IB Physics: The Principle of Polarized Light | IB物理：偏振光的原理

📚 IB Physics: The Principle of Polarized Light | IB物理：偏振光的原理

Light is a transverse electromagnetic wave, yet most of what we perceive seems indifferent to its vibrational orientation. Polarization reveals a hidden dimension of light, one that has profound implications in physics, technology, and everyday life. In this article, we will explore the principle of polarized light, from wave theory to Malus’s Law, and connect it directly to IB Physics exam requirements.

光是一种横电磁波，但我们日常感知到的光似乎并不”关心”其振动方向。偏振现象揭示了光的一个隐藏维度，它在物理学、科技和日常生活中都有着深远的意义。在这篇文章中，我们将从波动理论出发，系统地探讨偏振光的原理、马吕斯定律，并将其直接对接IB物理考纲要求。

---

1. Transverse Waves and the Direction of Vibration | 横波与振动方向

A transverse wave is one in which the particles of the medium (or the oscillating field, in the case of electromagnetic waves) vibrate perpendicular to the direction of energy propagation. For a wave traveling along the z-axis, the vibration can occur in any direction within the xy-plane. This freedom of orientation is the essential precondition for polarization.

横波是指介质中的质点（或电磁波中的振荡场）垂直于能量传播方向振动的波。对于沿 z 轴传播的波，振动可以在 xy 平面内的任意方向发生。这种方向的自由性正是偏振现象产生的前提条件。

If the vibration direction is random and changes rapidly over time, the wave is said to be unpolarized. If the vibration is confined to a single fixed line (for example, always along the x-axis), the wave is linearly polarized (or plane-polarized).

如果振动方向是随机的、随时间快速变化，则该波被称为非偏振光；如果振动被限制在一条固定的直线上（例如始终沿 x 轴），则该波为线偏振光（或平面偏振光）。

---

2. Electromagnetic Waves and Polarization | 电磁波与偏振

An electromagnetic wave consists of mutually perpendicular oscillating electric field E and magnetic field B, both perpendicular to the direction of propagation. By convention, the direction of polarization is defined by the orientation of the electric field vector.

电磁波由相互垂直的振荡电场 E 和磁场 B 组成，二者均垂直于传播方向。按照惯例，偏振方向由电场矢量的方向来定义。

When an electromagnetic wave is emitted by a typical light source such as the Sun or a light bulb, the electric field vectors of individual photons point in random directions. Each photon is a short wave train with a particular polarization, but the ensemble average yields no preferred direction. Such light is unpolarized.

当电磁波由典型光源（如太阳或灯泡）发出时，单个光子的电场矢量指向随机方向。每个光子都是一段具有特定偏振方向的短波列，但大量光子的统计平均不产生优先方向。这样的光就是非偏振光。

E ⟂ B ⟂ direction of propagation (k)

E ⊥ B ⊥ 传播方向 (k)

---

3. Unpolarized Light and Polarizing Filters | 非偏振光与偏振片

A polarizing filter (polarizer) is a material that transmits only the component of the electric field oscillating in a specific direction, called the transmission axis. When unpolarized light passes through an ideal polarizer, the transmitted light becomes linearly polarized along the transmission axis, and its intensity is reduced by half.

偏振片（起偏器）是一种只允许沿特定方向（称为透光轴）振荡的电场分量通过的材料。当非偏振光通过理想偏振片后，透射光变为沿透光轴线偏振的光，其强度减半。

The physical mechanism depends on the type of polarizer. In a wire-grid polarizer, conducting wires absorb or reflect the component of the electric field parallel to the wires, while the perpendicular component passes through. In a dichroic crystal such as Polaroid, anisotropic absorption selectively removes one polarization component.

偏振片的物理机制取决于其类型。在金属线栅偏振片中，导线会吸收或反射与导线平行的电场分量，而垂直分量则通过。在二向色性晶体（如偏光膜）中，各向异性吸收会选择性地移除某一偏振分量。

Key result: after an ideal polarizer, I = I₀ / 2 for unpolarized incident light.

关键结论：对于非偏振入射光，通过理想偏振片后，I = I₀ / 2。

---

4. Malus’s Law | 马吕斯定律

When linearly polarized light of intensity I₁ passes through a second polarizer (the analyzer) whose transmission axis makes an angle θ with the polarization direction of the incident light, the transmitted intensity is given by Malus’s Law:

当强度为 I₁ 的线偏振光通过第二个偏振片（检偏器）时，若检偏器的透光轴与入射光偏振方向之间的夹角为 θ，则透射强度由马吕斯定律给出：

I = I₁ cos² θ

Only the component of the electric field parallel to the analyzer’s transmission axis passes through. Since intensity is proportional to the square of the electric field amplitude, the cos² factor appears.

