Board exam focus — Wave Optics (CBSE & HBSE)

CBSE focuses on Huygens' principle, Young's double slit derivation, interference conditions, diffraction, and Malus's law for polarisation. HBSE emphasizes coherent sources, fringe width formula, diffraction vs interference, and Brewster's law.

Huygens' Principle and Wavefronts

Wavefront

A wavefront is the locus of all points in a medium that are oscillating in the same phase at a given instant.

Huygens' Principle

1. Every point on a wavefront acts as a secondary source of waves, emitting secondary wavelets in all directions.
2. The new wavefront at a later time is the forward tangent envelope (tangential surface) to all these secondary wavelets.
3. The amplitude of secondary wavelets decreases with angle; they are effective only in the forward direction.

Reflection Using Huygens' Principle

For plane wave on plane mirror:

• Wave reaches mirror surface at points successively
• Each surface point emits secondary wavelets
• Tangent to all wavelets gives reflected wavefront
• Proof: Shows ∠i = ∠r (law of reflection)

Refraction Using Huygens' Principle

Wave crosses boundary from medium n₁ to n₂:

• Speed changes: v₁ in medium 1, v₂ in medium 2
• Proof: sinθ₁/sinθ₂ = v₁/v₂ = n₂/n₁ → Snell's Law

Coherent Sources

For sustained interference, sources must be coherent — same frequency, constant phase difference.

Methods to get coherent sources:

1. Young's double slit (division of wavefront)
2. Lloyd's mirror
3. Thin film interference (division of amplitude)
4. LASER sources

Two independent sources are NOT coherent — they cannot produce sustained interference.

Wave Nature of Light: Evidence

• Interference (Young's 1801)
• Diffraction
• Polarization
• These phenomena CANNOT be explained by Newton's corpuscular theory.

Diagram Indicator: [Huygens' construction showing plane wavefront with secondary wavelets as circles and new wavefront as their common tangent; also spherical wavefront expanding from point source.]

Young's Double Slit Experiment

Young's Double Slit Experiment (YDSE)

Thomas Young (1801) demonstrated light interference, proving its wave nature.

Setup: Monochromatic light → single slit S → double slit S₁S₂ (separation d) → screen (distance D)

Path Difference and Phase Difference

For point P on screen at height y from center:

Path difference: Δ = yd/D = S₂P − S₁P

Phase difference: φ = (2π/λ)·Δ

Conditions for Bright Fringes (Constructive Interference)

Δ = nλ (n = 0, ±1, ±2, ...)

y_n = nλD/d (position of nth bright fringe)

Conditions for Dark Fringes (Destructive Interference)

Δ = (2n−1)λ/2

y_n = (2n−1)λD/2d (position of nth dark fringe)

Fringe Width

β = λD/d (distance between consecutive bright or dark fringes)

Key relations: β ∝ λ, β ∝ D, β ∝ 1/d

Intensity Distribution

I = 4I₀ cos²(φ/2)

• Maximum (bright): I_max = 4I₀ (when φ = 0, 2π, ...)
• Minimum (dark): I_min = 0 (when φ = π, 3π, ...)

Important Cases

Fresnel vs Fraunhofer Diffraction

• Fresnel (near-field): Screen and/or source at finite distance
• Fraunhofer (far-field): Plane wavefronts, screen at infinity (or use lens)
• YDSE is a special case of wavefront division interference

Diagram Indicator: [YDSE setup showing S₁, S₂ separated by d, screen at D; path difference calculation showing Δ=yd/D; intensity vs y graph showing alternating bright and dark bands with equal spacing β=λD/d.]

Diffraction and Polarisation

Diffraction

Diffraction is the bending of waves around obstacles and through slits, significant when slit width ≈ wavelength.

Single Slit Diffraction (Fraunhofer)

For single slit of width a, wavelength λ:

Condition for minima: a sinθ = mλ (m = ±1, ±2, ...)

Angular width of central maximum: 2λ/a (between first minima on both sides)

Linear width: 2λD/a (on screen at distance D)

Intensity Pattern

• Central maximum: Wide and bright
• Secondary maxima: Decrease rapidly (1/22 intensity)
• Minima: At a sinθ = mλ

Condition for maxima: a sinθ = (2m+1)λ/2

Difference: Interference vs Diffraction

Resolving Power

Rayleigh's criterion: Two sources are just resolved when central maximum of one falls on first minimum of other.

Resolving power of telescope: D/(1.22λ) (D = objective diameter) Resolving power of microscope: ∝ n sinα/λ (numerical aperture)

Polarisation

Polarisation is a property of transverse waves — restriction of vibrations to a single plane.

Unpolarised light: Electric field vibrates in all planes perpendicular to propagation. Plane polarised light: Electric field vibrates in only one plane.

Methods to Produce Polarised Light

1. Polaroid (dichroism): Selective absorption of one component
2. Reflection (Brewster's law): At Brewster angle, reflected light is polarised
3. Refraction through crystal: Double refraction (calcite, quartz)
4. Scattering: Sky appears blue due to Rayleigh scattering

Malus's Law

When polarised light of intensity I₀ passes through analyser at angle θ to polariser axis:

I = I₀ cos²θ

• θ = 0°: I = I₀ (maximum)
• θ = 90°: I = 0 (crossed polaroids)

Brewster's Law

At Brewster angle (polarising angle θ_B):

tan θ_B = n

At this angle, reflected light is completely plane polarised (⊥ to plane of incidence).

For glass (n=1.5): θ_B = tan⁻¹(1.5) ≈ 56.3°

Diagram Indicator: [Single slit diffraction pattern showing central bright maximum with secondary maxima of decreasing intensity; also polaroid diagram showing unpolarised light becoming plane polarised after passing through polariser, and Malus law setup with analyser at angle θ.]

Frequently asked questions

Are these Wave Optics notes free?

Yes — the Wave Optics notes for Physics (Class 12) on Siksha Sarovar are completely free to read, with no account required.

Do these notes follow CBSE and HBSE?

Yes. The Wave Optics notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.

What does the Wave Optics chapter cover?

Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Wave Optics.