Light and Optics: Reflection, Refraction, Color

• Light's nature has been understood only in the last 250 years; it is electromagnetic waves produced by moving charges.
• Light's importance drives inquiry into its nature.

The Speed of Light

• Early studies, including those by Galileo, aimed to measure light speed.

Galileo's Experiment

• In 1667, Galileo and an assistant attempted to measure the speed of light using lanterns on separate mountains.
• The impracticality of this method was due to the incredibly high speed of light

Roemer's Discovery

• In 1675, Ole Roemer observed Jupiter's moons and their eclipses at varying times depending on Earth's position.
• Eclipses appeared sooner when Earth was closer to Jupiter and were delayed by 16.6 minutes when farther away.
• Roemer estimated the speed of light at c = 2.3*10^8 m/s based on these time differences.

Fizeau's Experiment

• In 1849, Hippolyte Fizeau used a rotating cogwheel to measure the speed of light
• A light beam passed through gaps in the wheel's teeth, traveled to a distant mirror, and reflected back.
• The rotational speed of the wheel allowed Fizeau to accurately determine the speed of light.
• The light beam travels a total distance of 2L to the mirror and back
• The cogwheel has N teeth and an equal number of gaps
• Angular distance between consecutive teeth or gaps is 2π/2N = π/N
• The derived formula is C = 2Lω/θ ≈ 3*10^8 m/s
• L represents the distance to the mirror
• c is the speed of light
• θ is the angular distance between cogwheel teeth in radians
• ω is the angular velocity of the rotating wheel

Foucault's Experiment

• Léon Foucault improved upon Fizeau's work in 1860 with a rotating mirror system.
• A light source was directed towards an eight-sided rotating mirror.
• The light reflected from the mirror to a fixed mirror and back.
• The rotation speed was adjusted so the light returned to the observer through the same path.
• A signal occurred when the mirror rotated 1/8 turn in ΔT.
• This confirmed the finite speed of light, measured at c = 2.98 * 10^8 m/s.

The Nature of Light and Electromagnetic Waves

• Light travels at approximately 300,000 kilometers per second.
• Light can orbit Earth 7-8 times in one second.
• This explains why lightning is seen before thunder, as sound travels much slower (1100 m/s).

The Visible Spectrum

• Light is part of the electromagnetic spectrum.
• The visible range for humans spans from 400 nanometers (deep blue) to 700 nanometers (deep red).

White Light and Color Perception

• White light contains all colors in the visible spectrum.
• White light is perceived when all frequencies are approximately equal.
• Color combinations:
  • Blue and red make magenta.
  • Blue and green make cyan (light blue).
  • Red and green make yellow.
  • Combining red, blue, and green in equal amounts produces white.
• Objects appear colored based on the light they reflect.
• A yellow object reflects yellow light, while a white object reflects all colors.

Filters and Color Selection

• Color filters selectively allow specific colors from white light to pass through by absorbing others.
• A red filter allows only red light to pass through.

Light Dispersion

• White light disperses into its component colors when passing through a prism.
• This dispersion happens due to different wavelengths traveling at different speeds through the medium, resulting in a spectrum from blue to red.

Exploring Light: Reflection and Refraction

Experiment with a Laser and Mirror

• Part of the light passes through the mirror, while another part gets reflected.
• Key concepts of reflection:
  • Incident Ray: The incoming light ray that strikes the mirror.
  • Reflected Ray: The light ray that bounces off the mirror.
  • Angle of Incidence: The angle between the incident ray and the normal.
  • Angle of Reflection: The angle between the reflected ray and the normal.
• In a smooth mirror, the angle of incidence equals the angle of reflection.

Diffuse Reflection

• Light scatters in many directions upon hitting a rough surface.

Refraction of Light

Experiment with a Laser and Glass

• Light bends towards the normal upon entering the glass.
• Light bends away from the normal upon exiting the glass and re-entering the air.

Key Concepts of Refraction

• Refraction: The bending of light as it passes from one medium to another.
• Normal: A line perpendicular to the surface at the point of incidence.
• Angle of Incidence: The angle between the incident ray and the normal.
• Angle of Refraction: The angle between the refracted ray and the normal.
• Incident and transmitted light rays are parallel but displaced when light travels from air to glass and back to air.

