IB Physics: Refraction, Reflection and Diffraction | IB物理：折射、反射与衍射现象

📚 IB Physics: Refraction, Reflection and Diffraction | IB物理：折射、反射与衍射现象

Light behaves in fascinating ways when it encounters boundaries, gaps, or obstacles. Three fundamental wave phenomena—reflection, refraction, and diffraction—are central to IB Physics and appear across both Standard Level (SL) and Higher Level (HL) syllabuses. This article breaks down each phenomenon with definitions, laws, key equations, and real-world applications, pitched directly at the IB Diploma exam requirements.

当光遇到边界、狭缝或障碍物时，会表现出奇妙的行为。反射、折射和衍射是三种基本的波动现象，是 IB 物理课程的核心内容，在标准水平（SL）和高级水平（HL）大纲中均有涉及。本文将结合定义、定律、关键方程和实际应用，逐一剖析这些现象，直接对应 IB 文凭考试要求。

1. Reflection | 反射

Reflection occurs when a wave strikes a boundary between two media and bounces back into the original medium. The law of reflection states that the angle of incidence equals the angle of reflection, and both angles are measured relative to the normal—an imaginary line perpendicular to the surface at the point of incidence.

反射是指波在传播到两种介质的边界时，返回到原介质中的现象。反射定律指出：入射角等于反射角，且两个角均相对于法线——即在入射点处垂直于界面的假想线——来测量。

θᵢ = θᵣ

There are two types of reflection. Specular reflection occurs on smooth surfaces, where parallel rays reflect in parallel directions, producing clear images. Diffuse reflection occurs on rough surfaces, where parallel rays reflect in many different directions, making objects visible from many angles but not forming images.

反射分为两类。镜面反射发生在光滑表面上，平行光线反射后仍保持平行，形成清晰图像。漫反射发生在粗糙表面上，平行光线向各个方向反射，使物体从多个角度可见，但不形成图像。

Specular reflection: mirror-like, obeys θᵢ = θᵣ exactly, image formed.

镜面反射：类似镜面，严格满足 θᵢ = θᵣ，形成图像。
Diffuse reflection: scattering from rough surface, no image formed.

漫反射：粗糙表面引起的散射，不形成图像。

In IB Physics, you should also recall the mirror equation for plane mirrors: the image is virtual, upright, and the same size as the object, located as far behind the mirror as the object is in front.

在 IB 物理中，你还需要掌握平面镜成像规律：所成像是虚像、正立、与物体等大，且像与物关于镜面对称，像距等于物距。

2. Refraction | 折射

Refraction is the bending of a wave as it passes obliquely from one medium into another, due to a change in wave speed. When light enters a denser medium, it slows down and bends toward the normal; when it enters a less dense medium, it speeds up and bends away from the normal.

折射是波从一种介质斜射入另一种介质时，由于波速改变而发生的传播方向偏折。当光进入光密介质时，速度减慢，向法线方向偏折；当光进入光疏介质时，速度加快，偏离法线方向偏折。

The relationship between the angles and the speeds in the two media is given by Snell’s law:

两介质中角度与波速之间的关系由斯涅尔定律给出：

n₁ sin θ₁ = n₂ sin θ₂

where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction, measured from the normal. The refractive index n of a medium is defined as the ratio of the speed of light in vacuum c to the speed of light in the medium v:

其中 n₁ 和 n₂ 分别是两种介质的折射率，θ₁ 和 θ₂ 分别是入射角和折射角（均相对于法线测量）。介质的折射率 n 定义为真空中的光速 c 与介质中的光速 v 之比：

n = c / v

Since v is always less than c in a material medium, n is always greater than 1 for real media. For a vacuum, n = 1 exactly.

因为在实物介质中 v 始终小于 c，所以实际介质的折射率始终大于 1。对于真空，n 精确等于 1。

The refractive index also relates to the relative permittivity and permeability of the medium, but for IB purposes you mainly need the speed relation and Snell’s law.

折射率还与介质的相对介电常数和相对磁导率有关，但在 IB 考试中，你主要需要掌握速度关系和斯涅尔定律。

Medium \| 介质	Refractive Index \| 折射率
Vacuum (真空)	1.000
Air (空气)	1.0003 (≈1)
Water (水)	1.33
Glass (玻璃)	1.50–1.70
Diamond (金刚石)	2.42

A common exam question asks you to calculate the speed of light in a medium given its refractive index. For example, in water (n = 1.33), v = (3.0 × 10⁸ m/s) / 1.33 ≈ 2.26 × 10⁸ m/s.

