📚 Mastering Refraction of Light for A-Level WJEC Physics | A-Level WJEC 物理：光的折射 考点精讲
Refraction of light is a cornerstone topic in the WJEC A-Level Physics specification. Understanding how light bends when passing from one medium to another not only explains everyday phenomena like the apparent bending of a straw in water, but also underpins the working of lenses, optical fibres, and many modern technologies. This article will guide you through the key concepts, equations, experiments, and exam-style applications you need to master for success in your WJEC physics examination.
光的折射是WJEC A-Level物理考试大纲中的基石性主题。理解光从一种介质进入另一种介质时如何弯曲，不仅能解释吸管在水中看起来变弯等日常现象，还支撑着透镜、光纤以及许多现代技术的工作原理。本文将带你梳理核心概念、方程、实验和考试中常见的应用，帮助你全面掌握考点，在WJEC物理考试中取得成功。
1. What is Refraction? | 什么是折射？
Refraction is the change in direction of a wave when it passes from one transparent medium to another, caused by a change in its speed. For light, this occurs because the speed of light in a vacuum (approximately 3.00 × 10⁸ m s⁻¹) is different from its speed in materials like glass, water, or air. The change in speed leads to a bending of the light ray, unless the ray strikes the boundary exactly along the normal.
折射是波从一种透明介质进入另一种介质时，因传播速度改变而引起的方向变化。对于光而言，之所以发生折射，是因为光在真空中的速度（约 3.00 × 10⁸ m s⁻¹）与在玻璃、水或空气等材料中的速度不同。速度的变化导致光线发生弯曲，除非光线恰好沿法线方向射入界面。
The normal is an imaginary line drawn perpendicular to the surface at the point where the light ray meets the boundary. The angle of incidence (i) is measured between the incident ray and the normal, while the angle of refraction (r) is measured between the refracted ray and the normal. Both angles are always taken inside the respective media.
法线是一条假想的线，在光线与界面相交的点上垂直于表面。入射角 (i) 是入射光线与法线之间的夹角，折射角 (r) 是折射光线与法线之间的夹角。两个角度都始终在各自介质内部测量。
2. Wavefront Explanation of Refraction | 波前对折射的解释
Using Huygens’ principle, each point on a wavefront acts as a source of secondary wavelets. When a wavefront moves from a faster medium to a slower medium, the portion of the wavefront that enters the slower medium first is delayed, causing the wavefront to tilt. This tilting explains the change in direction. The wavelength decreases in a denser (optically slower) medium, while the frequency remains constant because the source determines the frequency.
根据惠更斯原理，波前上的每一点都可以看作次级子波的波源。当波前从较快介质进入较慢介质时，率先进入慢介质的部分受到延迟，导致波前发生倾斜。这种倾斜解释了方向的变化。在光密（光速较慢）介质中波长减小，但由于频率由光源决定，因此频率保持不变。
This wave-based explanation reinforces the relationship: v = fλ, where v is the speed, f is the frequency, and λ is the wavelength. Since f is constant, a reduction in v must be accompanied by a reduction in λ. The change in speed and wavelength produces the observed bending.
这种基于波动的解释强化了关系式：v = fλ，其中 v 为速度，f 为频率，λ 为波长。由于 f 恒定，v 减小必然导致 λ 减小。速度和波长的变化造成了观察到的弯曲现象。
3. Snell’s Law and Refractive Index | 斯涅尔定律与折射率
Snell’s law quantitatively describes the relationship between the angles of incidence and refraction for two given media. It is stated as: n₁ sin i = n₂ sin r, where n₁ and n₂ are the absolute refractive indices of medium 1 and medium 2 respectively. The absolute refractive index of a medium, n, is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v): n = c / v.
斯涅尔定律定量地描述了给定两种介质下入射角与折射角之间的关系。其表达式为：n₁ sin i = n₂ sin r，其中 n₁ 和 n₂ 分别是介质1和介质2的绝对折射率。介质的绝对折射率 n 定义为真空中光速 (c) 与介质中光速 (v) 的比值：n = c / v。
Since no medium can have a speed greater than c, the refractive index n is always greater than or equal to 1. Air has an index very close to 1 (approximately 1.0003), which is often approximated as 1 in calculations unless high precision is required. Typical values include water (n ≈ 1.33), crown glass (n ≈ 1.50), and diamond (n ≈ 2.42).