只有平行于检偏器透光轴的电场分量才能通过。由于强度与电场振幅的平方成正比，因此出现了 cos² 因子。

Special cases: When θ = 0°, I = I₁ (maximum transmission). When θ = 90°, I = 0 (crossed polarizers, complete extinction). When θ = 45°, I = I₁ / 2.

特殊情况：当 θ = 0° 时，I = I₁（透射最大）；当 θ = 90° 时，I = 0（正交偏振片，完全消光）；当 θ = 45° 时，I = I₁ / 2。

If unpolarized light passes through two crossed polarizers, the transmitted intensity is zero regardless of the first polarizer’s orientation. But if a third polarizer is inserted between them at a non-zero angle, light may reappear — a classic IB multiple-choice trap.

如果非偏振光通过两个正交偏振片，无论第一个偏振片的取向如何，透射强度都为零。但如果在这两者之间以非零角度插入第三个偏振片，光可能会重新出现——这是IB选择题的经典陷阱。

---

5. Polarization by Reflection: Brewster’s Angle | 反射偏振：布鲁斯特角

When unpolarized light reflects off a dielectric surface (such as glass or water), the reflected light becomes partially or completely polarized. At a specific angle of incidence, called Brewster’s angle θₚ, the reflected light is completely linearly polarized perpendicular to the plane of incidence.

当非偏振光在介质表面（如玻璃或水面）反射时，反射光会变成部分偏振光或完全偏振光。在特定的入射角——称为布鲁斯特角 θₚ——反射光将完全线偏振，其偏振方向垂直于入射面。

At Brewster’s angle, the reflected and refracted rays are exactly perpendicular to each other. This gives the condition:

在布鲁斯特角处，反射光线与折射光线恰好相互垂直。由此得到条件：

tan θₚ = n₂ / n₁

where n₁ and n₂ are the refractive indices of the two media. For air (n₁ ≈ 1) to glass (n₂ ≈ 1.5), θₚ ≈ 56.3°.

其中 n₁ 和 n₂ 分别是两种介质的折射率。对于空气（n₁ ≈ 1）到玻璃（n₂ ≈ 1.5），θₚ ≈ 56.3°。

Derivation sketch: Light reflecting at Brewster’s angle has no reflection component for the electric field oscillating in the plane of incidence, because the oscillation direction is parallel to the propagation direction of the refracted ray. Since electromagnetic waves are transverse, this orientation cannot radiate back, so that polarization component is entirely transmitted.

推导概要：在布鲁斯特角处，入射面内振动的电场分量无法反射，因为这个振动方向与折射光的传播方向平行。由于电磁波是横波，这种取向不能向后辐射，因此该偏振分量完全透射。

---

6. Polarization by Scattering | 散射偏振

When sunlight interacts with air molecules, it is scattered. The scattered light is partially polarized, with the degree of polarization being highest at 90° to the original direction of propagation.

当阳光与空气分子相互作用时，会发生散射。散射光为部分偏振光，在与原传播方向成 90° 的方向上偏振程度最高。

This explains why the blue sky is polarized and why bees and certain birds use sky polarization for navigation. It also allows photographers to darken a blue sky in photographs by using a polarizing filter on the camera lens.

这解释了为什么蓝天是偏振的，也解释了为什么蜜蜂和某些鸟类利用天空偏振进行导航。同时，摄影师可以通过在相机镜头上安装偏振滤光片来压暗蓝色天空。

---

7. Applications of Polarization | 偏振的应用

LCD displays: Liquid crystal displays use two crossed polarizers with a liquid crystal layer between them. The liquid crystal rotates the plane of polarization, and an applied voltage controls the rotation, thereby modulating the brightness of each pixel.

液晶显示器（LCD）：液晶显示器使用两个正交偏振片，中间夹着一层液晶。液晶会旋转偏振平面，施加的电压控制旋转程度，从而调节每个像素的亮度。

Polarized sunglasses: These reduce glare by absorbing reflected polarized light. Since reflection from horizontal surfaces (roads, water) produces light polarized predominantly horizontally, the vertical transmission axis of sunglasses blocks the glare.

偏振太阳镜：偏振太阳镜通过吸收反射偏振光来减少眩光。由于水平表面（道路、水面）反射的光主要为水平偏振光，太阳镜的垂直透光轴会阻挡眩光。

Stress analysis: Transparent materials under mechanical stress become birefringent and alter the polarization state of transmitted light. Viewing a stressed plastic model between crossed polarizers reveals colorful interference patterns that map the stress field.

