IGCSE CIE Physics: Refraction of Light – Key Points Revision | IGCSE CIE 物理：光的折射考点精讲

📚 IGCSE CIE Physics: Refraction of Light – Key Points Revision | IGCSE CIE 物理：光的折射考点精讲

Refraction is the change in direction of a wave when it passes from one medium to another due to a change in its speed. In IGCSE CIE Physics, light rays bending at boundaries between air, water, glass and other transparent materials form a crucial topic, directly tested through ray diagrams, calculations using Snell’s law, and understanding total internal reflection.

折射是波在从一种介质进入另一种介质时，由于速度改变而发生的方向变化。在 IGCSE CIE 物理中，光线在空气、水、玻璃等透明材料交界处的弯曲是一个关键主题，会通过光线图、斯涅尔定律的计算以及对全内反射的理解直接考查。

1. Introduction to Refraction | 折射简介

When a light ray travels from one transparent medium to another at an angle, its path bends at the boundary. This bending is called refraction. If light enters a denser medium (e.g. from air to glass), it slows down and bends towards the normal. If it enters a less dense medium (e.g. from glass to air), it speeds up and bends away from the normal.

当光线从一种透明介质倾斜射入另一种透明介质时，其路径在界面处发生弯曲，这就是折射。如果光进入光密介质（例如从空气到玻璃），速度变慢，向法线方向偏折；如果进入光疏介质（例如从玻璃到空气），速度变快，远离法线偏折。

The normal is an imaginary line perpendicular to the surface at the point of incidence. All angles – angle of incidence i, angle of refraction r – are measured between the ray and the normal. If light hits the boundary exactly along the normal (i = 0°), it continues straight without bending, although its speed and wavelength still change.

法线是一条在入射点处垂直于界面的假想线。所有角度——入射角 i、折射角 r——都是光线与法线之间的夹角。如果光恰好沿法线方向射入界面（i = 0°），光线继续直线传播不发生偏折，但其速度和波长仍然改变。

2. The Laws of Refraction | 折射定律

Refraction follows two fundamental laws. First, the incident ray, the refracted ray and the normal all lie in the same plane. Second, for any given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This second statement is Snell’s law, typically written as n = sin i / sin r where n is the refractive index of the second medium with respect to the first.

折射遵循两条基本定律。第一，入射光线、折射光线和法线位于同一平面内。第二，对于任意给定的两种介质，入射角的正弦与折射角的正弦之比为常数。这第二条就是斯涅尔定律，通常写作 n = sin i / sin r，其中 n 是第二种介质相对于第一种介质的折射率。

At IGCSE level, you are often given the refractive index from air to a material. Recall that n is always greater than 1 when light enters an optically denser medium. The law of reversibility also holds: if light reverses direction, it follows exactly the same path.

在 IGCSE 层面，通常会给出光从空气射入某种材料时的折射率。记住，当光进入光密介质时，n 总是大于 1。光路可逆原理也成立：如果光反向传播，它会遵循完全相同的路径。

3. Refractive Index | 折射率

The refractive index n of a medium measures how much it slows down light. By definition, n = speed of light in vacuum c / speed of light in medium v. Since v is always less than c, n is always greater than 1. For air, n is approximately 1.00, so in most IGCSE problems you can treat air as a vacuum.

介质的折射率 n 衡量光在该介质中减速的程度。定义为 n = 真空中的光速 c / 介质中的光速 v。由于 v 总是小于 c，n 总是大于 1。对于空气，n 近似为 1.00，因此在大多数 IGCSE 问题中，可以把空气视为真空。

The same n can also be expressed as n = sin i / sin r. This equation links the optical density to the bending effect. A higher refractive index means a greater change in speed and a larger bending towards the normal when entering from air.

同一个 n 也可以表示为 n = sin i / sin r。这个方程把光密度与偏折效应联系起来。折射率越高，意味着速度变化越大，从空气进入时向法线的偏折也越大。

Typical values to memorise: n for glass ≈ 1.5, for water ≈ 1.33, for diamond ≈ 2.4. These are approximate and can vary slightly with the type of glass or water condition, but the exam paper will provide the needed value.

