Geometrical Optics Study Notes

OPTICS COURSE OVERVIEW

  • Course Title: OPT 153: Geometrical Optics

  • Credits: 3

LEARNING OUTCOMES / COURSE OUTLINE

  • Topics To Be Covered:

    • Optics

    • Properties of Light

    • Reflection and Refraction

    • Pin-hole Camera

    • Sources of Line Waves

    • Virtual Images Formed by Plane Mirrors

    • Refraction of Light Waves by Rectangular and Triangular Prisms

    • Total Reflection Lenses

    • The Lens Equation and Examples

    • The Lens Makers Formula

    • Power of Lenses and Two Lenses in Contact

    • Spherical and Chromatic Aberration and Their Correction

    • Defects of Vision Including Astigmatism

    • Optical Instruments

ASSESSMENT

  • Breakdown of Grading:

    • Quiz, Assignments, Attendance, and Mid-Semester Exam: 30%

    • End of Semester Examination: 70%

TEXTBOOKS

  • Textbook: Giancoli, D.C. (2005). Physics for Scientists and Engineers with Modern Physics, Sixth Edition. Pearson Education International.

LECTURE 1 OVERVIEW

THE ELECTROMAGNETIC SPECTRUM

  • Wavelengths:

    • Ranges from radio waves to gamma rays

    • Heat from the sun, fires, and other radiators make things visible and are absorbed by the skin.

    • Uses in medicine for killing cancer cells and viewing inside bodies.

    • Electromagnetic spectrum includes microwaves, infrared, visible light, ultraviolet, X-rays, and others.

INTRODUCTION TO OPTOMETRY

  • Definition:

    • The practice of examining the eyes using suitable instruments or appliances for defects in vision and eye disorders to prescribe corrective lenses or other appropriate treatment.

WHAT IS OPTICS?

  • Definition:

    • Optics is a branch of physics involving the behavior and properties of light, including interactions with matter and the construction of instruments.

    • It describes the behavior of visible light, infrared light, and ultraviolet light.

    • Visible light is perceivable to the human eye within the wavelengths 4000 Å to 7000 Å (or 400 nm to 700 nm).

    • Imaging is enabled through an image-forming optical system.

    • Ray Optics (Geometrical Optics): Describes light propagation in terms of rays, considered to travel in fixed directions in straight lines until they encounter different media, causing changes in direction.

BRANCHES OF OPTICS

  • Main Branches:

    • Physical Optics:

    • Studies interference, diffraction, and polarization, where geometric optics approximations are invalid.

    • Geometrical Optics (Ray Optics):

    • Describes light propagation as geometric lines from sources through media to detectors.

    • Quantum Optics:

    • Concerns interactions of individual light quanta (photons) with atoms and matter.

LIGHT AND LIGHT BEAMS

  • Definitions:

    • Light is electromagnetic energy enabling vision.

    • A ray of light: Light traveling in one direction in a straight line.

    • Beam: A bundle of rays.

    • Photocells work on principle of electrons emitted by metals when exposed to light – translatable to human vision via the retina transmitting impulses through the optic nerve to the brain.

SOME PROPERTIES OF LIGHT

  • Light is produced by vibrating electric charges in atoms.

  • It travels straight and faster than sound.

  • Speed of light in vacuum: 300,000extkm/s300,000 ext{ km/s}, decreases in other media.

VISIBLE LIGHT AND THE EM SPECTRUM

  • White Light: Combination of all visible frequencies.

  • Black: Absence of light; objects appear black as they absorb all frequencies.

  • The perceived color of an object is due to reflected (opaque) or transmitted (transparent) light.

  • Light absorption occurs when its frequency matches natural vibration frequencies of electrons in material.

A RAY OF LIGHT

  • Light traveling straight is termed a ray; a collection of rays is a beam.

  • Rays in diagrams represented as straight lines; real rays possess a finite width.

  • Searchlights and torches emit parallel beams, with rays from distant point sources like the sun being nearly parallel.

SUN ECLIPSE AND PROPERTIES OF LIGHT

  • Non-luminous moon blocks light, causing shadows.

  • Eclipses formed based on angles of incidence and alignment of sun, moon, and earth.

  • Important distances:

    • Earth to Sun: 149.6 million km

    • Moon to Earth: 384,400 km

REFLECTION

  • Defined as the change of direction when light bounces off a surface.

  • Normal Line: Imaginary line at right angles where ray hits the surface.

  • We see objects because the reflected light reaches our eyes.

LAWS OF REFLECTION

  • First Law: Angle of incidence = Angle of reflection.

  • Second Law: Incident ray, normal, and reflected ray lie in the same plane.

TYPES OF REFLECTION

  • Irregular Reflection (Diffused): Occurs on rough surfaces, spreading light in all directions.

