Optics Chapter 2. Wave Optics
Recommended Article : 【Physics】 Physics Table of Contents
3. Young’s Experiment (Double-Slit Experiment)
1. Huygens’ Principle (also called Huygens’ construction)
⑴ Principle: Every point on a wavefront becomes a source of new wavefront
⑵ Principle of rectilinear propagation
① In modern quantum optics, atoms become point sources
② Question: If photons are absorbed by atoms and then re-emitted, why does light travel in straight lines? Why doesn’t it go backward?
③ Answer: Similar to how shockwaves exhibit reinforcement interference in the forward direction but destructive interference in other paths
⑶ Law of reflection
① Proof
Figure 1. Proof of the law of reflection based on Huygens’ principle [Footnote: 1]
○ Assumption 1: Due to the principle of rectilinear propagation, points O, P’’, Q’’ have the same phase
○ Assumption 2: Waves O’, P’, Q’ emitted from O, P’’, Q’’ after the same time have the same phase
○ Assumption 3: Points O, P, Q have the same phase difference
○ Conclusion: θ = θ’
② Light that doesn’t follow the law of reflection disappears due to destructive interference
③ Fixed end reflection: Reflection from a region with lower refractive index to a region with higher refractive index
○ Phase of the wave changes by π
④ Free end reflection: Reflection from a region with higher refractive index to a region with lower refractive index
○ Phase of the wave remains unchanged
⑷ Law of refraction
① Interpretation based on the wave nature of light
Figure 2. Proof of the law of refraction based on Huygens’ principle [Footnote: 2]
○ Assumption 1: Due to the principle of rectilinear propagation, points O, P’’, Q’’ have the same phase
○ Assumption 2: Waves O’, P’, Q’ emitted from O, P’’, Q’’ after the same time have the same phase
○ Assumption 3: Points O, P, Q have the same phase difference
○ Assumption 4: Define the time difference between O and Q as Δt
○ Conclusion
② Interpretation based on the particle nature of light
○ Light that doesn’t follow the law of refraction disappears due to destructive interference
○ Law of refraction can be analyzed from the energy-momentum perspective of photons
③ Example 1: Refraction of light by water: Objects appear shallower than their actual depth in water
④ Example 2: Refraction of light by lenses: Detailed description in Geometrical Optics
⑤ Example 3: Refraction of light by the atmosphere
○ Mirage phenomenon
○ Light travels slower in air with higher temperature
○ Cold air above, hot air below: Light from the sky passes through a layer of hot air and becomes visible
○ Cold air below, hot air above: Light from above bends downward, making objects appear suspended in the air
○ Phenomenon of the sun being visible below the horizon during sunrise and sunset
○ Phenomenon of the sun appearing elliptical near the horizon: Sun near the horizon appears elliptical
○ Fata Morgana
○ Twinkling stars
⑸ Principle of diffraction
⑹ Cherenkov radiation
① Phenomenon where charged particles move through a medium faster than the speed of light in that medium, emitting light
② Can be explained by reinforcement interference based on Huygens’ principle
2. Fermat’s Principle (also known as the Principle of Least Time)
⑴ Definition: Light traveling between two points follows the path that takes the least time
⑵ Interpretation of the law of reflection (to be updated)
⑶ Interpretation of the law of refraction (to be updated)
3. Young’s Experiment (Double-Slit Experiment)
Figure 3. Double-slit experiment with width a and spacing b
⑴ Double slit: Observing diffraction due to b
① d: Distance between slits
② L: Distance between screen and slits
③ Δx: Distance between points on the screen from the central point
⑵ Single slit: Observing diffraction due to a
① a: Width
② L: Distance between screen and slit
③ Δx: Distance between points on the screen from the central point
4. Electromagnetic Waves
⑴ Maxwell’s Equations
⑵ Wave Equations of Electromagnetic Waves
① The speed of electromagnetic waves can be derived from these wave equations
⑶ Poynting Vector
① Definition: Energy per unit area, per unit time
② Generation of electromagnetic waves
Figure 4. Generation of electromagnetic waves
③ Formulation
○ Electric field expression
○ Magnetic field expression
○ Common to electric field (E) and magnetic field (H)
○ e^3 component is 0
○ First derivative with respect to x is 0
○ First derivative with respect to y is 0
○ Maxwell’s Third Law: Introducing displacement current
○ Application of Maxwell’s Third Law
○ Final Poynting Vector expression
④ Permittivity
○ Definition: Property representing the electrical characteristics of non-conductors
○ Decrease in electric field intensity within a dielectric material due to polarization
○ Ordinary air has negligible conductivity
○ Rainy days show more attenuation due to increased air conductivity
⑤ Dielectric Loss Angle
○ Definition: For a specific frequency f, the dielectric loss angle θ such that f tanθ = fc
⑥ Intrinsic Impedance := Z = E / H
○ Relationship between electric field energy density We and magnetic field energy density Wm in space (η: intrinsic impedance)
○ Transmittance coefficient of the electric field
○ Transmittance coefficient of the magnetic field (Unit of H: AT / m)
○ Reflection coefficient = Reflected electric field intensity ÷ Incident electric field intensity
○ Changes in material are related to μ and ε, changing wavelength and amplitude but not frequency
○ Phase of electromagnetic waves is 90˚ behind displacement current
○ Z0 = E / H is real, so the phases of E and H are the same
⑦ Vector Magnetic Potential
○ In time-varying conditions
⑷ Types of Electromagnetic Waves
① Gamma-ray
○ Frequency range: > 8 × 1018 Hz
○ Wavelength range: < 0.04 nm
② X-ray
○ Frequency range: 8 × 1018 ~ 6 × 1016 Hz
○ Wavelength range: 0.04 ~ 5 nm
③ Ultraviolet (UV)
○ Frequency range: 6 × 1016 ~ 8 × 1014 Hz
○ Wavelength range: 5 ~ 380 nm
④ Visible light
○ Frequency range: 8 × 1014 ~ 4 × 1014 Hz
○ Wavelength range: 380 ~ 780 nm
⑤ Infrared (IR)
○ Near-infrared (NIR): 780 μm ~ 1.5 μm
○ Mid-infrared (MIR): 1.5 μm ~ 5 μm
○ Far-infrared (FIR): 5 μm ~ 15 μm
⑥ Microwave
○ Frequency range: 4 × 1011 ~ 8 × 1010 Hz
○ Wavelength range: 0.75 ~ 3.75 mm
○ Induces dipole rotation and ion polarization, generating heat: Principle behind heating water
○ Microwave ovens primarily use a frequency of 2.45 GHz
⑦ T-ray
○ Frequency range: 0.1 × 1012 ~ 10 × 1012 Hz
○ Wavelength range: 30 μm ~ 1 mm
⑧ Radio frequency (RF)
Input : 2019.04.11 14:36
Modified : 2020.04.01 16:33