IGCSE物理0625 波 v=fλ 折射 临界角
Cambridge IGCSE Physics 0625 的第三块内容叫 Waves，考纲把它拆成四节：波的一般性质、光的折射、电磁波谱、声音。2026 至 2028 年的考纲沿用了这个结构，Core 与 Supplement 逐条列出学习要求，选择题卷与结构题卷都会反复考这一块。
很多学生以为波这一章背下电磁波谱就够了，真正的失分点在波形图的读法和光线转折方向的判断上。下面按考纲顺序把十四个常考口子拆开，每一条给出公式、算例和常见的错误。
Waves is the third topic in the Cambridge IGCSE Physics 0625 syllabus, and the 2026 to 2028 version keeps the same four sections. Core and Supplement statements are listed side by side, and both the multiple choice paper and the structured theory paper return to this material in every series. Most of the marks sit in definitions, the wave equation and the direction a ray turns at a boundary.
波传的是能量不是物质
一列波从手传到绳子的另一端，绳子上的每一小段只在原位置上下摆动，最后回到出发点。考纲要求写出的句子是波传递能量而不传递物质，主语和两个宾语都不能丢。水面的浮标随波起伏却不会被推到岸边，正好说明这件事。声音也一样，空气分子来回振动，把能量送进耳朵，空气本身没有跑到你面前。这一条在 Core 里排第一位，简答题会直接问波传递的是什么。
A wave carries energy from a source to a receiver while the particles of the medium only oscillate about fixed equilibrium positions. A cork on a pond bobs up and down but never travels with the ripple, and a shout reaches you without any air being pushed across the room. An answer that says the wave moves matter along the rope scores nothing.
波形图先分清三个量
波长是两个相邻波峰之间的距离，量相邻波谷也可以。振幅从中线量到波峰，不是从波峰量到波谷，图上标着峰谷高度 6 cm 时振幅只有 3 cm，这是最常见的错误。周期是一次完整振动的时间，与频率互为倒数。频率是每秒振动次数，单位是 Hz。读图之前先看横轴写的是距离还是时间，同样是相邻两个峰，一个读波长一个读周期。
Wavelength is the distance from one crest to the next, and amplitude runs from the centre line to a crest rather than from crest to trough. A diagram labelling 6 cm from crest to trough means an amplitude of 3 cm. Period is the time for one complete oscillation and it is the reciprocal of frequency, so check whether the horizontal axis carries distance or time before reading a value.
v = fλ 的三种问法
波速等于频率乘波长，考纲要求会背也会用。算例：一列频率 250 Hz、波长 1.36 m 的声波，速度是 250 乘 1.36 等于 340 m/s，落在考纲给出的空气中 330 至 350 m/s 区间内。反过来求频率就用 f = v 除以 λ，求波长就用 λ = v 除以 f。单位换算是失分大户，波长给的是 cm 就先除以 100。频率由波源决定，进入另一种介质后不会改变。
Wave speed equals frequency multiplied by wavelength, and rearranging gives frequency as speed divided by wavelength. A 250 Hz sound wave of wavelength 1.36 m travels at 340 m/s, inside the 330 to 350 m/s range the syllabus quotes for air. Convert centimetres to metres before substituting, and remember that frequency is fixed by the source and survives any change of medium.
横波与纵波的区别
横波的振动方向与传播方向垂直，绳子上的波、水波、电磁波和地震 S 波都归这一类。纵波的振动方向与传播方向平行，弹簧一端被推拉时疏密相间地传出去就是纵波。声音是纵波，所以有压缩区和稀疏区，而不是波峰与波谷。答题时粒子与方向两个词都要出现，只写波是垂直的不给分。地震波是考纲里同时出现两种波形的例子，P 波是纵波，S 波是横波。
In a transverse wave the vibration is at right angles to the direction of travel, which covers light, all other electromagnetic waves, water waves and seismic S-waves. In a longitudinal wave the vibration is parallel to the direction of travel, so a slinky shows compressions and rarefactions instead of crests and troughs. Sound and seismic P-waves are longitudinal, and sound cannot cross a vacuum because it needs a medium to compress.
反射定律与平面镜成像
反射定律只有一句话，入射角等于反射角，两个角都从法线量起，不是从镜面量起。平面镜成的像是虚像，与物体等大，像到镜面的距离等于物到镜面的距离。作图时把反射光线反向延长，用虚线画到镜后，交点就是像的位置。反射只改变方向，速度、频率和波长都不变，所以反射波的波前间距与原波相同。题目若给出光线与镜面的夹角 30 度，入射角是 60 度，这一步换算常被漏掉。
The law of reflection says the angle of incidence equals the angle of reflection, and both are measured from the normal rather than from the mirror surface. A plane mirror forms a virtual image that is the same size as the object and the same distance behind the mirror. Extend the reflected rays backwards with dashed lines to find it; only direction changes, so speed, frequency and wavelength stay as they were.
