Wave Optics Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 10 notes: Huygens principle, Young's double slit interference and fringe width, single-slit diffraction and polarisation.
Wave Optics — Class 12 Physics Notes
Chapter Snapshot
Ray optics could not explain why light bends around edges or produces coloured fringes. This chapter treats light as a wave: Huygens principle and wavefronts, interference (Young's double slit), diffraction at a single slit, and polarisation — the phenomenon that proves light is a transverse wave.
Board relevance: part of the ~10-mark Optics unit. Expect a YDSE fringe-width numerical and a diffraction or polarisation question. Know the difference between interference and diffraction patterns.
Key Concepts & Definitions
Wavefront — the locus of all points vibrating in the same phase. Spherical near a point source, cylindrical near a line source, and effectively plane far from the source. A ray is always perpendicular to the wavefront.
Huygens principle: every point on a wavefront acts as a source of secondary wavelets spreading out with the wave's speed; the new wavefront is the forward envelope (tangent surface) of these wavelets. It explains reflection and refraction, and shows that in a denser medium light slows down (n = c/v).
Interference and Young's Double Slit Experiment
Interference — the superposition of two coherent waves, giving alternate bright and dark fringes. Energy is redistributed, not created or destroyed.
Coherent sources — same frequency and a constant phase difference. Without coherence, the phase varies randomly and the pattern washes out into uniform illumination. In YDSE, coherence is obtained by using a single source split into two slits.
Path difference at a point y on the screen: Δ = d sin θ ≈ dy/D.
Condition Path difference Result
Constructive Δ = nλ Bright fringe
Destructive Δ = (2n − 1)λ/2 Dark fringe
Fringe width (spacing between consecutive bright or dark fringes):
β = λD/d
where D = slit-to-screen distance, d = slit separation. All fringes are equally spaced and of equal intensity.
Intensity: I = I₁ + I₂ + 2√(I₁I₂) cos φ. For equal sources, Imax = 4I₀ and Imin = 0.
Effects on β: β increases with λ and D, decreases with d. Immersing the setup in a liquid of refractive index n reduces λ (and so β) by a factor n.
Diffraction at a Single Slit
Diffraction — the bending of light around obstacles/edges, giving a central bright band flanked by weaker maxima.
For a slit of width a:
- Minima: a sin θ = nλ (n = 1, 2, 3 …)
- Secondary maxima: a sin θ ≈ (2n + 1)λ/2
- Angular width of the central maximum: 2λ/a; its linear width on a screen at distance D is 2λD/a — twice the width of the other maxima.
Interference vs diffraction:
Interference Diffraction
Two (or more) coherent sources A single wavefront split by one slit
Fringes of equal width and intensity Central maximum widest and brightest; intensity falls off
All maxima equally bright Successive maxima get fainter
Polarisation
Light is a transverse wave, so its vibrations can be restricted to one plane — this is polarisation (impossible for longitudinal waves like sound, which is why polarisation proves light is transverse).
Malus' law — polarised light of intensity I₀ through an analyser at angle θ:
I = I₀ cos² θ
(Unpolarised light through a polaroid gives I₀/2, since the average of cos²θ is ½.)
Brewster's law — at the polarising angle ip, the reflected ray is completely plane polarised and is perpendicular to the refracted ray:
tan ip = n
Formulas
All the formulas of this chapter in one place:
Quantity Formula
Path difference (YDSE) Δ = d sin θ ≈ dy/D
Bright fringe (constructive) Δ = nλ
Dark fringe (destructive) Δ = (2n − 1)λ/2
Fringe width β = λD/d
Position of nth bright fringe yn = nλD/d
Position of nth dark fringe yn = (2n − 1)λD/2d
Resultant intensity I = I₁ + I₂ + 2√(I₁I₂) cos φ
Max / min intensity (equal sources) Imax = 4I₀, Imin = 0
Single-slit minima a sin θ = nλ
Single-slit secondary maxima a sin θ ≈ (2n + 1)λ/2
Central maximum width 2λD/a (angular 2λ/a)
Malus' law I = I₀ cos²θ
Unpolarised through one polaroid I = I₀/2
Brewster's law tan ip = n
Fringe width in a medium β' = β/n
Worked Examples
Example 1 — Fringe width: In YDSE, λ = 600 nm, d = 1 mm, D = 1 m. Find β.
β = λD/d = (600 × 10⁻⁹)(1)/(10⁻³) = 6 × 10⁻⁴ m = 0.6 mm.
Example 2 — Effect of a change: If the slit separation d is halved, what happens to β?
β = λD/d, so halving d doubles the fringe width.
Example 3 — Diffraction: A single slit of width 0.2 mm is lit by 500 nm light, screen at 1 m. Find the width of the central maximum.
Width = 2λD/a = 2(500 × 10⁻⁹)(1)/(0.2 × 10⁻³) = 5 × 10⁻³ m (5 mm).
Example 4 — Malus' law: Polarised light passes through an analyser at 60°. Find the fraction transmitted.
I/I₀ = cos²60° = (0.5)² = 0.25, i.e. 25%.
Example 5 — Brewster's law: Find the polarising angle for glass of n = 1.5.
tan ip = 1.5 → ip ≈ 56.3°.
Important Question Patterns
1. YDSE numerical (3 marks): find β, λ, d, or D; fringe position; effect of changing a parameter or immersing in a liquid.
2. Conditions (2 marks): constructive/destructive path differences; why coherent sources are essential.
3. Diffraction (3 marks): minima condition a sin θ = nλ; width of the central maximum; compare interference and diffraction.
4. Huygens (2–3 marks): state the principle; use wavefronts to explain refraction and show light slows in a denser medium.
5. Polarisation (2–3 marks): Malus' law calculation; Brewster's law; why polarisation proves light is transverse.
⚡ Quick Revision
- Wavefront = surface of constant phase; ray ⟂ wavefront. Huygens: new wavefront = envelope of secondary wavelets.
- Coherent sources (same frequency, constant phase difference) are essential for a steady interference pattern.
- YDSE: Δ = dy/D. Bright Δ = nλ; dark Δ = (2n−1)λ/2. Fringe width β = λD/d (equal spacing, equal intensity).
- β ∝ λ and D, ∝ 1/d; in a liquid of index n, β becomes β/n.
- Single-slit diffraction: minima at a sin θ = nλ; central maximum width 2λD/a — twice the others and brightest.
- Interference: equal fringes. Diffraction: central band widest, others fainter.
- Polarisation proves light is transverse. Malus: I = I₀cos²θ (unpolarised → I₀/2). Brewster: tan ip = n.
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