Wave Optics treats light as a wave and builds everything from Huygens’ principle, explaining reflection, refraction, interference, diffraction and polarisation. It covers Young’s double-slit experiment, single-slit diffraction and Malus’s law, which are reliable sources of NEET questions every year. Mastering the fringe-width and intensity formulas here makes a cluster of one and two mark questions almost automatic.
Key Concepts
1. Huygens’ Principle
Every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront is the forward envelope of all these secondary wavelets.
Used to derive the laws of reflection and refraction.
2. Interference - Young’s Double Slit Experiment (YDSE)
When light from two coherent sources (slits S₁ and S₂) overlaps, it produces a pattern of bright and dark fringes.
Condition for bright fringe: Path difference = nλ (n = 0, 1, 2, …)
Condition for dark fringe: Path difference = (n + ½)λ
Fringe width: β = λD/d
- λ = wavelength of light
- D = distance from slits to screen
- d = separation between slits
Central fringe is always bright and widest.
3. Diffraction - Single Slit
When light passes through a narrow slit, it spreads out and forms a pattern of bright and dark bands.
Central maximum: Width = 2λD/a (where a = slit width)
Minima condition: a sin θ = nλ (n = ±1, ±2, …)
Secondary maxima: a sin θ = (n + ½)λ
Central maximum is twice as wide as secondary maxima.
4. Polarisation
Light is a transverse wave. Polarisation is the restriction of vibrations of the electric field to a single plane.
Malus’s Law: I = I₀ cos² θ (intensity of polarised light through an analyser at angle θ)
Brewster’s Law: tan ip = n (ip = polarising angle; reflected and refracted rays are perpendicular)
Polaroid uses: Sunglasses, LCD screens, photography, 3D movies
Solved Examples
Example 1
In YDSE, slit separation d = 0.5 mm, screen distance D = 1 m, wavelength λ = 600 nm. Find the fringe width.
Answer: β = λD/d = (600 × 10⁻⁹ × 1)/(0.5 × 10⁻³) = 1.2 mm
Example 2
Unpolarised light of intensity I₀ passes through two polaroids with axes at 60°. Find final intensity.
Answer: After first polaroid: I₁ = I₀/2. After second: I₂ = (I₀/2)cos²60° = (I₀/2)(1/4) = I₀/8
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Important Questions for Board Exams
3-Mark
- Derive the expression for fringe width in YDSE.
- State and prove Malus’s law.
- What is diffraction? Compare the diffraction pattern with interference pattern.
5-Mark
- Describe Young’s double slit experiment. Derive expressions for bright, dark fringes and fringe width.
- What is polarisation? State Brewster’s law and Malus’s law with derivations.
Quick Revision Points
- Huygens: each point on wavefront → source of secondary wavelets
- YDSE: β = λD/d; bright: Δ = nλ; dark: Δ = (n+½)λ
- Diffraction: central max width = 2λD/a; minima: a sin θ = nλ
- Polarisation: transverse wave property; Malus: I = I₀cos²θ
- Brewster: tan ip = n; reflected light is fully polarised
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Wavefronts & Huygens’ Principle
A wavefront joins all points vibrating in the same phase, and every point on it acts as a new source of wavelets.
Rays are perpendicular to the wavefront and point the way light travels.
- Point source → spherical, line source → cylindrical, source at infinity → plane wavefronts.
- Forward envelope of the wavelets after time t gives the next wavefront.
- Explains reflection and refraction purely from wave geometry.
Refraction from Huygens
In a denser medium light slows down, so the wavefront bends toward the normal and Snell’s law drops out.
Frequency f stays constant across a boundary; speed and λ decrease in a denser medium.
- Speed drops in a denser medium, so wavelets travel less and the front tilts.
- Only λ and v change at a boundary; f is fixed.
- Recovers Snell’s law without Newton’s particle picture.
Superposition & Path Difference
When coherent waves overlap their displacements add, giving steady bright and dark patches.
Path difference Δx and phase difference φ are two languages for the same thing.
- Whole-wavelength path difference → crest meets crest → bright.
- Half-wavelength (odd) path difference → crest meets trough → dark.
- One wavelength of path = 2π radians of phase.
Interference Intensity
Two equal-amplitude coherent waves give an intensity that swings between zero and four times a single wave.
