What is Diffraction?
Diffraction is a wave phenomenon that occurs when a light ray encounters an obstacle or passes through a slit (aperture). After traveling through the aperture, the light changes direction and the wave spreads out — a behavior that cannot be explained by simple ray optics. The effect is most noticeable when the aperture size is comparable to the wavelength of light.
What is a Diffraction Grating?
A diffraction grating is an optical component with a regular, periodic structure — a large number of uniformly spaced parallel slits or rulings. When light passes through (transmission grating) or reflects off (reflection grating) such a surface, each slit acts as an individual source of waves, and these waves interfere with each other constructively in certain directions and destructively in others.
The result is that light is dispersed into its component wavelengths (colors), much like a prism — but with higher resolution and precision. Diffraction gratings are used in spectrometers, laser systems, monochromators, and many optical instruments.
The effects of diffraction are only visible if the spacing between apertures (slits) is comparable to or larger than the wavelength of the incident light. For visible light (380–780 nm), gratings typically have 100–3600 lines per millimeter.
Diffraction Grating Equation
When an incident light ray is perpendicular to the grating surface, the directions in which diffracted beams appear are described by the diffraction grating equation:
d · sin(θm) = m · λ
Where:
- d — grating spacing (distance between adjacent slits), in nanometers (nm) or other length units
- θm — diffraction angle for the m-th order (measured from the grating normal)
- m — diffraction order: an integer (0, ±1, ±2, ±3, …)
- λ — wavelength of the incident light (nm)
The zeroth order (m = 0) passes straight through without bending (θ = 0°). The first order (m = ±1) gives the first diffracted beams, the second order (m = ±2) the next, and so on. A diffraction order m only exists when |m · λ / d| ≤ 1, i.e., sin(θ) ≤ 1. The maximum possible order is therefore mmax = ⌊d / λ⌋.
Unit Systems
This calculator supports both the metric system (lines per millimeter, wavelength in nm) and the American (imperial) system (lines per inch). Common grating specifications:
- Metric: 300, 600, 1200, 1800, 2400 lines/mm
- American: 7,620 (≈ 300 l/mm), 15,240 (≈ 600 l/mm), 30,480 (≈ 1200 l/mm) lines/inch
FAQs
What wavelengths are visible to the human eye?
The visible spectrum ranges from approximately 380 nm (violet) to 780 nm (deep red). Common laser wavelengths: 405 nm (violet diode), 532 nm (green DPSS), 650 nm (red pointer), 780 nm (CD laser).
How does grating spacing affect diffraction?
Smaller grating spacing (more lines per mm) results in larger diffraction angles for the same wavelength. If d is smaller than λ, no first-order diffraction occurs at all — the light cannot be diffracted at any real angle.
What is the difference between reflection and transmission gratings?
The diffraction grating equation is the same for both. A transmission grating (like a glass slide with etched lines) lets light pass through; a reflection grating (like a CD or DVD surface) reflects light. Reflection gratings are more common in laboratory instruments.
Why do CDs and DVDs show rainbow colors?
The tracks on a CD are spaced approximately 1600 nm apart (625 lines/mm), acting as a reflection diffraction grating. White light (containing all visible wavelengths) is diffracted at different angles for each color, producing the characteristic rainbow pattern you see when light reflects off the surface.
Can I use this calculator for any wavelength?
Yes. While this calculator is optimized for visible light, you can enter any wavelength (e.g., UV at 200–380 nm, or near-IR at 780–2500 nm). Just keep in mind that the diffraction angle must satisfy sin(θ) ≤ 1 — orders that would require a larger sine are physically impossible.