Constructive interference: d·sin(θ) = mλ — build up slits and watch patterns sharpen
Grating Setup & Diffraction Pattern
2
3.0 μm
550 nm
0.5 μm
d·sin(θ) = mλ → θ_1 = arcsin(550nm/3.0μm) = 10.5°
Multi-slit interference: constructive at d·sin(θ)=mλ, destructive at d·sin(θ)=(m+½)λ. More slits → sharper peaks, lower background. Single-slit envelope: sinc²(πa·sin(θ)/λ).
Pattern Comparison
Increasing N from 1→20: peaks become sharper by factor N. Central max intensity ∝ N². The grating equation d·sinθ=mλ predicts where peaks appear regardless of N.
Phasor Diagram (angle θ)
0°
Each slit contributes a phasor of amplitude 1. Phase difference Δφ = 2πd·sinθ/λ between adjacent slits. Sum = resultant amplitude squared = intensity.