Knowt
wave optics
Wave Optics
10.1 Introduction
In 1637, Descartes presented the corpuscular model of light and derived Snell’s Law.
Explained reflection and refraction laws.
Predicted light speed would be greater in the medium the light bent toward.
Isaac Newton further developed this model in his book OPTICKS, leading to its widespread acceptance.
In 1678, Christiaan Huygens proposed the wave theory of light, which clarified reflection and refraction:
Contrary to the corpuscular model, it indicated light slows down when entering a denser medium.
Confirmed by Foucault in 1850's experiments.
Wave model faced initial opposition, as it suggested light needed a medium to travel, conflicting with light's vacuum propagation.
Maxwell's Electromagnetic Theory:
Proposed light as electromagnetic waves in varying electric and magnetic fields.
Successfully calculated light speed in vacuum, supporting the wave model.
10.2 Huygens Principle
Wavefront Definition:
A wavefront is the locus of points oscillating in phase, e.g., circles from a dropped stone in water.
Wave speed is defined as the speed at which the wavefront moves outward.
Types of Waves:
Spherical Waves: Emanate from a point source.
Plane Waves: Approximation of spherical waves at significant distance.
Huygens Principle: Each point on a wavefront serves as a source of secondary wavelets.
Secondary Wavelet Construction:
The new wavefront can be determined by drawing tangents to these wavelets.
10.3 Refraction and Reflection of Plane Waves Using Huygens Principle
10.3.1 Refraction of a Plane Wave
Use Huygens principle to derive laws of refraction.
Given a plane wavefront AB incident on an interface at angle i, laws yield:
Calculation of sin i and sin r using wave speeds in different media: n1 sin i = n2 sin r (Snell’s law).
Speed and wavelength relations: v2 < v1 if the wave bends toward the normal.
10.3.2 Refraction at a Rarer Medium
Shows that for v2 > v1, the angle of refraction (r) will exceed the angle of incidence (i).
Introduction of critical angle (iC), where:
If i > iC, total internal reflection occurs.
10.3.3 Reflection of Plane Waves
Analysis of plane wave AB hitting reflective surface MN reveals:
Angles of incidence and reflection are equal (law of reflection).
10.4 Coherent and Incoherent Addition of Waves
Discusses interference patterns from wave superposition principles.
Constructive Interference: Resulting amplitude is greater; I = 4I0.
Destructive Interference: Waves cancel, leading to zero intensity.
10.5 Interference of Light Waves and Young's Experiment
Ordinary light sources, e.g., sodium lamps, are incoherent due to phase variation.
Young's Double Slit Experiment:
Locks the phases of light waves from two closely placed pinholes to create interference fringes.
Formulas for fringe position based on coherent wave theory.
10.6 Diffraction
Diffraction: Light bending around obstacles, resulting in patterns beyond geometrical shadow.
Notable in a single slit experiment producing complex intensity distributions.
Related terms: maxima and minima observed with increasing angles.
10.7 Polarisation
Characterizes waves based on their direction of displacement which can be linear or unpolarised.
Demonstrates how polaroids polarise light, exhibiting Malus' Law for intensity changes.
Summary Points
Huygens Principle: Each point on a wavefront acts as a secondary source; determines future wave shapes.
Superposition Principle: Coherent light sources result in stable interference patterns.
Young’s Double Slit: Creates evenly spaced interference fringes based on path differences.
Diffraction: Explains phenomena observed in shadow regions where light bends.
Polarisation: Light can be filtered for intensity control and varies with the configuration of polarizing elements.
Exercises
Calculate properties of light transitioning between media (e.g., wavelength, frequency, speed).
Identify wavefront shapes for sources like point sources and lenses.
Apply Snell’s Law to analyze light behavior at interfaces and critical angles.