因为任何介质中的光速都不可能大于 c，所以折射率 n 始终大于或等于1。空气的折射率非常接近1（约 1.0003），除非要求高精度，计算中常将其近似为1。典型数值包括水 (n ≈ 1.33)、冕玻璃 (n ≈ 1.50) 和钻石 (n ≈ 2.42)。
An alternative form used when light travels from medium 1 to medium 2 is: ₁n₂ = sin i / sin r = v₁ / v₂ = n₂ / n₁, where ₁n₂ is the relative refractive index of medium 2 with respect to medium 1.
当光从介质1进入介质2时，另一种表达形式为：₁n₂ = sin i / sin r = v₁ / v₂ = n₂ / n₁，其中 ₁n₂ 是介质2相对于介质1的相对折射率。
4. Predicting the Direction of Bending | 判断光线的偏折方向
When light enters an optically denser medium (higher n), it slows down and bends towards the normal. Consequently, the angle of refraction is smaller than the angle of incidence (r < i). When light enters an optically less dense medium (lower n), it speeds up and bends away from the normal, so the angle of refraction is larger (r > i). A simple memory aid: from fast to slow, bends towards the normal; from slow to fast, bends away from the normal.
当光进入光密介质（较高的 n）时，速度减慢并偏向法线方向，因此折射角小于入射角 (r < i)。当光进入光疏介质（较低的 n）时，速度加快并偏离法线方向，因此折射角大于入射角 (r > i)。一个简单的记忆方法是：从快介质到慢介质，向法线偏折；从慢介质到快介质，偏离法线偏折。
If the light strikes the boundary along the normal (i = 0°), it passes straight through without any change in direction, regardless of the media. This special case must be remembered because sin 0° = 0, and Snell’s law then gives r = 0°.
如果光线沿法线射入界面 (i = 0°)，无论介质如何，光都会径直通过而不改变方向。必须记住这一特殊情况，因为 sin 0° = 0，斯涅尔定律此时给出 r = 0°。
5. Critical Angle and Total Internal Reflection | 临界角与全内反射
When light travels from a denser medium to a less dense medium (e.g., from glass to air), there is a particular angle of incidence for which the angle of refraction becomes 90°. This incident angle is called the critical angle, denoted by C. At the critical angle, the refracted ray skims along the boundary. For angles of incidence greater than the critical angle, all the light is reflected back into the denser medium; this phenomenon is known as total internal reflection (TIR).
当光从光密介质传播到光疏介质（例如从玻璃到空气）时，存在一个特定的入射角使得折射角变为 90°。该入射角称为临界角，记作 C。在临界角下，折射光线沿着界面掠射。当入射角大于临界角时，所有光线都被反射回光密介质中；这一现象称为全内反射 (TIR)。
The critical angle can be derived from Snell’s law. Setting the angle of refraction to 90° in the less dense medium (n₂, where n₂ < n₁), we get: n₁ sin C = n₂ sin 90° = n₂. Therefore, sin C = n₂ / n₁. If the less dense medium is air (n₂ ≈ 1), the formula simplifies to: sin C = 1 / n, where n is the refractive index of the denser medium.
临界角可以从斯涅尔定律推导得出。在光疏介质 (n₂，且 n₂ < n₁) 中将折射角设为 90°，得到：n₁ sin C = n₂ sin 90° = n₂。因此，sin C = n₂ / n₁。如果光疏介质是空气 (n₂ ≈ 1)，公式简化为：sin C = 1 / n，其中 n 为光密介质的折射率。
For total internal reflection to occur, two conditions must be satisfied: (1) the light must be travelling from a medium of higher refractive index to one of lower refractive index; (2) the angle of incidence inside the denser medium must exceed the critical angle for that interface.
