HKDSE Physics Core
Chapter 5: Wave Nature of Light | 光的波動性
Billy Sir’s Smart Notes: Master EM Waves, Dispersion, Interference, Young’s Double Slit, and Diffraction Grating.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握電磁波、色散、干涉、楊氏雙縫實驗及繞射光柵。
1. Electromagnetic (EM) Waves | 電磁波
Light is a type of electromagnetic wave. All EM waves are transverse waves that can travel through a vacuum at the speed of light (\( c = 3 \times 10^8 \text{ m s}^{-1} \)). 光是一種電磁波。所有電磁波都是橫波，能在真空中以光速傳播。
| EM Wave (電磁波) | Wavelength Trend (波長趨勢) | Common Uses (常見用途) |
|---|---|---|
| Radio Waves (無線電波) | Longest \( \lambda \), Lowest \( f \) | Broadcasting, communications (廣播、通訊) |
| Microwaves (微波) | ↓ | Radar, cooking, satellite comms (雷達、微波爐、衛星通訊) |
| Infrared (IR) (紅外線) | ↓ | Remote controls, thermal imaging (遙控器、熱成像) |
| Visible Light (可見光) | \( \sim 400\text{nm} – 700\text{nm} \) | Vision, optical fibres (視覺、光纖) |
| Ultraviolet (UV) (紫外線) | ↓ | Sterilization, fluorescent tubes (殺菌、螢光燈) |
| X-rays (X射線) | ↓ | Medical imaging, security scanning (醫學影像、安檢) |
| Gamma Rays (伽馬射線) | Shortest \( \lambda \), Highest \( f \) | Cancer treatment, sterilization (癌症治療、殺菌) |
2. Light Reflection & Refraction | 光的反射與折射
Like all waves, light undergoes reflection and refraction. 與所有波一樣，光會發生反射和折射。
🌈 Dispersion of White Light | 白光的色散
When white light passes through a glass prism, it splits into a spectrum of colors (Red, Orange, Yellow, Green, Blue, Indigo, Violet). 當白光穿過玻璃稜鏡時，會分裂成光譜（紅橙黃綠青藍紫）。
- Reason: Different colors of light have different speeds in a medium (like glass), meaning the medium has a slightly different refractive index for each color. (原因：不同顏色的光在介質中的速度不同，導致折射率不同。)
- Red light: Travels fastest in glass, bends the least. (紅光：在玻璃中速度最快，偏折最少)
- Violet light: Travels slowest in glass, bends the most. (紫光：在玻璃中速度最慢，偏折最多)
3. Light Diffraction | 光的繞射
Light can diffract (spread out) when passing through narrow slits or around obstacles. However, because the wavelength of visible light is very short (\( 400 – 700 \text{ nm} \)), the slit must be extremely narrow to observe significant diffraction. 光在穿過狹縫或繞過障礙物時會發生繞射。但由於可見光波長極短，狹縫必須非常窄才能觀察到明顯的繞射。
4. Young’s Double Slit Experiment | 楊氏雙縫實驗
This experiment proves the wave nature of light by demonstrating interference. 這個實驗透過展示干涉現象，證明了光的波動性。
⚠️ Crucial Concept: Coherent Sources | 關鍵概念：相干波源
Why do we use a single light source passing through a double slit, instead of just using two separate light bulbs? (為什麼我們使用單一光源穿過雙縫，而不是直接使用兩個獨立的燈泡？)
To form a stable interference pattern, the waves must come from coherent sources. Two separate light bulbs emit light randomly, meaning their phase difference changes constantly. By using one source and splitting it through two slits, the light emerging from both slits has the same frequency and a constant phase difference, fulfilling the requirement for coherent sources.
為了形成穩定的干涉圖案，波必須來自相干波源。兩個獨立的燈泡會隨機發光，相位差不斷改變。透過將單一光源的光穿過兩個狹縫，從雙縫出來的光具有相同的頻率和恆定的相位差，滿足了相干波源的要求。
📏 Fringe Separation Formula | 條紋間距公式
- \( \Delta y \): Separation between consecutive bright (or dark) fringes (相鄰亮紋或暗紋的間距)
- \( \lambda \): Wavelength of light (光的波長)
- \( D \): Distance from slits to screen (狹縫到屏幕的距離)
- \( a \): Slit separation (雙縫間距)
5. Diffraction Grating | 繞射光柵
A diffraction grating consists of thousands of parallel, closely spaced slits. It produces an interference pattern that is much sharper and brighter than a double slit. 繞射光柵由數千條平行且密集的狹縫組成。它產生的干涉圖案比雙縫更清晰、更明亮。
📐 Grating Equation | 光柵公式
- \( d \): Grating spacing (distance between adjacent slits, \( d = \frac{1}{N} \) where N is lines per mm) (光柵間距)
- \( \theta \): Angle of diffraction (繞射角)
- \( n \): Order of maximum (\( 0, 1, 2… \)) (極大值的階數)
- \( \lambda \): Wavelength (波長)
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