需要记住的典型值：玻璃的 n 约为 1.5，水的 n 约为 1.33，钻石的 n 约为 2.4。这些都是近似值，会因玻璃种类或水的状态略有变化，但试卷会提供所需的数值。

4. Snell’s Law Calculations | 斯涅尔定律计算

Snell’s law allows you to find an unknown angle or refractive index. Use n₁ sin θ₁ = n₂ sin θ₂, where n₁, n₂ are the absolute refractive indices of the two media, and θ₁, θ₂ are angles measured from the normal. For the common case of light travelling from air (n₁ = 1) into a medium, this simplifies to n₂ = sin i / sin r.

斯涅尔定律可用于求解未知角度或折射率。使用 n₁ sin θ₁ = n₂ sin θ₂，其中 n₁、n₂ 是两种介质的绝对折射率，θ₁、θ₂ 是与法线的夹角。对于光从空气（n₁ = 1）射入某种介质的常见情况，可简化为 n₂ = sin i / sin r。

In calculations, always double-check that your calculator is in degree mode. Rearrange the formula firmly: for example, sin r = (n₁ sin i) / n₂. Show all working; marks are awarded for correct substitution even if the final answer has a slip.

计算时，务必确认计算器处于角度（度）模式。牢固掌握公式变形：例如 sin r = (n₁ sin i) / n₂。写出完整步骤；即使最终答案有误，只要代入正确就能得分。

For a ray going from glass (n = 1.5) into water (n = 1.33), calculate the angle of refraction if the angle of incidence is 30°. sin r = (n_g sin i) / n_w = (1.5 × sin 30°) / 1.33 ≈ (1.5 × 0.5) / 1.33 = 0.75 / 1.33 ≈ 0.564. Then r = sin⁻¹(0.564) ≈ 34.3°. Always check that r > i when moving to a less dense medium, which is correct here.

对于光线从玻璃（n=1.5）进入水（n=1.33），若入射角为 30°，折射角计算如下：sin r = (n_g sin i) / n_w = (1.5 × sin 30°) / 1.33 ≈ (1.5 × 0.5) / 1.33 = 0.75 / 1.33 ≈ 0.564，然后 r = sin⁻¹(0.564) ≈ 34.3°。记住：当进入光疏介质时，r > i，此处符合规律。

5. Refraction through a Glass Block | 光线通过玻璃块的折射

A classic IGCSE experiment traces a ray through a rectangular glass block. The ray bends towards the normal upon entering the block and away from the normal upon exiting. Because the two surfaces are parallel, the emergent ray is parallel to the incident ray but laterally displaced. The amount of lateral shift depends on the thickness, the angle of incidence, and the refractive index.

一个经典的 IGCSE 实验是追踪光线通过矩形玻璃块。光线进入时向法线偏折，离开时远离法线偏折。由于两个表面平行，出射光线与入射光线平行，但发生了横向位移。横向位移的大小取决于厚度、入射角和折射率。

Diagram drawing conventions are important: use a ruler, draw normals as dashed lines, label all angles, and mark the rays with arrows. There is no change in wavelength or frequency inside the medium, but the speed and wavelength are reduced proportionally while frequency remains constant.

画图规范很重要：使用直尺，法线画成虚线，标注所有角度，用箭头标记光线方向。在介质内部，频率不变，但速度和波长成比例减小，频率保持不变。

When a ray passes from glass to air, if the angle inside the glass is gradually increased, at some point the refracted ray bends 90° to the normal. That special angle links directly to the critical angle and total internal reflection, discussed next.

当光线从玻璃射入空气时，如果逐渐增大玻璃内的入射角，折射光会在某一点偏折到与法线成 90°。这一特殊角度直接关联到临界角和全内反射，下面会讲到。

6. 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, there is a critical angle c for which the angle of refraction is 90°. If the angle of incidence is greater than c, the light undergoes total internal reflection (TIR): no light is refracted; the boundary acts like a perfect mirror.

