🌊 Physics — Class XII

Wave Optics

Light as a wave — interference, diffraction, and polarisation phenomena

📖 Chapter 10 ⏱ ~50 min read 🏷️ Optics

Introduction
Huygens' Principle
Refraction Using Huygens' Principle
Young's Double Slit Experiment
Interference of Light
Diffraction of Light
Polarisation

10.1 Introduction

In 1637 Descartes gave the corpuscular model of light and derived Snell's law. It explained the laws of reflection and refraction of light at an interface. However, the corpuscular model could not explain phenomena like interference, diffraction, and polarisation — which require the wave nature of light.

10.2 Huygens' Principle

Huygens' principle states that every point on a wavefront acts as a source of secondary wavelets. The new wavefront is the tangential surface (envelope) of all these secondary wavelets.

Figure 10.1 — Young's double slit experiment, single slit diffraction, and key wave optics concepts

Each point on the wavefront becomes a source of secondary wavelets
Secondary wavelets spread out in all directions with speed of light
The new wavefront is the forward envelope of secondary wavelets
Explains rectilinear propagation, reflection, and refraction

10.3 Refraction Using Huygens' Principle

Huygens' principle explains Snell's law of refraction. When a wavefront passes from one medium to another with different speed, the secondary wavelets travel at different speeds, causing the wavefront to bend.

10.4 Young's Double Slit Experiment

Young's double slit experiment (YDSE) provides definitive evidence of the wave nature of light through interference:

β = λD/d

β = fringe width, λ = wavelength, D = distance to screen, d = separation between slits.

Bright fringes: Path difference = nλ (constructive interference)
Dark fringes: Path difference = (n+½)λ (destructive interference)
Fringes are equally spaced and parallel to the slits
Fringe width increases with wavelength (violet → red)

10.5 Interference of Light

Interference occurs when two coherent waves superpose. The resultant intensity depends on the phase difference:

I = I₁ + I₂ + 2√(I₁I₂) cos φ

φ = phase difference. For equal intensities: I = 4I₀cos²(φ/2). Constructive: I_max = 4I₀. Destructive: I_min = 0.

10.6 Diffraction of Light

Diffraction is the bending of light around obstacles and through apertures. In single slit diffraction:

a sin θ = nλ (minima)

a = slit width. Central maximum is twice as wide as secondary maxima. Intensity: I = I₀ sinc²(β/2).

💡 Diffraction vs Interference

Interference: Superposition of waves from two coherent sources. All bright fringes have equal intensity.
Diffraction: Superposition of waves from different parts of the same wavefront. Central maximum is brightest, secondary maxima decrease in intensity.

10.7 Polarisation

Polarisation proves that light is a transverse wave. A polariser selects only one direction of vibration:

I = I₀ cos²θ (Malus' Law)

θ = angle between polariser axis and incident light's plane of polarisation. Unpolarised light becomes half after passing through one polariser.

Ch 9 — Ray Optics Ch 11 — Dual Nature of Radiation