The Diffraction Angle Calculator helps determine the angle at which light, X-rays, or other waves bend around obstacles or pass through narrow slits and gratings. This calculation is essential in physics, crystallography, optics, and material science. By applying principles such as Bragg's Law or single-slit diffraction equations, users can compute the diffraction angle based on the wavelength of the wave, the order of diffraction, and the spacing between obstacles.
Formula of Diffraction Angle Calculator
Bragg's Law (for X-ray Diffraction)
θ = sin⁻¹( (n × λ) / (2 × d) )
where:
- θ (Diffraction Angle) is the angle at which diffraction occurs.
- n is the order of diffraction (usually 1 for first-order diffraction).
- λ (Wavelength) is the wavelength of the incident wave, typically in nanometers (nm) or meters (m).
- d (Lattice Spacing) is the distance between atomic layers in the crystal, typically in nanometers (nm) or angstroms (Å).
Single-Slit Diffraction (for Light Passing Through a Slit)
θ = sin⁻¹( m × λ / W )
where:
- m is the order of diffraction (m = 1, 2, 3, etc.).
- λ (Wavelength) is the wavelength of the incident light.
- W (Slit Width) is the width of the slit through which light passes.
Diffraction Angle Reference Table
This table provides estimated diffraction angles for different wavelengths and lattice spacings using Bragg's Law.
| Wavelength (nm) | Lattice Spacing (nm) | Order of Diffraction (n) | Diffraction Angle (θ) |
|---|---|---|---|
| 0.154 | 0.3 | 1 | 30.7° |
| 0.154 | 0.5 | 1 | 18.1° |
| 0.200 | 0.4 | 1 | 29.5° |
| 0.300 | 0.6 | 1 | 28.1° |
| 0.400 | 0.8 | 1 | 26.5° |
Example of Diffraction Angle Calculator
A researcher is analyzing an X-ray diffraction pattern using a crystal with a lattice spacing of 0.4 nm. The incident X-ray has a wavelength of 0.200 nm, and they are interested in the first-order diffraction angle.
Using Bragg’s Law:
θ = sin⁻¹( (1 × 0.200) / (2 × 0.4) ) θ = sin⁻¹( 0.25 ) θ = 14.5°
Thus, the first-order diffraction angle is 14.5°.
Most Common FAQs
The diffraction angle is used in X-ray crystallography, optics, and material science to determine atomic structures, analyze diffraction patterns, and understand wave behavior in different media.
A longer wavelength results in a larger diffraction angle, while a shorter wavelength produces a smaller diffraction angle.
Yes, diffraction occurs in phenomena such as the spreading of sound waves around obstacles, the rainbow effect seen in CDs, and the patterns created when light passes through small openings.