要发生全内反射，必须满足两个条件：(1) 光必须从折射率较高的介质射向折射率较低的介质；(2) 光密介质内的入射角必须大于该界面的临界角。
6. Applications of Total Internal Reflection: Optical Fibres | 全内反射的应用：光纤
Optical fibres are thin strands of highly transparent glass or plastic that exploit total internal reflection to transmit light signals over long distances with minimal loss. A typical optical fibre consists of a core with a relatively high refractive index, surrounded by cladding with a lower refractive index. When light enters the core at an angle greater than the critical angle for the core–cladding interface, it undergoes repeated total internal reflections and propagates along the fibre.
光纤是由高透明度的玻璃或塑料制成的细丝，利用全内反射以极低的损耗远距离传输光信号。典型的光纤由折射率相对较高的纤芯和折射率较低的包层组成。当光以大于纤芯-包层界面临界角的角度进入纤芯时，会反复发生全内反射并沿光纤传播。
Key advantages of optical fibres in communications include: higher data transmission rates, lower signal attenuation compared to copper wires, immunity to electromagnetic interference, and greater security because light does not leak readily from the fibre. In WJEC exams, you may be asked to calculate the critical angle for the core–cladding interface or explain why cladding is necessary (it protects the core, reduces signal loss, and ensures the critical angle is maintained even if the fibre is bent).
光纤在通信中的主要优点包括：数据传输速率更高，与铜线相比信号衰减更低，不受电磁干扰，且由于光不易从光纤泄漏而具有更高的安全性。在WJEC考试中，可能会要求你计算纤芯-包层界面的临界角，或解释为什么需要包层（它保护纤芯、降低信号损失，并确保即使光纤弯曲也能维持临界角）。
7. Investigating Refraction Experimentally | 通过实验研究折射
A common practical to determine the refractive index of a glass or Perspex block involves using a ray box, a protractor, and a rectangular block. The block is placed on a sheet of paper, and its outline is traced. A ray of light is directed at an angle to one face, and the incident ray, refracted ray inside the block, and the emergent ray are marked. By drawing the normal and measuring the angles of incidence and refraction with a protractor, Snell’s law can be used to calculate n. The experiment is repeated for several angles, and a graph of sin i against sin r is plotted; the gradient gives the refractive index.
测量玻璃或有机玻璃块折射率的常见实验需要使用光线箱、量角器和矩形块。将矩形块放在一张纸上并描绘其轮廓。将光线以一定角度投射到一个面上，标记出入射光线、块内的折射光线以及出射光线。通过画出法线并用量角器测量入射角和折射角，可以利用斯涅尔定律计算 n。对多个角度重复该实验，并绘制 sin i 对 sin r 的图线；图线的斜率即为折射率。
When light passes through a rectangular block, the emergent ray is parallel to the incident ray but laterally displaced. This demonstrates that the ray undergoes two refractions which cancel each other’s angular deviation, provided the two faces are parallel. In a semicircular block, a common alternative, the ray enters along the radius so that it strikes the curved surface normally and exits without ref
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📚 Mastering Refraction of Light for A-Level WJEC Physics | A-Level WJEC 物理：光的折射 考点精讲
Refraction of light is a cornerstone topic in the WJEC A-Level Physics specification. Understanding how light bends when passing from one medium to another not only explains everyday phenomena like the apparent bending of a straw in water, but also underpins the working of lenses, optical fibres, and many modern technologies. This article will guide you through the key concepts, equations, experiments, and exam-style applications you need to master for success in your WJEC physics examination.
光的折射是WJEC A-Level物理考试大纲中的基石性主题。理解光从一种介质进入另一种介质时如何弯曲，不仅能解释吸管在水中看起来变弯等日常现象，还支撑着透镜、光纤以及许多现代技术的工作原理。本文将带你梳理核心概念、方程、实验和考试中常见的应用，帮助你全面掌握考点，在WJEC物理考试中取得成功。
1. What is Refraction? | 什么是折射？
Refraction is the change in direction of a wave when it passes from one transparent medium to another, caused by a change in its speed. For light, this occurs because the speed of light in a vacuum (approximately 3.00 × 10⁸ m s⁻¹) is different from its speed in materials like glass, water, or air. The change in speed leads to a bending of the light ray, unless the ray strikes the boundary exactly along the normal.
