | Double Slit | Diffraction Grating |
|---|---|---|---|
| Number of slits | 1 | 2 | Hundreds to thousands |
| Pattern type | Wide central maximum | Alternating fringes | Sharp bright lines |
| Fringe sharpness | Broad | Moderate | Very sharp |
| Key equation | a·sin(θ) = mλ | d·sin(θ) = mλ | d·sin(θ) = mλ |
| Application | Measuring slit width | Young's experiment | Spectroscopy |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Light Polarization
Light polarization is a property of transverse waves that describes the orientation of the oscillations of the electric field vector in a specific direction perpendicular to the direction of wave propagation. Unpolarized light, such as sunlight, has electric field oscillations in all directions, while polarized light has oscillations confined to a single plane. Polarization is exploited in LCD screens, polarized sunglasses, photography filters, and scientific instruments like polarimeters.
Speed of Light
The speed of light in vacuum, denoted by c, is a universal physical constant equal to exactly 299,792,458 metres per second, representing the maximum speed at which any information, energy, or matter can travel in the universe. As established by Albert Einstein's special theory of relativity (1905), c is invariant regardless of the motion of the source or observer. In transparent media such as glass or water, light travels at a reduced speed given by v = c/n, where n is the refractive index of the medium.
Refractive Index
The refractive index (n) of a medium is a dimensionless number that describes how much slower light travels through that medium compared to its speed in a vacuum, defined as the ratio of the speed of light in vacuum to the speed of light in the medium. It also quantifies how much a ray of light bends (refracts) when entering the medium from vacuum, as described by Snell's Law. The refractive index determines critical phenomena such as total internal reflection, the sparkle of gemstones, and is essential in designing optical fibres, lenses, and camera systems.
From Latin "diffractus", past participle of "diffringere" (to break apart), from "dis-" (apart) + "frangere" (to break). The wave theory of diffraction was developed by Augustin-Jean Fresnel and Thomas Young in the early 19th century.