Schooling · Class 12 · Physics · Wave Optics · Chapter on a page
CBSE Class 12 · Physics · NCERT Physics Part-II
Wave Optics: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Huygens's principle
- Coherent sources
- Superposition and interference
- Young's double-slit experiment
- Diffraction
- Resolving power
- Polarisation
- Formulas and facts
- Condition for constructive…
- Condition for destructive interference
- Young's fringe width
- Position of n-th bright fringe
- Single-slit first minimum
- Malus's law
- Brewster's angle
- Worked examples
- Fringe width calculation
- Single-slit diffraction angle
- Malus's law
- Watch out for
- Confusing path difference with phase…
- Using fringe-width formula for…
- Forgetting that unpolarised light…
- Mixing up conditions for maxima and…
- Assuming wavelength stays the same…
What this chapter is about
Wave optics treats light as a wave rather than a ray. While ray optics explains reflection and refraction using straight-line paths, wave optics explains phenomena that ray optics cannot: interference, diffraction and polarisation. These effects become noticeable when light interacts with obstacles or apertures whose size is comparable to its wavelength (roughly 400–700 nm for visible light).
Key ideas
- Huygens's principle: Every point on a wavefront acts as a source of secondary spherical wavelets; the new wavefront is the forward envelope of all these wavelets. This explains reflection and refraction without invoking rays.
- Coherent sources: Two sources are coherent if they have a constant phase difference over time. Only coherent sources produce a stable interference pattern; ordinary lamps are incoherent.
- Superposition and interference: When two waves meet, the resultant displacement is the algebraic sum. Constructive interference (bright fringe) occurs when path difference = nλ; destructive interference (dark fringe) occurs when path difference = (n + ½)λ, where n is an integer.
- Young's double-slit experiment: Two narrow slits illuminated by monochromatic light act as coherent sources; alternate bright and dark fringes appear on a distant screen. Fringe width β = λD/d, where D is slit-to-screen distance, d is slit separation, λ is wavelength.
- Diffraction: Bending of light around edges or through narrow apertures. In single-slit diffraction the first minimum occurs at angle θ where a sin θ = λ, with a the slit width.
- Resolving power: The ability of an optical instrument to distinguish two close objects. A smaller aperture or longer wavelength worsens resolution.
- Polarisation: Restriction of the electric-field vibration to a single plane. Polarisation proves light is a transverse wave. Malus's law: I = I₀ cos²θ, where I₀ is intensity after the polariser and θ is the angle between polariser and analyser axes.
Formulas and facts to remember
- Item: Condition for constructive interference · Formula / Statement: Path difference Δ = nλ · Meaning: Waves arrive in phase; bright fringe.
- Item: Condition for destructive interference · Formula / Statement: Path difference Δ = (n + ½)λ · Meaning: Waves arrive out of phase; dark fringe.
- Item: Young's fringe width · Formula / Statement: β = λD / d · Meaning: Larger wavelength or screen distance gives wider fringes; larger slit separation gives narrower fringes.
- Item: Position of n-th bright fringe · Formula / Statement: yₙ = nλD / d · Meaning: Distance from central bright to n-th bright fringe.
- Item: Single-slit first minimum · Formula / Statement: a sin θ = λ · Meaning: Central maximum has angular width 2λ/a.
- Item: Malus's law · Formula / Statement: I = I₀ cos²θ · Meaning: Intensity through analyser depends on angle with polariser.
- Item: Brewster's angle · Formula / Statement: tan θ_B = n₂ / n₁ · Meaning: Reflected light is completely polarised when refracted and reflected rays are perpendicular.
- Item: Speed relation in medium · Formula / Statement: v = c / n · Meaning: Light slows inside a denser medium; wavelength shrinks, frequency unchanged.
Common mistakes
- Confusing path difference with phase difference → Path difference is in metres; phase difference = (2π/λ) × path difference.
- Using fringe-width formula for diffraction minima → β = λD/d applies only to double-slit interference; single-slit uses a sin θ = mλ.
- Forgetting that unpolarised light loses half its intensity on passing the first polariser → Always halve before applying Malus's law.
- Mixing up conditions for maxima and minima → For double-slit, nλ gives bright; for single-slit diffraction, nλ gives dark (n ≠ 0).
- Assuming wavelength stays the same inside a medium → Wavelength λ_medium = λ_vacuum / n; frequency does not change.
Quick revision
- Huygens's principle explains wave propagation by treating each wavefront point as a new source.
- Stable interference needs coherent sources with constant phase difference.
- Fringe width β = λD/d; larger D or λ widens fringes, larger d narrows them.
- First single-slit minimum: a sin θ = λ.
- Polarisation confirms light is a transverse wave; Malus's law: I = I₀ cos²θ.
- Brewster's angle: tan θ_B = n; reflected ray is fully polarised.