• Tags: optical-path, phase, path-difference
• Difficulty: Moderate

Optical path = geometrical path × refractive index = μt. Phase difference φ = 2π × (path difference)/λ = 2π$\Delta x$/λ. For a source with initial phase difference δ: total phase difference = 2π$\Delta x$/λ + δ. Converting between representations: path difference $\Delta x$ = nλ gives φ = 2nπ (constructive); $\Delta x$ = (n+1/2)λ gives φ = (2n+1)π (destructive). The relationship between intensity and phase: I = $I_{1}$ + $I_{2}$ + 2√(I_{1}$$I_{2})cosφ. For finding intensity at a specific point, first calculate the path difference from geometry, convert to phase difference, then substitute into the intensity formula. This systematic approach prevents sign errors common in JEE problems.