Interactive Diffraction Grating Calculator
How to Use This Calculator
This calculator uses the diffraction grating equation (d sinθ = mλ) to determine parameters related to light diffraction.
- Select which variable you want to calculate: Diffraction Angle (θ), Wavelength (λ), or Grating Spacing (d).
- Enter the order of diffraction (m), which must be a positive integer (e.g., 1, 2, 3...).
- Specify the grating constant: either directly as "Grating Spacing (d)" or as "Lines per unit length". Select appropriate units.
- Enter the known values for the other parameters, selecting appropriate units for wavelength.
- If providing the Diffraction Angle, enter it in degrees.
- Click the "Calculate" button.
- Results, including the calculated variable, maximum diffraction order, and a step-by-step solution, will be displayed.
Theory: Diffraction Grating
A diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light.
When light passes through a grating, each slit (or reflecting line) acts as a source of secondary wavelets. Constructive interference occurs at specific angles where the path difference between light from adjacent slits is an integer multiple of the wavelength. This condition is described by the grating equation.
Diffraction gratings are commonly used in spectrometers, monochromators, and for wavelength division multiplexing in optical communications.
Formulas Used
Grating Equation:
d sin(θ) = mλ
d= Grating spacing (distance between adjacent slits/lines)θ(theta) = Angle of diffraction for the m-th order maximumm= Order of diffraction (a positive integer: 1, 2, 3, ... for constructive interference maxima)λ(lambda) = Wavelength of the incident light
Rearranged forms for calculation:
- To find θ:
sin(θ) = mλ / d=>θ = arcsin(mλ / d) - To find d:
d = mλ / sin(θ) - To find λ:
λ = d sin(θ) / m
Maximum order of diffraction (mmax): mmax = floor(d / λ) (since sin(θ) ≤ 1)