一个常见考题是：已知介质的折射率，求光在该介质中的速度。例如，在水中（n = 1.33），v = (3.0 × 10⁸ m/s) / 1.33 ≈ 2.26 × 10⁸ m/s。

3. Total Internal Reflection | 全内反射

When light travels from a denser medium to a less dense medium, the refracted ray bends away from the normal. As the angle of incidence increases, the refraction angle approaches 90°. The critical angle c is the angle of incidence for which the angle of refraction is exactly 90°.

当光从光密介质射向光疏介质时，折射光线偏离法线。随着入射角增大，折射角趋近于 90°。临界角 c 是指折射角恰好为 90° 时对应的入射角。

n₁ sin c = n₂ sin 90° = n₂

For a light ray going from a medium of refractive index n₁ to a less dense medium n₂:

对于从折射率为 n₁ 的介质射向折射率较小的 n₂ 介质的光线：

sin c = n₂ / n₁

If the second medium is air (n₂ ≈ 1), then sin c = 1 / n₁. For glass with n = 1.50, the critical angle is about 41.8°.

如果第二种介质是空气（n₂ ≈ 1），则 sin c = 1 / n₁。对于 n = 1.50 的玻璃，临界角约为 41.8°。

Total internal reflection occurs when two conditions are satisfied: (1) light is travelling from a denser to a less dense medium, and (2) the angle of incidence exceeds the critical angle. At this point, no light is refracted; all light is reflected back into the denser medium.

全内反射的发生需要满足两个条件：(1) 光从光密介质射向光疏介质；(2) 入射角大于临界角。此时，没有光线被折射，所有光线都反射回光密介质中。

Applications of total internal reflection include optical fibres used in telecommunications and medicine (endoscopes), and prism binoculars. In an optical fibre, light signals travel along the core by repeated total internal reflection, allowing low-loss transmission over long distances.

全内反射的应用包括用于电信和医学（内窥镜）的光纤，以及棱镜双筒望远镜。在光纤中，光信号沿纤芯通过反复的全内反射传播，实现长距离低损耗传输。

4. Dispersion | 色散

Dispersion is a special case of refraction in which the refractive index of a medium depends on the wavelength (or frequency) of light. Because different colours of visible light have different wavelengths in a medium, they bend by different amounts when entering a prism, spreading white light into a spectrum.

色散是折射的一种特殊情况：介质的折射率与光的波长（或频率）有关。由于可见光的不同颜色在介质中具有不同的波长，因此当白光进入棱镜时，不同颜色的光偏折程度不同，从而展开成光谱。

In most transparent materials, the refractive index decreases with increasing wavelength. Thus violet light (shorter wavelength) is bent more than red light (longer wavelength). This is why a prism produces a rainbow order: red, orange, yellow, green, blue, indigo, violet.

在大多数透明材料中，折射率随波长增大而减小。因此，紫光（波长较短）比红光（波长较长）偏折得更厉害。这就是棱镜产生彩虹色序（红、橙、黄、绿、蓝、靛、紫）的原因。

In IB exams, you may be asked to sketch the dispersion of white light through a triangular prism, labelling the red and violet ends of the spectrum. Remember: red is deviated least, violet is deviated most.

在 IB 考试中，你可能会被要求画出白光通过三棱镜的色散图，并标出光谱的红端和紫端。请记住：红光的偏折最小，紫光的偏折最大。

5. Diffraction | 衍射

Diffraction is the spreading of waves when they pass through a narrow opening or around an obstacle. The amount of diffraction depends on the ratio of the wavelength to the size of the aperture or obstacle. Significant diffraction occurs when the aperture size is comparable to the wavelength.

衍射是波通过窄缝或绕过障碍物时发生的展宽现象。衍射程度取决于波长与缝宽（或障碍物尺寸）之比。当缝宽与波长相差不大时，衍射现象显著。

For a single slit of width a, the condition for the first minimum (dark fringe) in the diffraction pattern is:

对于宽度为 a 的单缝，衍射图样中第一级暗纹（暗条纹）的条件是：

a sin θ = m λ

where m = ±1, ±2, ±3, … gives the order of the minima, λ is the wavelength, and θ is the angle from the central axis to the minimum. The central maximum is twice as wide as the secondary maxima, and its intensity is much greater.

其中 m = ±1, ±2, ±3, … 为暗纹级数，λ 为波长，θ 为从中心轴到暗纹的角位置。中央亮纹的宽度是次级亮纹宽度的两倍，且强度远大于次级亮纹。

Key features of a single-slit diffraction pattern:

单缝衍射图样的关键特征：

A broad, bright central maximum centred on the axis.

位于轴上的宽阔明亮中央亮纹。
Alternating dark and bright fringes of decreasing intensity on either side.

