Describe Young's double slit experiment with a labelled diagram. Obtain the conditions for bright and dark fringes and derive the expression for the fringe width.

1. 1 · State the principle. Light from two coherent sources superposes and forms interference fringes.
2. 2 · Draw the set-up. [Source slit S; double slit S₁ and S₂ with separation d; screen at distance D; overlapping wavefronts; point P at distance x from the centre O; alternate bright and dark bands with the central bright fringe at O]
3. 3 · Explain why the slits are coherent. S₁ and S₂ take light from the same wavefront of S, so their phase difference stays constant.
4. 4 · Write the intensity. I ∝ 4a² cos²(δ/2): bright for δ = 2nπ, dark for δ = (2n + 1)π.
5. 5 · Find the path difference. Δ = d sin θ ≈ xd/D, since sin θ ≈ tan θ = x/D for small θ.
6. 6 · Write the fringe positions.
   • Bright: xd/D = nλ, so xₙ = nλD/d
   • Dark: xd/D = (2n + 1)λ/2, so xₙ = (n + ½)λD/d
7. 7 · Derive the fringe width. β = xₙ₊₁ − xₙ = λD/d, the same for bright and dark fringes.
8. 8 · Close in one line. So, Young's experiment shows the wave nature of light, and β = λD/d.

Scoring tip: Label d, D and x clearly on the diagram, and write β = λD/d with every symbol named.