\[d\sin(\theta)=m\lambda\]
Variables
dgrating spacing
theta[θ]diffraction angle [rad]
mdiffraction order
lambda[λ]wavelength
Description
What is this formula?
This formula determines the angular position of diffraction maxima produced by a diffraction grating. Constructive interference occurs when light from adjacent slits arrives in phase.
When to use it
Use this formula for diffraction gratings, spectroscopy systems, wavelength measurements, and optical analysis.
Example
Given:
d=1×10^-6 m
m=1
λ=5×10^-7 m
Formula:
d·sin(θ)=mλ
Rearranged:
θ=sin^-1((mλ)/d)
Substitution:
θ=sin^-1((1×5×10^-7)/(1×10^-6))
Result:
θ=30°
Applications
- Spectrometers
- Wavelength measurements
- Optical instruments
- Laser systems
- Spectral analysis