All Problems

Interference of Light

Problem 5.68

A stationary radiating system consists of a linear chain of parallel oscillators separated by a distance \(d\), with the oscillation phase varying linearly along the chain. Find the time dependence of the phase difference \(\Delta \varphi\) between the neighbouring oscillators at which the principal radiation maximum of the system will be "scanning" the surroundings with the constant angular velocity \(\omega\).

Reveal Answer
Δφ=2π[k(d/λ)sin(ωt+α)], where k=0,±1±2\Delta \varphi=2 \pi[k-(d / \lambda) \sin (\omega t+\alpha)], \quad \text { where } k=0,\pm 1 \pm 2