\[a\sin(\theta)=m\lambda\]
Variables
aslit width
theta[θ]diffraction angle [rad]
mminimum order
lambda[λ]wavelength
Description
What is this formula?
This formula determines the angular positions of dark fringes in a single-slit diffraction pattern. Destructive interference occurs when light from different parts of the slit cancels out.
When to use it
Use this formula when analyzing diffraction patterns produced by a narrow slit and monochromatic light.
Example
Given:
a=5×10^-5 m
m=1
λ=6×10^-7 m
Formula:
a·sin(θ)=mλ
Rearranged:
θ=sin^-1((mλ)/a)
Substitution:
θ=sin^-1((1×6×10^-7)/(5×10^-5))
Result:
θ=0.687°
Applications
- Diffraction experiments
- Laser optics
- Spectroscopy
- Optical measurements
- Wave optics analysis