应力分析：处于机械应力下的透明材料会产生双折射，改变透射光的偏振状态。在正交偏振片之间观察受力的塑料模型，可以看到描绘应力场的彩色干涉条纹。

3D movie glasses: Different polarizations (or circular polarizations) encode the left-eye and right-eye images. Each lens transmits only its corresponding polarization, creating a three-dimensional effect.

3D电影眼镜：不同的偏振态（或圆偏振态）分别编码左眼和右眼的图像。每个镜片只透过对应偏振方向的光，从而产生立体效果。

---

8. IB Exam Tips and Common Mistakes | IB考试要点与常见错误

Tip 1: In calculations, always distinguish between unpolarized incident light (factor of ½ from the first polarizer) and already polarized incident light (Malus’s Law with cos²θ).

要点1：在计算中，务必区分非偏振入射光（第一偏振片产生 ½ 因子）和已经偏振的入射光（马吕斯定律使用 cos²θ）。

Tip 2: When light passes through multiple polarizers, apply the ½ rule only once (for unpolarized light entering the first polarizer). Thereafter, apply I = Iₙ cos²θ between consecutive polarizers using the angle between their transmission axes.

要点2：当光通过多个偏振片时，½ 规则只应用一次（即非偏振光进入第一片时）。此后，连续偏振片之间使用 I = Iₙ cos²θ，其中 θ 是相邻透光轴之间的夹角。

Common mistake 1: Using cos²θ when the incident light is unpolarized — this is incorrect. Unpolarized light has no defined θ; the correct factor is ½, not cos²θ averaged over all angles.

常见错误1：对非偏振光使用 cos²θ——这是错误的。非偏振光没有确定的 θ；正确因子是 ½，而不是对所有角度取平均的 cos²θ。

Common mistake 2: Forgetting that for transverse waves only, polarization can occur. Longitudinal waves (sound) cannot be polarized.

常见错误2：忘记只有横波才能发生偏振。纵波（声波）不能偏振。

Common mistake 3: Mixing up the definition of Brewster’s angle. It is the angle of incidence at which the reflected light is completely polarized, not the refracted light.

常见错误3：混淆布鲁斯特角的定义。它是使反射光完全偏振的入射角，而不是使折射光偏振的入射角。

---

9. Graphical Representation: Intensity Curves | 图形表示：强度曲线

IB questions often ask students to sketch the variation of transmitted intensity versus the analyzer angle. For polarized incident light, the graph of I versus θ is a cos² curve: maximum at 0° and 180°, zero at 90° and 270°.

IB题目经常要求学生画出透射强度随检偏器角度变化的图像。对于偏振入射光，I 随 θ 变化的曲线是 cos² 曲线：在 0° 和 180° 处最大，在 90° 和 270° 处为零。

For unpolarized incident light passing through a single polarizer, the transmitted intensity is constant (I₀/2) regardless of the polarizer’s rotation, because every orientation transmits equal average energy.

对于经过单个偏振片的非偏振光，无论偏振片如何旋转，透射强度始终保持 I₀/2，因为每个取向透射的平均能量相等。

Situation | 情境	Intensity | 强度
Unpolarized → ideal polarizer | 非偏振光→理想偏振片	I = I₀ / 2
Polarized → analyzer at angle θ | 偏振光→检偏器夹角θ	I = I₁ cos² θ
Two crossed polarizers, unpolarized input | 两个正交偏振片，非偏振输入	I = 0
Three polarizers (angles 0°,45°,90°), unpolarized input | 三个偏振片(0°,45°,90°)，非偏振输入	I = (I₀/2)(cos²45°)(cos²45°) = I₀/8

---

10. Summary and Final Advice | 总结与备考建议

Polarization is a direct consequence of the transverse nature of electromagnetic waves. The IB Physics syllabus expects you to understand the concept of polarization, apply Malus’s Law, and describe Brewster’s angle as an example of polarization by reflection. You should also be familiar with one or two practical applications.

偏振是电磁波横波性质的直接结果。IB物理考纲要求你理解偏振的概念、应用马吕斯定律、将布鲁斯特角描述为反射偏振的例子，并熟悉一两个实际应用。

As you prepare for exams, practice sketching the cos² intensity curve, master the distinction between the ½ factor and the cos² factor, and remember that polarization is definitive evidence for the transverse nature of light — a crucial conceptual point that often appears in Paper 1 and Paper 2 questions.

在备考过程中，请练习绘制 cos² 强度曲线，掌握 ½ 因子与 cos² 因子的区别，并记住偏振是光是横波的决定性证据——这一关键概念经常出现在Paper 1和Paper 2题目中。

---

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）