两侧交替出现、强度逐渐减弱的暗纹和亮纹。
Minima occur at a sin θ = m λ (m = ±1, ±2, …).

暗纹出现在满足 a sin θ = m λ（m = ±1, ±2, …）的位置。

6. Diffraction Grating | 衍射光栅

A diffraction grating consists of many equally spaced parallel slits. It produces much sharper and more widely separated maxima than a single slit. The condition for constructive interference (bright maxima) is given by the grating equation:

衍射光栅由大量等间距的平行狭缝组成。相比单缝，它产生的亮纹更尖锐、间隔更大。相邻狭缝光线的干涉加强（亮纹）条件由光栅方程给出：

d sin θ = n λ

where d is the slit spacing (grating spacing), θ is the diffraction angle, n is the order number (n = 0, 1, 2, …), and λ is the wavelength.

其中 d 为狭缝间距（光栅常数），θ 为衍射角，n 为级数（n = 0, 1, 2, …），λ 为波长。

The slit spacing d is related to the number of lines per metre N by d = 1 / N. For example, a grating with 500 lines per mm has N = 500,000 lines per metre, so d = 1 / 500,000 = 2.0 × 10⁻⁶ m.

光栅常数 d 与每米线数 N 的关系为 d = 1 / N。例如，一个每毫米 500 条线的光栅，N = 500,000 条/米，因此 d = 1 / 500,000 = 2.0 × 10⁻⁶ m。

Since sin θ ≤ 1, the maximum order n is limited. If d = 2.0 × 10⁻⁶ m and λ = 6.0 × 10⁻⁷ m, then n λ / d ≤ 1 gives n ≤ 3.33, so only orders n = 0, 1, 2, 3 are observable.

由于 sin θ ≤ 1，最大级数 n 是有限的。若 d = 2.0 × 10⁻⁶ m，λ = 6.0 × 10⁻⁷ m，则 n λ / d ≤ 1 给出 n ≤ 3.33，因此只能观察到 n = 0, 1, 2, 3 级。

Diffraction gratings are used in spectrometers to measure wavelengths of light emitted by atoms, and in optical devices to separate different colours.

衍射光栅用于光谱仪中测量原子发射光的波长，也用于光学设备中分离不同颜色的光。

7. Huygens’ Principle | 惠更斯原理

Huygens’ principle states that every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront at a later time is the envelope of these secondary wavelets. This principle explains reflection, refraction, and diffraction qualitatively.

惠更斯原理表明：波前上的每一点都可以看作发出次级球面子波的新波源。在稍后的时刻，新的波前就是这些子波包络面的切面。该原理可以定性解释反射、折射和衍射。

In reflection, the secondary wavelets re-emit into the original medium, and the law of reflection emerges from the geometry. In refraction, the secondary wavelets travel at different speeds in the two media, causing the wavefront to change direction. In diffraction, only part of the wavefront passes through the aperture; the secondary wavelets at the edges spread into the geometric shadow region.

在反射中，子波在原始介质中重新发射，由几何关系可推导出反射定律。在折射中，子波在两种介质中传播速度不同，导致波前方向改变。在衍射中，只有部分波前通过狭缝，边缘处的子波向几何阴影区域扩展。

Huygens’ principle is an important conceptual tool in the IB syllabus. You should be able to draw diagrams showing how a plane wave or circular wave evolves through an aperture using Huygens’ construction.

惠更斯原理是 IB 大纲中重要的概念工具。你应该能够使用惠更斯作图法，画出平面波或圆形波通过狭缝后的演变图。

8. Interference and Diffraction Compared | 干涉与衍射的比较

Interference and diffraction are closely related phenomena. Interference refers to the superposition of waves from two (or more) coherent sources, such as in Young’s double-slit experiment. Diffraction refers to the spreading of a single wave after passing through an aperture or around an obstacle. In practice, diffraction at each slit also modifies the interference pattern in Young’s experiment.

干涉和衍射是密切相关的现象。干涉是指来自两个（或多个）相干波源的波叠加，如杨氏双缝实验。衍射是指单个波通过狭缝或绕过障碍物后的展宽。实际上，在杨氏双缝实验中，每个缝的衍射效应也会调制干涉图样。

For Young’s double-slit experiment, the condition for bright fringes is:

对于杨氏双缝实验，亮纹条件为：

s λ / d = y / D

where s is the slit separation, d is often written as the separation a, y is the fringe separation on the screen, and D is the distance from the slits to the screen. In IB notation, the fringe spacing Δy is given by:

其中 s 为双缝间距，y 为屏幕上相邻亮纹的间距，D 为双缝到屏幕的距离。在 IB 标准记法中，条纹间距 Δy 为：

Δy = λ D / a

where a is the separation between the slits. This formula holds for small angles. Remember to convert all units to metres before substituting.