Understanding Refractive Index and Light Behavior

Definition of Refractive Index

• Refractive index (n) is the ratio of the speed of light in a vacuum (c) to its speed in a medium (v):
  • Refractive index = Speed of light in vacuum / Speed of light in material

Reasons for Light Slowing Down

• Electrons in the medium interact with the light's electromagnetic field, causing them to vibrate and emit electromagnetic radiation, resulting in a new wave that moves slower

Refractive Index of Common Materials

• Air: 1.0003
• Water: 1.33
• Alcohol: 1.36
• Oil: 1.5
• Diamond: 2.42

Light Refraction Experiment with Water

• A laser beam bends towards the normal as water is added to a glass due to water's higher refractive index (1.33).

Effects of Refraction

• Objects submerged in water appear bent or displaced due to changes in light direction between water and air.

Fermat's Principle

• Light takes the path that requires the least time when traveling between two points, explained in "Kitab al-Manazir" by Ibn Al-Haytham.

Fermat's Principle Explained Light in Free Space:

• In free space or a vacuum, light travels in straight lines
• This is because a straight line is the shortest and quickest path between two points.

Refraction and Snell's Law

• Light bends when traveling from one medium to another due to changes in speed caused by different refractive indices.
• n₁ sin θ₁ = n₂ sin θ₂ (Snell's law of refraction)

Total Internal Reflection

• Light traveling from a higher to a lower refractive index medium can be totally internally reflected if the angle of incidence exceeds a critical angle.
  • Critical Angle: The angle beyond which light is totally internally reflected within the medium.

Applications:

• Optical fibers for communication.
• Diamond brilliance due to low critical angle and high refractive index.

Optical Fibers

• Optical fibers use total internal reflection to transmit light signals over long distances with minimal loss
• These consist of a core with a high refractive index surrounded by cladding with a lower refractive index.
• Light entering the fiber reflects internally, ensuring it travels through the core without escaping.

Structure of Optical Fiber

• Core: Thin glass thread with a high refractive index
• Cladding: Surrounds the core, providing a lower refractive index for total internal reflection
• Protective Covering: Encases the cladding

Optical Fiber in Communication

• 100 years ago, cables supported only 50-60 telephone calls; modern optical fibers handle millions due to total internal reflection.
• Advantages: high capacity and minimal signal loss.

The Nature of Light: Particle or Wave?

Historical Debate

• Newton's Particle Theory: Light consists of particles.
• Wave Theory: Light behaves as waves.

Modern Understanding

• Light exhibits both particle and wave properties (wave-particle duality).

Concept of Wavefronts

• Wavefronts:
  • Circular Wavefront: Originates from a point source and spreads in circles.
  • Plane Wavefront: Forms when circular wavefronts travel far.

Interaction with Obstacles:

• Waves change direction upon hitting obstacles, creating new wavefronts.
• This bending and spreading of light waves are due to their wave nature

Huygens' Principle

• Each point on a wavefront acts as a source of new wavelets when light encounters an obstacle.

Light as Electromagnetic Radiation

• Light is generated by accelerating charges.
• Power radiated by a single charge is P = (2 e²a²) / (3 c³)
• Includes Quantum Mechanics and Electromagnetic waves

Quantum Mechanics

• Introduced to explain atomic behavior and energy quantization.

Electromagnetic Waves

• Composed of electric and magnetic fields oscillating perpendicularly.
• Energy carried depends on field amplitude.
• They transport linear momentum and energy
• p = U/c
• Radiation pressures can be experimentally determined

Colors and Temperature

• The color of light indicates an object's temperature.
• Hotter objects emit shorter wavelengths (blue), while cooler objects emit longer wavelengths (yellow).

Radiation Pressure

• Light exerts pressure on objects when absorbed or reflected, stemming from the momentum carried by electromagnetic waves.

Solar Radiation Pressure

• Within the sun, radiation pressure counteracts gravitational pull, maintaining equilibrium.

Radiant Flux

• Total energy passing through a surface per unit time, called power, and is measured in watts (W) or joules/second (J/s)

Test your knowledge of light and optics. This quiz covers topics such as light perception, color mixing, reflection, refraction, and the behavior of light interacting with mirrors and filters. Questions cover the angles of incidence and reflection.