  • Regular Reflection (Specular): Occurs on smooth surfaces, forming clear images of the object.

IMAGE CHARACTERISTICS OF REFLECTION

  • Plane Mirrors:

    • The image formed is virtual, same size, erect, and laterally inverted.

REFRACTION

  • Change in direction of light from one medium to another due to speed change.

  • Occurs at angles into different refractive indices, causing light to bend.

  • Enables optical instruments like lenses and prisms; necessary for focusing images on the retina.

INDEX OF REFRACTION

  • Measures ray bending when passing from one medium to another, expressed as: n=cvn = \frac{c}{v}

    • Where:

    • cc = speed of light in vacuum,

    • vv = speed of light in the medium.

SNELL’S LAW

  • States that the incident ray, normal, and refracted ray all lie in the same plane.

  • The formula is given as: n<em>1sin⁡(θ</em>1)=n<em>2sin⁡(θ</em>2)n<em>1 \sin(\theta</em>1) = n<em>2 \sin(\theta</em>2)

    • Frequency of light remains constant across mediums while speed changes.

DISPERSION OF LIGHT

  • Occurs when white light passes through a prism, splitting into a spectrum of colors (VIBGYOR).

  • Different colors travel at different speeds, e.g., red travels faster than violet in glass.

TOTAL INTERNAL REFLECTION

  • Phenomenon when light travels from denser to less dense media, causing it to reflect internally.

  • Example: Water to air transition, light ray bends away from the normal.

CRITICAL ANGLE

  • Angle of incidence where refracted ray travels along the interface.

  • If incidence exceeds critical angle, total reflection occurs.

APPLICATIONS OF TOTAL INTERNAL REFLECTION

  • Fiber Optics: Light signals reflected within fibers for data transmission.

  • Medical Applications: In endoscopes for image capture.

  • Mirages: Examples from hot air bending light above roads and creating illusions.

PIN-HOLE CAMERA

  • Simplest camera design: box with a small opening.

  • Light rays hit the back of the box, forming an inverted image.

IMAGE CHARACTERISTICS

  • Real Images: Can be captured on screen, inverted and smaller than the object.

  • Photographic film captures light for developing a latent image.

MAGNIFICATION

  • Magnification (M) defined as: M=h<em>ih</em>oM = \frac{h<em>i}{h</em>o}

    • Where:

    • hih_i = height of the image,

    • hoh_o = height of the object.

    • If M > 1 , image is enlarged; M < 1 , image is reduced.

DISTANCE RELATIONSHIP

  • Expressed as: h<em>ih</em>o=d<em>id</em>o\frac{h<em>i}{h</em>o} = \frac{d<em>i}{d</em>o}

    • Where:

    • did_i = distance of image,

    • dod_o = distance of object.

EXAMPLE PROBLEM

  • Problem: Determine the size and magnification of an image from an 8.0 m tree standing 80 m in front of a 20 cm long pinhole camera.

    • hi=0.2080×8.0=0.02extmh_i = \frac{0.20}{80} \times 8.0 = 0.02 ext{ m}

    • Calculating magnification: M=0.2080=0.00025extxM = \frac{0.20}{80} = 0.00025 ext{x}

DEVIATION DUE TO A TRIANGULAR PRISM

  • Light refracted twice when passing through.

  • Ray bends upon entering and exiting based on refractive index changes.

  • Deviation defined as the angle between original and exiting paths.

ANGLE DEFINITIONS

  • Four critical angles to define:

    • ϕ1\phi_1: Angle of incidence entering prism

    • θ1\theta_1: Angle of refraction upon entering

    • ϕ2\phi_2: Angle of incidence exiting prism

    • θ2\theta_2: Angle of refraction upon exiting

DEVIATION ANGLE FORMULATION

  • Internal angles give expressible relations using geometry of prism:

    • α=ϕ<em>1−ϕ</em>2−θ<em>1+θ</em>2\alpha = \phi<em>1 - \phi</em>2 - \theta<em>1 + \theta</em>2

MINIMUM ANGLE OF DEVIATION

  • Varied by incidence angle until a minimum is found when light paths are parallel to base.

  • Relationship between angles when deviation is minimum: α<em>0=ϕ</em>0+θ0−A\alpha<em>0 = \phi</em>0 + \theta_0 - A

    • With ϕ<em>0\phi<em>0 = θ</em>0\theta</em>0.

REFRACTIVE INDEX IN TERMS OF DEVIATION

  • Express nn using:
    n=sin⁡(α0+A2)sin⁡(A2)n = \frac{\sin(\alpha_0 + \frac{A}{2})}{\sin(\frac{A}{2})}

  • Valid in small-angle approximations where α0\alpha_0 and AA are in radians.