其中 a 为双缝间距。该公式在小角度条件下成立。代入计算前记得将所有单位换算为米。

9. Applications and IB Exam Tips | 应用与 IB 考试提示

Here are some high-yield applications and common pitfalls to avoid:

以下是一些高价值应用和常见易错点，请务必注意：

Phenomenon (现象)	Example (实例)
Reflection (反射)	Mirrors, periscopes, radar (镜子、潜望镜、雷达)
Refraction (折射)	Lenses, prisms, apparent depth (透镜、棱镜、视深)
Total internal reflection (全内反射)	Optical fibres, diamond sparkle (光纤、钻石闪耀)
Diffraction (衍射)	Sound around corners, X-ray crystallography (绕过角落的声音、X射线晶体学)
Diffraction grating (光栅)	Spectrometers, laser wavelength measurement (光谱仪、激光波长测量)

Common pitfalls:

常见易错点：

Forgetting that angles in Snell’s law are measured from the normal, not from the surface.

忘记斯涅尔定律中的角度是从法线而不是从界面测量的。
Using degrees instead of radians when required, or vice versa—check the problem statement.

需要弧度时误用角度，或反之——务必看清题目要求。
Confusing the grating equation d sin θ = n λ with the single-slit minimum condition a sin θ = n λ. In the grating equation n is the order number; in the single-slit condition m is used for minima.

混淆光栅方程 d sin θ = n λ 与单缝暗纹条件 a sin θ = n λ。光栅方程中 n 表示级数；单缝暗纹条件中常用 m 表示暗纹级数。
Not knowing that the central maximum in single-slit diffraction is twice as wide as the others.

不知道单缝衍射中央亮纹宽度是其他亮纹宽度的两倍。
Forgetting to check whether n λ / d > 1 before calculating an order that does not exist.

计算不存在的级数前，忘记检查是否满足 n λ / d > 1 的条件。

10. Worked Example | 典型例题

Let us work through a typical IB-style question step by step.

让我们一步一步解答一道典型的 IB 风格题目。

Question | 题目: Monochromatic light of wavelength 5.5 × 10⁻⁷ m passes through a diffraction grating with 400 lines per mm. Calculate the angle of the second-order maximum.

题目：波长为 5.5 × 10⁻⁷ m 的单色光通过每毫米 400 条线的衍射光栅。求第二级亮纹的衍射角。

Solution | 解答:

First find the grating spacing d. Since there are 400 lines per millimetre, the distance between adjacent lines is:

首先求光栅常数 d。由于每毫米有 400 条线，相邻线之间的距离为：

d = (1 × 10⁻³ m) / 400 = 2.5 × 10⁻⁶ m

Using the grating equation for n = 2:

对 n = 2 使用光栅方程：

sin θ = n λ / d = (2 × 5.5 × 10⁻⁷) / (2.5 × 10⁻⁶) = 0.44

Therefore θ = arcsin(0.44) ≈ 26.1°.

因此 θ = arcsin(0.44) ≈ 26.1°。

Always show the substitution step clearly to earn full method marks.

务必清晰写出代入步骤，以获取完整方法分。

11. Exam-Style Summary | 考试要点总结

Reflection obeys θᵢ = θᵣ. Refraction obeys Snell’s law n₁ sin θ₁ = n₂ sin θ₂, with refractive index n = c/v. Total internal reflection occurs only from dense to less dense media, with critical angle given by sin c = n₂/n₁. Diffraction spreads waves through apertures, with single-slit minima at a sin θ = m λ. Diffraction gratings produce sharp maxima at d sin θ = n λ.

反射满足 θᵢ = θᵣ。折射满足斯涅尔定律 n₁ sin θ₁ = n₂ sin θ₂，折射率 n = c/v。全内反射仅发生在光密介质向光疏介质传播时，临界角满足 sin c = n₂/n₁。衍射使波通过狭缝后展宽，单缝暗纹在 a sin θ = m λ 处。衍射光栅在 d sin θ = n λ 处产生尖锐亮纹。

In the exam, draw labelled diagrams wherever possible—they earn credit and clarify your reasoning. For quantitative questions, always check units, use the correct angle convention, and consider physical limits such as sin θ ≤ 1.

考试中，尽可能画出标注清晰的示意图——这既得分又能理清思路。对于计算题，务必检查单位、使用正确的角度约定，并考虑 sin θ ≤ 1 等物理限制。

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IB Physics: Refraction, Reflection and Diffraction | IB物理：折射、反射与衍射现象