折射是波从一种透明介质进入另一种介质时，因传播速度改变而引起的方向变化。对于光而言，之所以发生折射，是因为光在真空中的速度（约 3.00 × 10⁸ m s⁻¹）与在玻璃、水或空气等材料中的速度不同。速度的变化导致光线发生弯曲，除非光线恰好沿法线方向射入界面。
The normal is an imaginary line drawn perpendicular to the surface at the point where the light ray meets the boundary. The angle of incidence (i) is measured between the incident ray and the normal, while the angle of refraction (r) is measured between the refracted ray and the normal. Both angles are always taken inside the respective media.
法线是一条假想的线，在光线与界面相交的点上垂直于表面。入射角 (i) 是入射光线与法线之间的夹角，折射角 (r) 是折射光线与法线之间的夹角。两个角度都始终在各自介质内部测量。
2. Wavefront Explanation of Refraction | 波前对折射的解释
Using Huygens’ principle, each point on a wavefront acts as a source of secondary wavelets. When a wavefront moves from a faster medium to a slower medium, the portion of the wavefront that enters the slower medium first is delayed, causing the wavefront to tilt. This tilting explains the change in direction. The wavelength decreases in a denser (optically slower) medium, while the frequency remains constant because the source determines the frequency.
根据惠更斯原理，波前上的每一点都可以看作次级子波的波源。当波前从较快介质进入较慢介质时，率先进入慢介质的部分受到延迟，导致波前发生倾斜。这种倾斜解释了方向的变化。在光密（光速较慢）介质中波长减小，但由于频率由光源决定，因此频率保持不变。
This wave-based explanation reinforces the relationship: v = fλ, where v is the speed, f is the frequency, and λ is the wavelength. Since f is constant, a reduction in v must be accompanied by a reduction in λ. The change in speed and wavelength produces the observed bending.
这种基于波动的解释强化了关系式：v = fλ，其中 v 为速度，f 为频率，λ 为波长。由于 f 恒定，v 减小必然导致 λ 减小。速度和波长的变化造成了观察到的弯曲现象。
3. Snell’s Law and Refractive Index | 斯涅尔定律与折射率
Snell’s law quantitatively describes the relationship between the angles of incidence and refraction for two given media. It is stated as: n₁ sin i = n₂ sin r, where n₁ and n₂ are the absolute refractive indices of medium 1 and medium 2 respectively. The absolute refractive index of a medium, n, is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v):
斯涅尔定律定量地描述了给定两种介质下入射角与折射角之间的关系。其表达式为：n₁ sin i = n₂ sin r，其中 n₁ 和 n₂ 分别是介质1和介质2的绝对折射率。介质的绝对折射率 n 定义为真空中光速 (c) 与介质中光速 (v) 的比值：
n = c / v
Since no medium can have a speed greater than c, the refractive index n is always greater than or equal to 1. Air has an index very close to 1 (approximately 1.0003), which is often approximated as 1 in calculations unless high precision is required. Typical values include water (n ≈ 1.33), crown glass (n ≈ 1.50), and diamond (n ≈ 2.42).
因为任何介质中的光速都不可能大于 c，所以折射率 n 始终大于或等于1。空气的折射率非常接近1（约 1.0003），除非要求高精度，计算中常将其近似为1。典型数值包括水 (n ≈ 1.33)、冕玻璃 (n ≈ 1.50) 和钻石 (n ≈ 2.42)。
An alternative form used when light travels from medium 1 to medium 2 is: ₁n₂ = sin i / sin r = v₁ / v₂ = n₂ / n₁, where ₁n₂ is the relative refractive index of medium 2 with respect to medium 1.
