Geometrical Optics

In this section, we will explore the fundamental principles that govern how light behaves when it encounters different media and surfaces.

Learning Objectives

By the end of this section, you should be able to:

  • Understand and apply the laws of reflection and refraction.
  • Analyze image formation by mirrors, lenses, and prisms.
  • Describe the working principles of various optical instruments.
  • Explain phenomena such as dispersion and imaging errors.

Topics Covered

  1. Reflection Explore how light reflects off surfaces following the law of reflection.

  2. Refraction and Total Internal Reflection Understand how light bends when passing through different media and the conditions for total internal reflection.

  3. Mirrors,Prisms and Lenses Learn about various optical elements and how they form images.

  4. Optical Instruments Study devices like telescopes and microscopes that utilize mirrors and lenses.

  5. Dispersion Discover how different wavelengths of light refract differently, leading to phenomena like rainbows.

  6. Imaging Errors Examine common aberrations in optical systems and methods to correct them.

Introduction

Geometrical optics is an approximate description of light propagation in the limit of infinitely small wavelength, where all wave phenomena like diffraction can be neglected.

Light rays passing through a lens system generated with Tantalum

Light interacts with materials in predictable ways, allowing us to design optical systems for imaging, magnification, and more.

Assumptions of Geometrical Optics

Geometrical optics provides an approximate description of light behavior and is based on several key assumptions. These assumptions simplify the complex nature of light while still allowing for accurate predictions in many practical scenarios.

Core Assumptions
  1. Light Sources and Detection:
    • Light rays emerge from a light source
    • Light rays are detected by a detector
  2. Light-Matter Interaction:
    • Interaction is characterized by a refractive index \(n\)
    • The speed of light in a medium is given by \(c=c_0/n\), where \(c_0\) is the speed of light in vacuum
    • The speed in vacuum is 299.792.458 m/s and is connected to the definition of the meter
  3. Light Propagation:
    • Light propagates in straight line paths (rays) in a homogeneous medium
    • Light bends to a curved path in inhomogeneous media with varying refractive index \(n(\textbf{r})\)
  4. Behavior at Interfaces:
    • Rays may be reflected and refracted at interfaces between media

These assumptions form the foundation for understanding and predicting light behavior in the context of geometrical optics.