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Optics Chapter 2. Wave Optics

Recommended Article : 【Physics】 Physics Table of Contents


1. Huygens’ Principle

2. Fermat’s Principle

3. Young’s Experiment (Double-Slit Experiment)

4. Electromagnetic Waves



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

Example 1: Refraction of light by water: Objects appear shallower than their actual depth in water

Example 2: Refraction of light by lenses: Detailed description in Geometrical Optics

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

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

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