折射的成因是速度变化
光从空气斜射进玻璃或水，速度变慢，光线向法线偏折，折射角小于入射角。从玻璃射回空气时速度变快，光线偏离法线。沿法线入射时速度照样变化，方向却不变。这里最容易被扣分的说法是折射因为振幅变了，真正的原因是波前的一端先减速，整条波前随之转向。频率始终不变，所以红光在玻璃里仍然是红光。
Refraction happens because the speed changes at the boundary, so a wavefront arriving at an angle pivots as one end slows before the other. Light entering glass bends towards the normal, light leaving glass bends away from it, and a ray along the normal changes speed without changing direction. Frequency is untouched, which is why colour is unaffected.
折射率 n 的两个算法
折射率定义为光在两种介质中速度的比值，也等于 sin i 除以 sin r，其中 i 要取空气一侧的角。n 没有单位，永远大于 1，玻璃约 1.5，水约 1.33。算例：光以 45 度入射到 n 等于 1.5 的玻璃，sin r 等于 sin 45 除以 1.5 等于 0.471，查表得 r 约 28 度。用 n = c 除以 v 可以反求介质中的光速，3.0 乘 10^8 除以 1.5 等于 2.0 乘 10^8 m/s。n 只由这两种介质决定，与入射角大小无关，判断题常在这里设陷阱。算 sin r 时先算比值再取反正弦，不要把两个角度直接相除。
Refractive index is the ratio of the speed of light in one region to the speed in the other, and it also equals sine i divided by sine r with i taken in air. It carries no unit and is always above one, roughly 1.5 for glass and 1.33 for water. Use n equals c divided by v to get the speed inside the material, so light moves at 2.0 times 10^8 m/s in glass of index 1.5.
临界角与全反射
光从玻璃射向空气时折射角大于入射角，入射角增大到某一数值，折射角正好 90 度，这个入射角就是临界角。超过临界角，光线全部反射回玻璃内部，没有折射光线射出，这叫全反射。全反射要同时满足两个条件，光从光密介质射向光疏介质，入射角大于临界角。临界角用 sin c 等于 1 除以 n 求，n 等于 1.5 时得到约 42 度。光纤通信、钻石的闪光、45 度棱镜转像全都靠它。入射角正好等于临界角时折射光线沿着界面走，作图要画成贴着表面的一条线。
The critical angle is the angle of incidence inside the denser medium for which the angle of refraction is exactly 90 degrees, so the refracted ray runs along the surface. Past that angle nothing escapes and the light is totally internally reflected. Both conditions must hold, namely travel from the denser to the less dense medium and an angle of incidence above the critical value. Calculate it from sine c equals 1 divided by n, about 42 degrees for glass, and the same effect runs optical fibres, diamond sparkle and 45 degree prisms.
棱镜色散与波长
白光通过三棱镜分成七种颜色，这个现象叫色散，原因是不同颜色在玻璃中的速度略有差别。紫光速度最慢、折射最多，红光速度最快、折射最少，所以紫光偏折得最厉害。考纲给出的两个参考波长是红光 700 nm、蓝光 470 nm。很多学生以为色散就是衍射，两者完全不同，衍射是波绕过缝隙或障碍后散开，色散是速度随颜色不同造成的光线分离。考纲只要求知道色散由速度差异造成，不要求算出各种颜色的折射率。
White light splits into its colours in a prism because each colour travels at a slightly different speed in glass, so violet bends most and red least. The syllabus quotes 700 nm for red and 470 nm for blue as reference wavelengths. Dispersion is not diffraction, since diffraction is spreading after a gap or an edge while dispersion separates colours through a speed difference.
凸透镜成像的三段区间
凸透镜把平行于主光轴的光线会聚到主焦点，焦点到透镜中心的距离叫焦距。物距大于二倍焦距时成倒立缩小的实像，物距介于一倍与二倍焦距之间成倒立放大的实像，物距小于焦距成正立放大的虚像，虚像不能用光屏承接。放大率等于像高除以物高，也等于像距除以物距。作图用三条特殊光线里的两条就够，平行光线过焦点，过焦点的光线出射后平行，过光心的光线不偏折。焦距越短，透镜会聚光线的本领越强，实像的位置也越靠近透镜。
A converging lens brings rays parallel to the principal axis to the principal focus, and focal length is the distance from the centre of the lens to that point. An object beyond twice the focal length gives a real, inverted and diminished image, an object inside the focal length gives a virtual, upright and magnified one that no screen can catch. Magnification is image height over object height, and two of the three standard rays locate any image.
