Used to explain reflection, refraction, diffraction, and interference.

Path difference: Δx = d sinθ ≈ d y/D

Constructive (bright): Δx = nλ → y = nλD/d

Destructive (dark): Δx = (2n–1)λ/2 → y = (2n–1)λD/(2d)

Fringe width (β): β = λD/d

Minima (dark): a sinθ = nλ, n = ±1, ±2,…

Central maxima width: 2λD/a

Intensity distribution: I = I₀ (sinβ/β)², β = (πa sinθ)/λ

Malus' law: I = I₀ cos²θ (θ = angle between polarizer & analyzer).

Brewster's angle: tan i_p = n₂/n₁ (reflected light is completely polarized).

At i_p, reflected and refracted rays are 90° apart.

For telescope: R = a/(1.22λ) (a = aperture diameter).

For microscope: R = 2n sinθ / λ (n = refractive index, θ = half angle).

💡 NEET TIPS & SHORTCUTS

• YDSE fringe width β ∝ λ; if wavelength increases, fringe width increases.
• In diffraction, central maxima is twice as wide as secondary maxima.
• Polarization proves light is a transverse wave.
• For coherent sources, phase difference = (2π/λ) × path difference.

⚠️ COMMON MISTAKES

• Confusing diffraction and interference conditions.
• Using YDSE formula for diffraction minima (different n).
• Forgetting that in polarization, only transverse component is transmitted.
• Assuming interference pattern disappears if sources are not coherent.

YDSE bright fringes: y = nλD/d

YDSE dark fringes: y = (2n–1)λD/(2d)

Fringe width: β = λD/d

Single slit minima: a sinθ = nλ

Malus law: I = I₀ cos²θ

Brewster angle: tan i_p = n₂/n₁

Resolving power (telescope): a/(1.22λ)