Lecture on Light and Wave Theory

Introduction

• Question: What does the shadow of a coin hanging in mid-air look like?
  • It has a bright spot of light in the middle.
• Experiment: Coin's shadow with a bright spot proves light is a wave.

17th and 18th Century Physics

• Initial belief: Light was a particle.
• Shift over time: Evidence built up that light might be a wave.
• Current understanding: Light is both a particle and a wave.

Huygens' Principle

• Christian Huygens: Dutch physicist who believed light acted as a wave.
• Huygens' Principle: Predicts a wave's future position by analyzing its current position.
  • Each point on the wave acts as the source of its own smaller wave.
  • Velocity x Time = Distance principle applies to each wave point.
  • Wavelets: Small half-circles drawn in front of each wave point.
  • Tangent line to wavelets predicts the wave's position over time.

Wave Diffraction

• Diffraction: Wave re-shaping by obstacles.
  • Example: Wave passing the edge of a flat object curves around the edge.
  • Slits the same width as the wavelength cause wave to spread out circularly.
• Contrast with Particles: Particles like marbles would hit directly opposite the doorway without spreading.

Diffraction and Interference

• Interference Types: Constructive and Destructive
  • Constructive: Waves' crests and troughs align, increasing amplitude.
  • Destructive: Crests and troughs misalign, reducing amplitude.
• Example: Double-slit experiment by Thomas Young (1801)
  • Single stream of light through two slits creates multiple bright lines (diffraction pattern).
  • Path difference determines constructive or destructive interference.

Wave Properties

• Intensity: Energy transported by light per unit area over time, proportional to amplitude squared.
  • Larger amplitude = higher intensity (brightness).
• Frequency and Wavelength: Determine light's color and visibility.
  • Higher frequency = blue.
  • Lower frequency = red.
  • White light is a combination of all colors.

Single Slit Diffraction

• Pattern: Series of lines that get dimmer farther from the center.
  • Bright line opposite the slit, caused by zero path difference.
  • Different angles cause different path differences, influencing interference.
  • Destructive interference: Light rays cancel out if shifted by half a wavelength.
  • Constructive interference: Total path difference of 1.5 wavelengths creates bright lines.

Coin Shadow Phenomenon

• Diffraction: Light waves curve around the coin's edges.
  • Constructive Interference: Bright spot where waves combine crest and troughs.
  • Destructive Interference: Shadows created by wave misalignment.

Conclusion

• Summary: Light's wave theory, Huygens' principle, diffraction, and interference.
• Double-slit experiment and diffraction patterns explained.
• Application in real-world phenomenon like the coin's shadow bright spot.