Energy is only redistributed from dark to bright regions, never lost.
- Constructive max = 4 I0 at φ = 0; destructive min = 0 at φ = π.
- Unequal sources: brightness uses the sum/difference of √I.
- Interference conserves total energy.
Coherence
A steady fringe pattern needs sources locked in a constant phase relationship.
That is why one source is split into two, not two separate bulbs.
- Sources must keep a constant phase difference in time.
- They must have the same frequency.
- Two independent bulbs are incoherent, so no fringes form.
Young’s Double-Slit (YDSE)
Two coherent slits a distance d apart throw equally spaced fringes onto a screen at distance D.
Central fringe is bright (zero path difference); fringes are equally spaced and equally bright.
- β grows with λ and D, shrinks with d.
- Angular fringe width θ = λ/d is independent of D.
- Immerse in liquid of index n → β becomes β/n.
YDSE with White Light
White light gives a white centre flanked by coloured fringes.
Because β ∝ λ, longer-wavelength colours spread out more.
- Zero path difference is white for all colours → white central fringe.
- Violet (small λ) sits closest to the centre.
- Higher orders overlap and wash out into white.
Single-Slit Diffraction
One slit of width a spreads light into a wide central band with fainter side bands.
Here nλ marks DARK, the reverse of double-slit; central max is twice as wide as side maxima.
- Pairing trick: top-half source cancels its partner a/2 below.
- Side maxima are weaker and fall off sharply (unlike equal YDSE fringes).
- Narrower slit → wider central peak (more spreading).
Resolving Limit
Diffraction sets the finest detail an instrument can separate.
Smaller θ_min = better resolution; bigger aperture D helps, shorter λ helps.
- Larger aperture D → smaller θ_min → sharper resolution.
- Shorter wavelength → finer detail resolved.
- Why telescopes and microscopes chase large apertures / short λ.
Polarisation & Malus’s Law
Light is transverse, so its vibration can be confined to one plane by a polaroid.
Sound is longitudinal and CANNOT be polarised (a classic NEET one-marker).
- A polaroid passes exactly half of unpolarised intensity.
- θ = 0 → full transmission; θ = 90° → crossed polaroids → zero.
- Transmitted light is plane-polarised along the polaroid’s axis.
Brewster’s Angle
At one special incidence angle the reflected ray is completely plane-polarised.
At θ_B the reflected and refracted rays are perpendicular; for glass (n ≈ 1.5), θ_B ≈ 57°.
- Reflected ray at θ_B is fully plane-polarised.
- Reflected ⟂ refracted at this angle.
- Brewster’s angle increases with refractive index n.
📝 Practice Wave Optics — 10 NEET PYQs
Real previous-year questions · with answers & solutions
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Chapter Navigation
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Related Chapters in Class 12 Physics
- Ray Optics and Optical Instruments Class 12 Notes
- Dual Nature of Radiation and Matter Class 12 Notes
- Electromagnetic Waves Class 12 Notes
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Frequently Asked Questions
Huygens’ principle states that every point on a wavefront acts as a source of secondary wavelets that spread out at the wave speed, and the forward envelope (tangent surface) of these wavelets gives the new wavefront a moment later. It is used to derive the laws of reflection and refraction from a pure wave picture.
The fringe width, the spacing between two consecutive bright or dark fringes, is beta = lambda D / d, where lambda is the wavelength, D is the slit-to-screen distance and d is the slit separation. So fringe width increases with wavelength and screen distance, and decreases as the slits move farther apart.
Yes, Wave Optics is part of the Class 12 NEET physics syllabus and usually contributes one to two questions every year. Young’s double-slit experiment (fringe width), single-slit diffraction and Malus’s law are the most frequently tested ideas.
Interference is the superposition of waves from two or more separate coherent sources, giving equally spaced and equally bright fringes, while diffraction is the bending and spreading of light from a single slit or edge, giving a wide central maximum with weaker, unequal side maxima. A handy contrast is that in a single slit a sin theta = n lambda marks the dark minima, the reverse of the double-slit bright condition.
Light is a transverse wave, so its electric field vibration can be restricted to a single plane, which is what polarisation means. Sound is a longitudinal wave with vibrations along the direction of travel, so it has no transverse plane to restrict and cannot be polarised, a point NEET often tests directly.