当光从光密介质射向光疏介质时，存在一个临界角 c，此时折射角为 90°。如果入射角大于 c，则发生全内反射（TIR）：没有折射光，界面就像一块完美的镜子一样将光全部反射回来。

The relationship for the critical angle is given by sin c = n_air / n_medium = 1 / n (when the second medium is air with n=1). From n = 1 / sin c, you can calculate n if c is known. For glass with n=1.5, sin c = 1/1.5 ≈ 0.667, so c ≈ 41.8°.

临界角的关系式为 sin c = n_air / n_medium = 1 / n（当第二种介质为空气，且 n=1 时）。由 n = 1 / sin c，如果已知 c，可求出折射率。对于 n=1.5 的玻璃，sin c = 1/1.5 ≈ 0.667，因此 c ≈ 41.8°。

Two conditions must be met for TIR: (i) light must be moving from a denser to a rarer medium; (ii) the angle of incidence in the denser medium must exceed the critical angle. This principle is exploited in optical fibres and prisms in periscopes.

发生全内反射必须满足两个条件：（i）光必须从光密介质射向光疏介质；（ii）光密介质内的入射角必须大于临界角。光纤和潜望镜中的棱镜都利用了此原理。

7. Applications: Optical Fibres | 应用：光纤

Optical fibres use total internal reflection to transmit light signals over long distances with minimal loss. A fibre consists of a thin glass core surrounded by cladding with a lower refractive index. Light entering one end strikes the core-cladding boundary at angles greater than the critical angle and travels along the fibre by repeated TIR.

光纤利用全内反射，以极低的损耗长距离传输光信号。光纤由极细的玻璃纤芯和环绕其外的低折射率包层构成。从一端进入的光线以大于临界角的角度射向纤芯与包层的界面，通过反复的全内反射沿光纤传播。

Advantages include high transmission speed, immunity to electromagnetic interference, and greater data capacity. In IGCSE, you need to label a diagram showing a ray zigzagging inside a fibre and explain why the cladding is necessary: it protects the core and ensures that total internal reflection occurs even if the fibre bends slightly.

其优点包括传输速度快、不受电磁干扰以及更大的数据容量。在 IGCSE 中，你需要能画图标出光线在光纤内曲折传播的路径，并解释为什么需要包层：它保护纤芯，并且即使光纤轻微弯曲，也能保证全内反射的发生。

8. Dispersion of White Light | 白光的色散

When a beam of white light enters a triangular prism, it is refracted twice – on entry and on exit – and split into its constituent colours, a phenomenon called dispersion. This occurs because the refractive index of glass varies slightly with wavelength: violet light is slowed more and bent most, while red is slowed least and bent least.

当一束白光射入三棱镜时，它经过两次折射——进入和离开——并被分解为其组成色光，这一现象叫做色散。这是因为玻璃对不同波长的光的折射率略有不同：紫光减速最多，偏折最大；红光减速最少，偏折最小。

The spectrum produced is a continuous band: red, orange, yellow, green, blue, indigo, violet (ROYGBIV). You should recall that red has the longest wavelength and smallest deviation; violet has the shortest wavelength and greatest deviation. Monochromatic light cannot be dispersed.

产生的光谱是一条连续的色带：红、橙、黄、绿、蓝、靛、紫（ROYGBIV）。需要记住，红光波长最长，偏折最小；紫光波长最短，偏折最大。单色光则无法被色散。

9. The Refraction of Light in Prisms | 棱镜中的折射

Triangular prisms are often used to demonstrate TIR in optical instruments. A 45°–45°–90° prism can act as a perfect reflector, sending light through 90° or 180°. Unlike plane mirrors, prisms do not tarnish and give a brighter image because total internal reflection is 100% efficient.

三棱镜常用于演示光学仪器中的全内反射。一个 45°–45°–90° 棱镜可以充当完美的反射镜，使光线偏转 90° 或 180°。与平面镜不同，棱镜不会氧化变暗，并且因为全内反射是 100% 高效的，能提供更亮的像。

In a periscope, two 45° prisms replace mirrors to reflect light along the tube. In a binocular, Porro prisms invert the image. If asked to draw a prism, show the incident ray, the TIR inside the prism, and the emergent ray perpendicular to the faces. Always indicate normal lines at each boundary.