当光从介质1进入介质2时，另一种表达形式为：₁n₂ = sin i / sin r = v₁ / v₂ = n₂ / n₁，其中 ₁n₂ 是介质2相对于介质1的相对折射率。
4. Predicting the Direction of Bending | 判断光线的偏折方向
When light enters an optically denser medium (higher n), it slows down and bends towards the normal. Consequently, the angle of refraction is smaller than the angle of incidence (r < i). When light enters an optically less dense medium (lower n), it speeds up and bends away from the normal, so the angle of refraction is larger (r > i). A simple memory aid: from fast to slow, bends towards the normal; from slow to fast, bends away from the normal.
当光进入光密介质（较高的 n）时，速度减慢并偏向法线方向，因此折射角小于入射角 (r < i)。当光进入光疏介质（较低的 n）时，速度加快并偏离法线方向，因此折射角大于入射角 (r > i)。一个简单的记忆方法是：从快介质到慢介质，向法线偏折；从慢介质到快介质，偏离法线偏折。
If the light strikes the boundary along the normal (i = 0°), it passes straight through without any change in direction, regardless of the media. This special case must be remembered because sin 0° = 0, and Snell’s law then gives r = 0°.
如果光线沿法线射入界面 (i = 0°)，无论介质如何，光都会径直通过而不改变方向。必须记住这一特殊情况，因为 sin 0° = 0，斯涅尔定律此时给出 r = 0°。
5. Critical Angle and Total Internal Reflection | 临界角与全内反射
When light travels from a denser medium to a less dense medium (e.g., from glass to air), there is a particular angle of incidence for which the angle of refraction becomes 90°. This incident angle is called the critical angle, denoted by C. At the critical angle, the refracted ray skims along the boundary. For angles of incidence greater than the critical angle, all the light is reflected back into the denser medium; this phenomenon is known as total internal reflection (TIR).
当光从光密介质传播到光疏介质（例如从玻璃到空气）时，存在一个特定的入射角使得折射角变为 90°。该入射角称为临界角，记作 C。在临界角下，折射光线沿着界面掠射。当入射角大于临界角时，所有光线都被反射回光密介质中；这一现象称为全内反射 (TIR)。
The critical angle can be derived from Snell’s law. Setting the angle of refraction to 90° in the less dense medium (n₂, where n₂ < n₁), we get: n₁ sin C = n₂ sin 90° = n₂. Therefore:
临界角可以从斯涅尔定律推导得出。在光疏介质 (n₂，且 n₂ < n₁) 中将折射角设为 90°，得到：n₁ sin C = n₂ sin 90° = n₂。因此：
sin C = n₂ / n₁
If the less dense medium is air (n₂ ≈ 1), the formula simplifies to:
如果光疏介质是空气 (n₂ ≈ 1)，公式简化为：
sin C = 1 / n
where n is the refractive index of the denser medium.
其中 n 为光密介质的折射率。
For total internal reflection to occur, two conditions must be satisfied: (1) the light must be travelling from a medium of higher refractive index to one of lower refractive index; (2) the angle of incidence inside the denser medium must exceed the critical angle for that interface.
要发生全内反射，必须满足两个条件：(1) 光必须从折射率较高的介质射向折射率较低的介质；(2) 光密介质内的入射角必须大于该界面的临界角。
6. Applications of Total Internal Reflection: Optical Fibres | 全内反射的应用：光纤
Optical fibres are thin strands of highly transparent glass or plastic that exploit total internal reflection to transmit light signals over long distances with minimal loss. A typical optical fibre consists of a core with a relatively high refractive index, surrounded by cladding with a lower refractive index. When light enters the core at an angle greater than the critical angle for the core–cladding interface, it undergoes repeated total internal reflections and propagates along the fibre.
光纤是由高透明度的玻璃或塑料制成的细丝，利用全内反射以极低的损耗远距离传输光信号。典型的光纤由折射率相对较高的纤芯和折射率较低的包层组成。当光以大于纤芯-包层界面临界角的角度进入纤芯时，会反复发生全内反射并沿光纤传播。
Key advantages of optical fibres in communications include: higher data transmission rates, lower signal attenuation compared to copper wires, immunity to electromagnetic interference, and greater security because light does not leak readily from the fibre. In WJEC exams, you may be asked to calculate the critical angle for the core–cladding interface or explain why cladding is necessary (it protects the core, reduces signal loss, and ensures the critical angle is maintained even if the fibre is bent).
