Introduction
Early Models of Light
Corpuscular Model (1637): Proposed by Descartes, developed by Isaac Newton. Explained laws of reflection and refraction. Predicted that speed of light is greater in the second medium if the ray bends towards the normal.
Wave Theory (1678): Proposed by Christiaan Huygens. Explained phenomena of reflection and refraction. Predicted that speed of light is less in the second medium if the wave bends towards the normal.
Establishment of Wave Theory
Experiment by Foucault (1850): Confirmed that speed of light in water is less than in air, supporting the wave theory.
Interference Experiment by Thomas Young (1801): Demonstrated that light is a wave phenomenon. Measured wavelength of visible light (e.g., yellow light: 0.6 μm).
Geometrical Optics
Definition: Branch of optics that neglects the finiteness of wavelength, assuming light travels in straight lines.
Ray: Defined as the path of energy propagation in the limit of wavelength tending to zero.
Electromagnetic Theory of Light
Maxwell's Theory: Light is an electromagnetic wave, associated with changing electric and magnetic fields.
Wave Equation: Derived from Maxwell's equations, predicting the existence of electromagnetic waves.
10.2 Huygens Principle
Example: A photograph of a pool of water with circular rings of disturbance after a stone is dropped.
Types of Wavefronts:
1. Spherical Wave: Locus of points with same amplitude and phase are spheres.
2. Plane Wave: A small portion of a sphere at a large distance from the source, considered as a plane.
Huygens Principle-Definition
Huygens Principle is a geometrical construction to determine the shape of a wavefront at a later time. According to Huygens principle, each point of the wavefront is the source of a secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of the wave. These wavelets emanating from the wavefront are usually referred to as secondary wavelets and if we draw a common tangent to all these spheres, we obtain the new position of the wavefront at a later time.
Application of Huygens Principle
We can use Huygens principle to determine the shape of the wavefront for a diverging wave and plane wave propagating through a medium.
Huygens' Adhoc Assumption: The model predicts a backwave, which is not observed. He argued the amplitude of secondary wavelets is maximum in the forward direction and zero in the backward direction. But the absence of the backwave is justified by more rigorous wave theory.
10.3 Refraction and Reflection of Plane Waves using Huygens Principle
Refraction of a Plane Wave:
- Assumptions: A plane wavefront AB propagating in medium 1, incident on the interface with medium 2 at an angle i.
- Speed of light: v1 in medium 1, v2 in medium 2
- Time taken: t for the wavefront to travel distance BC
Derivation of Refraction Laws