Light and Optical Systems Study Notes

Learning Unit 2: Light, Optical Systems, Rays, and the Eye

Table of Contents

  • Light

  • Gaussian Optics

  • Optical Systems

  • Examples of Optical Systems

  • The Eye as an Optical System

  • The Ray

  • Snell’s Law

  • Index of Refraction

  • The Ray Traversing a System

  • Looking Ahead to Three-dimensions

  • References

  • Outline of Solutions to Exercises

Light

  • Light is that part of the electromagnetic spectrum to which the human eye is sensitive for vision.

  • The approximate frequency range of light spans from 4.0 imes 10^{14} ext{ Hz} (red end) to 7.5 imes 10^{14} ext{ Hz} (violet end).

  • Light in vacuum travels at approximately 300,000 ext{ km/s}.

  • Light of wavelength 550 nm (in vacuum between 760 ext{ nm} to 393 ext{ nm}) corresponds to yellow; in different media, wavelengths differ but frequency remains constant.

  • Ultra-violet and infra-red radiation are outside the visible range.

  • UV light claims surrounding health and its necessity for the body in regulated amounts brings skepticism towards advertised products claiming to block all UV.

Gaussian Optics

  • Gaussian optics is a two-dimensional framework for modeling optical systems using ray diagrams and relationships (object distance, image distance, focal length).

    • Definitions & Levels of Optics

    • Gaussian Optics: Fundamental and lower-level optics for practical applications.

    • Linear Optics: A three-dimensional extension, applying linear algebra to model vision.

    • Geometric Optics: Commonly taught in schools, including laws of reflection, and refraction (Snell's law). Higher level, less focus in this course.

    • Wave Optics: Includes diffraction, interference, and polarization.

    • Electrodynamics: Addresses electromagnetic optics without quantum effects.

    • Quantum Electrodynamics: Current light theory involving photons; a blend of particle and wave explanations.

    • Eddington described a photon as a ‘wavicle’.

    • Importance of Gaussian optics in vision, mainly due to the linear behavior of light.

Optical Systems

  • Optical systems consist of directed longitudinal axes and may not align with common optical axes.

  • Optical systems include lenses and the eye. They are portrayed generally as systems through which light traverses.

    • General Representation: Optical systems are represented as S and include examples like:

    • A homogeneous gap of water.

    • A single gently curved refracting interface.

    • A glass lens in air with thickness t.

    • A spectacle lens in front of the eye.

    • A telescope composed of multiple lenses.

The Eye as an Optical System

  • Notable observations: the human eye can detect as few as five photons under ideal experimental conditions.

  • Structure representations:

    • Components include interfaces, aqueous humor, cornea, lens, vitreous body, and retina.

    • The eye is divided into an anterior section (front) and posterior section (back).

The Ray

  • Rays are theoretical concepts within Gaussian optics; they are directed lines without specific physical attributes, thus lacking wavelength and inherent speed.

  • Rays convey information through their orientation (inclination heta) and position relative (y).

    • Information expressed as ray vectors or ray states observed at transverse planes (T) with defined positions y and inclinations a.

Snell’s Law

  • Describes the relationship of angles and refraction across media:
    n_1 imes ext{sin}( heta_1) = n_2 imes ext{sin}( heta_2) where n is the index of refraction.

  • Reduced angle remains constant across different materials without applying the higher complexity of geometric optics.

Index of Refraction

  • Index values for various media listed include:

    • Vacuum: 1

    • Air: 1.0003

    • Water: 1.333

    • Crown Glass: 1.52

    • Diamond: 2.42

    • Special materials (Bose-Einstein condensates) postulate indices nearing -1 or as complex numbers.

The Ray Traversing a System

  • A ray’s state changes when it moves across an optical system. This transformation affects the way light is processed by the retina for visual interpretation.

  • Exercises related to ray state estimations, calculations involving refractive indices, and geometric interpretations conducted.

Looking Ahead to Three-dimensions

  • Future discussions will integrate three-dimensional optical systems with the concept of varying ray state via 4D lists of coordinates incorporating horizontal and vertical components.

References

  1. Pendry JB. Negative refraction makes a perfect lens. Phys Rev Letters 2000 85 3966-3969.

  2. Harris WF. Stigmatic optical systems. Optom Vis Sci 2004 81 947-952.

Outline of Solutions to Exercises

  • Exercise solutions provided for conceptual understanding of ray optics, vergence, and exercises can further help in practical applications and calculations in optics.

Additional Concepts

Pencils, Vergence and Wavefronts

  • Pencils refer to sets of rays converging/diverging towards points.

  • The concept of vergence versus wavefront representation is crucial in understanding light behavior in optical contexts.

Exercises & Practice Problems

  • Included at the end of the unit, with many practical assessments of understanding, calculations, and graphical interpretations of optical phenomena.