Duel Nature of Light

Light Waves

• Light is an electromagnetic wave with electric and magnetic fields propagating at speed: $$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}\approx 3\times 10^8\text{ m/s}$$ where: $${ϵ}_0=8.85\times 10^{-12}\frac{C^2}{N\cdot m^2},{\mu }_0=4\pi \times 10^{-7}\frac{T\cdot m}{A}$$
• Wave equations: $$E(x,t)=E_0\sin (kx-vt),B(x,t)=B_0\sin (kx-vt)$$ with $B_0=\frac{E_0}{c}$ and $E$ and $B$ being perpendicular. You will learn more about this in Introductory Electromagnetic Theory

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Light Intensity

• Definition: $$I=\frac{P}{A}$$
• Electromagnetic wave intensity: $$I=\frac{E_0^2}{2{\mu }_{0}c}{\text{(W/m}}^2\text{)}$$
• Interference of two equal beams with phase difference ( \Delta \phi ): $$I_T=4I_1{\cos }^2\left(\frac{\Delta \varphi }{2}\right)$$

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Michelson Interferometer

• Intensity split at mirrors: $$I_1=I_2=\frac{I_0}{2},I_{1d}=\frac{I_0}{4}$$
• Final intensity at detector: $$I_{\text{detector}}=I_0{\cos }^2\left(\frac{\Delta \varphi }{2}\right)$$
• Phase difference: $$\Delta \varphi =\frac{2\pi }{\lambda }2(L_1-L_2)$$

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LIGO Interferometer

• A large-scale Michelson interferometer used to detect gravitational waves.

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Young’s Double-Slit Experiment

• Light passes through two slits and interferes on a screen.
• Path difference determines phase difference and interference pattern.

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Two-Slit Interference: Arithmetic

• Constructive interference: $$\Delta L=d\sin {\theta }_m=m\lambda$$
• Destructive interference: $$\Delta L=d\sin {\theta }_m=(m+\frac{1}{2})\lambda$$
• Phase difference: $$\Delta \varphi =\frac{2\pi }{\lambda }\Delta L$$

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Light: Wave or Particle?

• Light is unique because:
  • It is the fastest carrier of information.
  • It consists of massless particles carrying energy and momentum.
  • It interacts directly with our senses.
  • It has wave-like and particle-like properties.

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Interference and Diffraction Effects

• Examples:
  • Soap bubble colors
  • Opalescence (e.g., opals)
  • Butterfly wing coloration
  • Laser speckle patterns
  • Halo around the sun or moon
• Applications:
  • Holography
  • Film thickness measurement
  • High-precision spectroscopy

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Thin Film Interference

• Interference from reflections in thin films causes color patterns.
• Observed as fringes when using monochromatic light.
• Observed as color bands with white light.

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The Photoelectric Effect

• Observation:

  • Light ejects electrons from a metal surface.
  • The energy of ejected electrons depends on light frequency, not intensity.
  • No measurable time delay for electron ejection.

• Photoelectric equation:

  $$K_{\text{max}}=hf-\Phi$$

  where:

  • ( h ) is Planck’s constant (( 6.626 \times 10^{-34} ) J·s),
  • ( f ) is the frequency of light,
  • ( \Phi ) is the work function of the material.

• Stopping potential:

  $$K_C+e{V}_{\text{AC}}=0\Rightarrow K_C=e{V}_0$$

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Einstein’s Photon Hypothesis

• Light consists of quanta or photons.
• Each photon has energy: $$E=hf$$
• The concept helped explain the photoelectric effect and led to quantum mechanics.

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