Geometrical Optics - Lecture Notes

Light

Introduction

  • Light enables us to perceive the world through vision.
  • Eyes convert light into electrical signals, which the brain processes into images.
  • Light helps us understand atoms and stellar systems.
  • Optics is the branch of physics that studies light's generation, propagation, and interaction with matter.

Brief History

  • Geometric Optics:
    • Euclid (300 B.C.): Angle of incidence equals the angle of reflection.
    • Hero of Alexandria: Light takes the shortest path between two points.
    • Claudius Ptolemy (130 A.D.): Measured angles of incidence and refraction.
    • Francis Bacon (1215-1294): Suggested using lenses to improve eyesight.
    • 1280: Spectacle lenses used to correct vision.
    • 1609: Galileo devised a practical telescope.
    • 1632-1723: Van Leeuwenhoek developed the first microscope.
    • John Kepler: Discovered total internal reflection.
    • 1621: Willebrod Snell (1591-1626) & 1637: Rene Descartes (1596-1650): Discovered the law of refraction.
      • Snell's Law: sin⁡isin⁡r=μ\frac{\sin i}{\sin r} = \mu
    • 1658: Fermat (1601-1655): Principle of least time. Light follows the path of shortest time.
    • 1660: Grimaldi (1618-1663): Noticed diffraction.
    • 1667: Newton: White light is composed of seven independent colors.
    • 1670: Bartholinus (1625-1698): Discovered double refraction.
    • 1675: Isaac Newton (1642-1727): Corpuscular theory.
      • Luminous bodies emit corpuscles.
      • Corpuscles travel in straight lines with finite velocity.
      • Could explain straight line propagation and sharp shadows.
      • Failed to explain continuous loss of weight from light sources.
      • Predicted light travels faster in denser media.
    • 1676: Romer (1644-1710): Proved light travels with a finite velocity.
    • Robert Hooke (1635-1703): Studied thin film interference.
  • Wave Optics:
    • 1678: Huygens (1629-1695): Proposed wave theory.
      • Light energy transfers via waves.
      • Explained reflection and refraction.
      • Predicted light travels slower in denser media.
      • Explained double refraction with two types of waves.
      • Initially not accepted because wave motion requires a medium, but light travels through vacuum.
    • 1803: Thomas Young (1773-1829): Demonstrated interference of light beams.
      • Explained Newton's rings and thin film colors.
      • Supported wave theory.
    • 1808: Malus (1775-1812): Discovered polarization of light.
    • 1815: Augustin Fresnel (1788-1827): Developed wave theory, explained rectilinear propagation and diffraction.
      • Both Young and Fresnel assumed longitudinal light waves which required an elastic medium called luminiferous ether.
      • Later they realized light is a transverse wave and explained polarization.
    • 1850: Jean Foucault (1791-1868): Established light travels slower in liquids than in air.
    • 1823: Fresnel Derived expressions for reflection and transmission coefficients based on ether theory.
  • Nature of Light:
    • Around 1836: Faraday (1791-1867): Showed varying magnetic field induces electromotive force, linking electricity and magnetism; polarization of light affected by magnetic field.
    • 1873: Clerk Maxwell (1831-1879): Unified electricity and magnetism into electromagnetism.
      • Showed electromagnetic wave speed equals light speed.
      • Predicted light is a high-frequency electromagnetic wave.
    • 1887: Hertz (1857-1894): Confirmed Maxwell's prediction by producing and detecting electromagnetic waves.
    • H.A. Lorentz (1853-1928): Assumed ether is in absolute rest as carrier of electromagnetic field.
    • 1887: Michelson-Morley: Ether-drift experiment showed light travels at same speed regardless of Earth's position, leading to conclusion that ether does not exist. Light is a self-sustaining electromagnetic wave.
      • This is known as Field Theory.
  • Quantum Optics:
    • 1814: Fraunhofer: Discovered dark lines in solar spectrum.
    • 1861: Bunsen and Kirchhoff: Attributed dark lines to absorption by gases in the sun's atmosphere. Every element has a characteristic line spectrum.
    • 1900: Max Planck (1858-1947): Light is absorbed or emitted in elementary quanta.
    • 1905: Einstein (1879-1955): Explained photoelectric emission using the quantum concept; Light is a stream of photons.
    • 1913: Niels Bohr (1885-1962): Devised atomic model for emission and absorption of light using Planck's quantum hypothesis.
    • 1960: First coherent source of light (laser) was built.
  • A photon is a bundle of electromagnetic radiation with definite frequency and speed.
  • Photons have energy and momentum, exhibiting particle-like properties.
  • Large numbers of photons behave as continuous waves.
  • Phenomena like interference, diffraction, and polarization are explained by electromagnetic wave theory.
  • Experiments involving light-matter interaction (photoelectric effect) are explained by light as a particle.

The Four Important Theories

  1. Corpuscular theory
  2. Wave theory
  3. Electromagnetic theory
  4. Quantum theory
Corpuscular Theory
  • Postulated by ancient Greeks and favored by Isaac Newton.
  • Luminous bodies emit tiny, light, and elastic particles called corpuscles.
  • These particles travel through matter and reflect from polished surfaces or transmit through transparent media.
  • Falling on the retina produces the sensation of vision.

The Sources of Light

  • Luminous bodies (e.g., sun, stars, lamps) emit light.
  • Non-luminous bodies (e.g., moon, mountains, trees) are visible by reflected light.
  • Whether a body is luminous depends on conditions and material.
  • Bodies emit light at the expense of various kinds of energy, such as thermal radiation.
  • When bodies are heated, they emit electromagnetic radiation.
  • At 300∘C300^{\circ}C, they emit infrared radiation (λ=5μm\lambda = 5 \mu m).
  • At 800∘C800^{\circ}C, they emit visible radiant energy (red hot).
  • At around 3000∘C3000^{\circ}C, they appear white hot (incandescent).
  • Emission of light due to supply of energy through processes other than heat is called luminescence.
    • Electroluminescence: Emission of light when charged particles are accelerated by an electric field partly transmit their kinetic energy to the atoms of the gas.
    • Chemiluminescence: Emission of light due to chemical reactions (e.g., fireflies).
    • Photoluminescence: Emission of cold light when a phosphor material emits visible light under the action of UV light (e.g., tube lights).
    • Cathodoluminescence: Emission of light when a screen is bombarded by high-energy electrons (e.g., TV screens).

Properties of Light

Reflection, refraction, dispersion, and velocity are important properties of light.

Reflection of Light
  • When light encounters a boundary, part of it returns to the first medium.
  • Reflection from a smooth surface is specular reflection.
  • Reflection from a rough surface is diffuse reflection.
  • The term