光纤在通信中的主要优点包括：数据传输速率更高，与铜线相比信号衰减更低，不受电磁干扰，且由于光不易从光纤泄漏而具有更高的安全性。在WJEC考试中，可能会要求你计算纤芯-包层界面的临界角，或解释为什么需要包层（它保护纤芯、降低信号损失，并确保即使光纤弯曲也能维持临界角）。
7. Investigating Refraction Experimentally | 通过实验研究折射
A common practical to determine the refractive index of a glass or Perspex block involves using a ray box, a protractor, and a rectangular block. The block is placed on a sheet of paper, and its outline is traced. A ray of light is directed at an angle to one face, and the incident ray, refracted ray inside the block, and the emergent ray are marked. By drawing the normal and measuring the angles of incidence and refraction with a protractor, Snell’s law can be used to calculate n. The experiment is repeated for several angles, and a graph of sin i against sin r is plotted; the gradient gives the refractive index.
测量玻璃或有机玻璃块折射率的常见实验需要使用光线箱、量角器和矩形块。将矩形块放在一张纸上并描绘其轮廓。将光线以一定角度投射到一个面上，标记出入射光线、块内的折射光线以及出射光线。通过画出法线并用量角器测量入射角和折射角，可以利用斯涅尔定律计算 n。对多个角度重复该实验，并绘制 sin i 对 sin r 的图线；图线的斜率即为折射率。
When light passes through a rectangular block, the emergent ray is parallel to the incident ray but laterally displaced. This demonstrates that the ray undergoes two refractions which cancel each other’s angular deviation, provided the two faces are parallel. In a semicircular block, a common alternative, the ray enters along the radius so that it strikes the curved surface normally and exits without refraction, allowing direct measurement of the incident and refracted angles at the flat surface.
当光通过矩形块时，出射光线平行于入射光线，但发生了横向位移。这表明光线经历了两次折射，而这两次折射的角偏转相互抵消，前提是两个面是平行的。在半圆形块（一种常用的替代方案）中，光线沿半径方向射入，从而垂直照射到曲面并毫无折射地射出，这样就可以直接测量平面上的入射角和折射角。
8. Relationship Between Refractive Index and Wavelength (Dispersion) | 折射率与波长的关系（色散）
The refractive index of a material is not constant for all wavelengths of light; it varies slightly with the colour (wavelength) of the light. This phenomenon is called dispersion. Generally, the refractive index is higher for shorter wavelengths (blue/violet light) and lower for longer wavelengths (red light). As a result, when white light passes through a prism, different colours are refracted by different amounts, splitting the light into a spectrum.
材料的折射率对所有波长的光并非恒定；它会随光的颜色（波长）发生微小变化。这种现象称为色散。通常，折射率对较短波长（蓝/紫光）较高，对较长波长（红光）较低。因此，当白光通过棱镜时，不同颜色的光被不同程度地折射，将光分解为光谱。
In WJEC physics, you need to be aware that values of refractive index quoted in data sheets are usually for yellow light (specifically the sodium D-line, λ ≈ 589 nm). This wavelength-dependent property is why lenses suffer from chromatic aberration and why rainbows form through refraction and internal reflection in water droplets.
在WJEC物理中，你需要知道数据表中引用的折射率值通常对应于黄光（特别是钠的D线，λ ≈ 589 nm）。这种与波长相关的特性就是为什么透镜会出现色差，以及为什么阳光通过水滴的折射和内反射能形成彩虹的原因。
9. Real and Apparent Depth | 实深与视深
Due to refraction, objects submerged in water appear to be shallower than they actually are. The apparent depth (d_a) is the depth at which the object seems to be located when viewed from above the surface, while the real depth (d_r) is the actual distance from the surface to the object. For a plane surface and near-normal viewing (small angles), the refractive index of the medium can be related to these depths by:
由于折射，浸在水中的物体看起来比实际深度要浅。视深 (d_a) 是从水面上方观察时物体看似所在的深度，而实深 (d_r) 是水面到物体的实际距离。对于平面和接近法线的观察（小角度），介质的折射率与这些深度的关系为：
n = real depth / apparent depth = d_r / d_a
This formula is valid only when the observer’s eye is directly above the object and angles are small. This principle explains why a swimming pool looks shallower than it is, and why a ruler part-immersed in water appears bent at the surface.