在潜望镜中，两个 45° 棱镜代替镜子使光线沿管筒反射。双筒望远镜中，波罗棱镜使图像倒转。如果要求画棱镜，要画出入射光线、棱镜内部的全内反射以及垂直于表面的出射光线。在每个界面处都要标出法线。

10. Experimental Determination of Refractive Index | 折射率的实验测定

The standard IGCSE practical uses a rectangular glass block and a ray box with a narrow slit. You shine a ray into the block at an angle, mark the incident ray and emergent ray on paper, remove the block, join the entry and exit points, draw normals, measure angles i and r with a protractor, and then calculate n = sin i / sin r.

标准的 IGCSE 实验使用矩形玻璃块和带有狭缝的光线盒。将光线以一定角度射入玻璃块，在纸上标记入射光线和出射光线，移开玻璃块，连接入射点和出射点，画出法线，用量角器测量 i 和 r，然后计算 n = sin i / sin r。

Obtain multiple pairs of i and r by varying the incident angle. Plot a graph of sin i against sin r – it should yield a straight line through the origin, whose gradient equals the refractive index n. This reduces random error. Use a sharp pencil and thin lines for accuracy.

通过改变入射角获取多组 i 和 r 数据。绘制 sin i 关于 sin r 的图像——应得到一条过原点的直线，其梯度就等于折射率 n。这样做能减小随机误差。使用削尖的铅笔和细线条以确保准确性。

11. Common Mistakes and Tips | 常见错误与技巧

Mistake 1: Confusing angle i and r with the angle between the ray and the surface. Always measure from the normal. Mistake 2: Forgetting that n = sin i / sin r works only when the first medium is air (or vacuum). Use n₁ sin θ₁ = n₂ sin θ₂ for two media with different refractive indices.

错误 1：混淆入射角 i 和折射角 r 与光线和表面之间的夹角。一定要从法线开始测量。错误 2：忘记 n = sin i / sin r 仅在第一种介质为空气（或真空）时适用。当两种介质折射率不同时，应使用 n₁ sin θ₁ = n₂ sin θ₂。

Mistake 3: In TIR problems, incorrectly identifying the critical angle. Remember: the critical angle is in the denser medium. Mistake 4: Claiming that frequency changes during refraction – it does not; speed and wavelength change. A handy check: when light slows down, wavelength shortens; frequency remains constant.

错误 3：在全内反射问题中，错误地识别临界角。记住：临界角是在光密介质中量度的。错误 4：声称折射时频率改变——实际上频率不变；变化的是速度和波长。一个便捷的记忆法：当光速变慢时，波长变短；频率保持不变。

When drawing ray diagrams, always put arrows on rays and label angles with i, r, and normal. Show at least one normal line at each boundary. For TIR to occur, make sure the angle inside the denser medium exceeds c and that the ray is travelling towards a rarer medium.

画光线图时，务必在光线上标箭头，并用 i、r 和法线标注角度。每个界面处至少画出一条法线。发生全内反射时，确保光密介质内的入射角大于 c，且光线正向光疏介质传播。

12. Summary | 总结

Mastering refraction involves knowing what causes it (change in speed), applying Snell’s law confidently, and visualising ray paths in different media. Total internal reflection and its applications in optical fibres and prisms are heavily examined. Practise calculations, diagram drawing, and describing experiments until they feel routine.

掌握折射需要理解其成因（速度的改变），熟练运用斯涅尔定律，并能想象光线在不同介质中的路径。全内反射及其在光纤和棱镜中的应用是高频考点。反复练习计算、画图和描述实验，直到这些内容成为你的本能。

Finally, link the concept to everyday phenomena: the apparent bending of a straw in water, the sparkle of diamonds (high n and small critical angle), and mirages caused by atmospheric refraction. Such context strengthens your understanding and helps in explanation questions.

最后，将概念与日常现象联系起来：水中吸管看似弯曲、钻石因高折射率和小临界角而闪耀、以及大气折射造成的海市蜃楼。这些情境能加深你的理解，在解释题中大有帮助。

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IGCSE CIE Physics: Refraction of Light – Key Points Revision | IGCSE CIE 物理：光的折射 考点精讲