What is interference of light? Two coherent waves of equal amplitude meet with a phase difference φ. Find the resultant intensity and give the conditions for maximum and minimum intensity.

1. 1 · Define interference. The change in intensity when two coherent waves superpose, giving bright and dark points.
2. 2 · Write the two waves. y₁ = a cos ωt and y₂ = a cos(ωt + φ).
3. 3 · Add them. y = 2a cos(φ/2) cos(ωt + φ/2), so the amplitude is 2a cos(φ/2).
4. 4 · Find the intensity. I ∝ amplitude², so I = 4I₀ cos²(φ/2).
5. 5 · Give the conditions.
   • Maximum 4I₀: φ = 0, 2π, 4π, ..., or path difference nλ
   • Minimum 0: φ = π, 3π, ..., or path difference (n + ½)λ
6. 6 · Real life. The colours of soap bubbles come from interference.
7. 7 · Close in one line. So, interference redistributes light energy; it does not destroy it.

Scoring tip: Write the identity cos A + cos B = 2 cos((A + B)/2) cos((A − B)/2); it earns a mark.