HKDSE Physics – Reflection and Refraction of Light

HKDSE Physics Core
Chapter 1: Reflection and Refraction of Light | 光的反射與折射

Billy Sir’s Smart Notes: Master Ray Model, Laws of Reflection & Refraction, Total Internal Reflection, and Optical Fibres.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握光線模型、反射及折射定律、全內反射及光纖原理。

1. Ray Model of Light | 光線模型

Light travels in straight lines in a homogeneous medium. A light ray is represented by a straight line with an arrowhead showing the direction of propagation. 在均勻介質中，光沿直線傳播。光線由帶有箭頭的直線表示，箭頭指示傳播方向。

2. Reflection of Light | 光的反射

📏 Laws of Reflection | 反射定律

Law 1: The incident ray, the reflected ray, and the normal all lie in the same plane. (入射光線、反射光線和法線均處於同一平面上。)
Law 2: The angle of incidence (\( i \)) is equal to the angle of reflection (\( r \)). (入射角等於反射角。)

$$ i = r $$

Regular vs Diffuse Reflection | 單向反射與漫反射

Type (類型)	Surface (表面)	Characteristics (特徵)
Regular Reflection 單向反射	Smooth and polished (e.g., mirror) 平滑光澤 (如鏡子)	Parallel incident rays are reflected as parallel rays. Forms clear images. 平行入射光反射後仍為平行光。能形成清晰影像。
Diffuse Reflection 漫反射	Rough and uneven (e.g., paper) 粗糙不平 (如紙張)	Parallel incident rays are scattered in different directions. No clear image. 平行入射光向不同方向散射。無法形成清晰影像。

🪞 Plane Mirror Image & Periscope | 平面鏡影像與潛望鏡

Properties of a Plane Mirror Image (平面鏡影像的特性):

Virtual (cannot be formed on a screen) 虛像 (不能在屏幕上成像)
Erect (upright) 正立
Laterally inverted (left and right swapped) 橫向倒置 (左右對調)
Same size as the object 與物體大小相同
Image distance equals object distance 像距等於物距

Periscope (潛望鏡): Uses two plane mirrors placed at 45° to reflect light twice, allowing observation over obstacles. 利用兩塊呈45°角的平面鏡進行兩次反射，以便越過障礙物進行觀察。

3. Refraction of Light | 光的折射

Refraction is the bending of light when it passes from one medium to another with a different optical density, caused by a change in the speed of light. 折射是光從一種介質進入另一種光密度不同的介質時發生的偏折現象，其原因是光速的改變。

📐 Snell’s Law (Laws of Refraction) | 斯涅爾定律 (折射定律)

For light traveling from medium 1 to medium 2:

n_1 \sin \theta_1 = n_2 \sin \theta_2

Less dense to denser medium (e.g., air to glass): Light bends towards the normal. Speed decreases. (光疏至光密介質：光線偏向法線。光速減慢。)
Denser to less dense medium (e.g., water to air): Light bends away from the normal. Speed increases. (光密至光疏介質：光線偏離法線。光速增加。)

🐟 Apparent Depth | 視深

Objects underwater appear closer to the surface than they actually are due to refraction. 由於折射，水下的物體看起來比實際位置更淺。

n = \frac{\text{Real Depth (實深)}}{\text{Apparent Depth (視深)}}

4. Total Internal Reflection (TIR) | 全內反射

When light travels from an optically denser medium to a less dense medium, and the angle of incidence exceeds a certain value, all light is reflected back into the denser medium. 當光從光密介質進入光疏介質，且入射角大於某個特定值時，所有光線都會反射回光密介質中。

⚠️ Conditions for TIR | 全內反射的條件

Light must travel from an optically denser medium to an optically less dense medium. (光必須由光密介質射向光疏介質。)
The angle of incidence (\( i \)) must be greater than the critical angle (\( c \)). (入射角必須大於臨界角。)

Critical Angle Formula | 臨界角公式

\sin c = \frac{1}{n}

其中 \( n \) 是介質的折射率 (假設另一介質為空氣/真空)。

🌐 Application: Optical Fibre | 應用：光纖

Optical fibres use Total Internal Reflection to transmit light signals over long distances with minimal energy loss. 光纖利用全內反射，在極少能量損耗的情況下長距離傳輸光信號。

Core (核心): High refractive index (optically denser). (高折射率，光密介質)
Cladding (包層): Lower refractive index (optically less dense). (低折射率，光疏介質)

Light entering the core hits the core-cladding boundary at an angle greater than the critical angle, undergoing continuous TIR. 進入核心的光線以大於臨界角的角度撞擊核心與包層的邊界，經歷連續的全內反射。

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