电磁波谱的顺序与用途
按频率从低到高排列是无线电波、微波、红外线、可见光、紫外线、X 射线、伽马射线，按波长排列顺序正好相反。所有电磁波在真空中的速度都是 3.0 乘 10^8 m/s，在空气中近似相同。它们都是横波，传播不需要介质。用途常考：微波对应卫星电视与手机通信，红外对应遥控器、热成像与光纤，紫外对应验钞与净水，X 射线对应医学成像与安检，伽马射线对应食品与器械灭菌以及癌症治疗。背顺序时按波长从长到短走更稳，无线电波最长，伽马射线最短，中间隔着可见光。
The spectrum runs from radio through microwave, infrared, visible light, ultraviolet, X-rays and gamma rays as frequency rises, and the order reverses for wavelength. Every electromagnetic wave travels at 3.0 times 10^8 m/s in a vacuum and at about the same speed in air, and all of them are transverse and need no medium. The syllabus names microwaves for satellite television and mobile phones, infrared for remote controls and thermal imaging, ultraviolet for detecting fake bank notes and sterilising water, X-rays for medical scanning, and gamma rays for sterilising equipment and treating cancer.
过量照射的危害与防护
危害按波段分开记：微波造成体内组织受热，红外造成皮肤灼伤，紫外线损伤表层细胞和眼睛并可能引发皮肤癌，X 射线和伽马射线会损伤细胞、引起突变。防护的通用思路是缩短暴露时间、增大距离、加合适屏蔽。考试问为什么 X 射线能成像却不该反复做，要把穿透能力强和电离作用这两件事分开写，前者解释成像，后者解释危害。紫外线是考纲里明确提到眼睛的波段，答危害时不要只写皮肤。屏蔽材料按穿透能力选，X 射线机房用铅，微波炉门上用金属网。
Harm depends on the region: microwaves heat tissue internally, infrared burns skin, ultraviolet damages surface cells and eyes, and X-rays and gamma rays damage cells and may cause mutation. Protection works the same way each time, through less exposure, more distance and suitable shielding. When asked why X-rays can image the body but should not be repeated, keep penetration and ionisation as two separate points.
声音、音调与回声测距
声音由振动源产生，是纵波，必须有介质，真空不能传声。人耳可听范围是 20 Hz 到 20000 Hz，空气中声速约 330 至 350 m/s，一般在固体中最快、液体次之、气体最慢。振幅决定响度，频率决定音调，这两组对应关系几乎每份卷都会考。回声测距用 s 等于 v 乘 t 再除以 2，除以 2 是因为声音往返走了一去一回。测空气中声速的经典做法是两人相隔一段距离，一人击掌，另一人在看到动作时按下秒表。
Sound comes from a vibrating source and travels as a longitudinal wave that needs a medium, so it cannot pass through a vacuum. Human hearing spans 20 Hz to 20 000 Hz, the speed of sound in air is about 330 to 350 m/s, and sound is generally fastest in solids and slowest in gases. Amplitude sets loudness and frequency sets pitch; echo ranging uses speed multiplied by time and then halved, because the pulse travels out and back.
超声波与卷面写法
频率高于 20000 Hz 的声音叫超声，波长短、方向性好、能量集中，用于医学扫描、材料探伤和声呐测距。卷面结构方面，0625 的每个考生考三份卷：选择题卷 45 分钟占 30%，理论题卷 1 小时 15 分钟占 50%，实验卷或替代实验卷占 20%。计算题要写出公式、代入过程和单位，只给答案通常拿不到满分。作图题的法线、角度标注与光线箭头都是独立的给分点。替代实验卷与实验卷考同一批技能，只是用纸笔描述操作、读数和处理数据。
Ultrasound means sound above 20 000 Hz, and its short wavelength and concentrated energy suit medical scanning, testing materials and sonar. In 0625 each candidate sits three components, a 45 minute multiple choice paper worth 30 per cent, a 1 hour 15 minute theory paper worth 50 per cent, and the practical test or its alternative worth 20 per cent. Write the equation, the substitution and the unit on every calculation, since a bare answer rarely earns full credit.
复习顺序建议照考纲四节走：先把 v = fλ 与波形图读法练到稳定，再练折射与全反射的光路作图，最后整理电磁波谱的顺序、用途与危害对照表。每一条都练到能用一句完整的中文或英文写出来，比记住一个孤立的词更有用。
Revision works best in the order the syllabus uses, starting with the wave equation and waveform reading, then ray diagrams for refraction and total internal reflection, and finally the spectrum with its uses and hazards set side by side. For each statement, practise one complete sentence in English rather than a remembered keyword.
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