该公式仅在观察者的眼睛位于物体正上方且角度很小时有效。这一原理解释了为什么游泳池看起来比实际浅，以及为什么部分浸入水中的尺子在水面处看起来是弯折的。
10. Worked Calculation Examples | 计算实例详解
Example 1: Light travels from air (n = 1.00) into glass with a refractive index of 1.50. If the angle of incidence is 30°, find the angle of refraction inside the glass. Using Snell’s law: 1.00 sin 30° = 1.50 sin r → 0.5 = 1.50 sin r → sin r = 0.333 → r = sin⁻¹(0.333) ≈ 19.5°.
示例1：光从空气 (n = 1.00) 进入折射率为1.50的玻璃。如果入射角为30°，求玻璃内的折射角。使用斯涅尔定律：1.00 sin 30° = 1.50 sin r → 0.5 = 1.50 sin r → sin r = 0.333 → r = sin⁻¹(0.333) ≈ 19.5°。
Example 2: Calculate the critical angle for light travelling from water (n = 1.33) into air. Using sin C = 1 / n = 1 / 1.33 = 0.752 → C = sin⁻¹(0.752) ≈ 48.8°. Any incident angle greater than 48.8° will result in total internal reflection inside the water.
示例2：计算光从水 (n = 1.33) 进入空气的临界角。使用 sin C = 1 / n = 1 / 1.33 = 0.752 → C = sin⁻¹(0.752) ≈ 48.8°。任何大于48.8°的入射角都会导致光在水中发生全内反射。
Example 3: A microscope is focused on a scratch on the bottom of a glass block (n = 1.50) of thickness 4.0 cm. How far below the surface does the scratch appear to be? Using n = d_r / d_a → 1.50 = 4.0 cm / d_a → d_a = 4.0 / 1.50 ≈ 2.67 cm.
示例3：一台显微镜聚焦在一块厚度为4.0厘米、折射率为1.50的玻璃块底部的一处划痕上。划痕看起来位于表面下方多深处？使用 n = d_r / d_a → 1.50 = 4.0 cm / d_a → d_a = 4.0 / 1.50 ≈ 2.67 cm。
11. Exam Tips and Common Pitfalls | 考试技巧与常见误区
Always check that your calculated angle of refraction is physically sensible: when entering a denser medium, r must be smaller than i; when entering a less dense medium, r must be larger. A common mistake is to invert the refractive index ratio when applying Snell’s law. Remember that sin C = 1/n only applies when the second medium is air (or vacuum); if it is another material, you must use n₁ sin C = n₂.
一定要检查你计算出的折射角在物理上是合理的：进入光密介质时，r 必须小于 i；进入光疏介质时，r 必须大于 i。一个常见的错误是在应用斯涅尔定律时颠倒了折射率比值。记住，sin C = 1/n 只适用于第二介质是空气（或真空）的情况；如果是另一种材料，你必须使用 n₁ sin C = n₂。
In ray diagrams, draw continuous straight lines with arrows indicating the direction of light travel. Always label the normal, the angles (i and r or C), and the two media. When describing an experiment, include detail about how you ensured the ray was accurately traced (e.g., using a sharp pencil, placing pins, or using a laser). Explain repeated measurements to reduce random error and how systematic errors (such as zero error on a protractor) might be eliminated.
在光线图中，用连续的直线绘制光线，并用箭头标明光的传播方向。务必标出法线、角度（i 和 r 或 C）以及两种介质。在描述实验时，详细说明你是如何确保光线被精确追踪的（例如，使用尖细的铅笔、插大头针或使用激光）。解释如何通过重复测量来减小随机误差，以及如何消除系统误差（比如量角器的
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