IGCSE Physics: Waves, Light, Sound and the Electromagnetic Spectrum

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IGCSE Physics: Waves, Light, Sound and the Electromagnetic Spectrum

TL;DR

You'll learn how to calculate wave speed, frequency and wavelength using one formula, and apply it to light, sound and the EM spectrum. You'll master reflection and refraction rules well enough to draw accurate ray diagrams. You'll also know exactly which EM spectrum uses and dangers examiners test every year.

1. The Mental Model

A wave carries energy from one place to another without carrying matter with it. Everything else — reflection, refraction, diffraction — is just the wave meeting something that changes its speed or direction. Once you accept that waves are energy transfers governed by one speed equation, the whole topic becomes arithmetic and careful diagrams. Waves move energy, not stuff.

2. The Core Material

2.1 Wave Basics and the Speed Equation

Every wave — water, sound, light, radio — obeys the same relationship:

$$v = f\lambda$$

where $v$ is speed (m/s), $f$ is frequency (Hz), and $\lambda$ is wavelength (m). Frequency is how many complete waves pass a point per second; wavelength is the distance between two identical points on consecutive waves (crest to crest, or compression to compression).

Transverse waves (light, water, all EM waves) oscillate perpendicular to the direction of travel — think of shaking a rope up and down while it travels sideways. Longitudinal waves (sound, ultrasound) oscillate parallel to the direction of travel — compressions and rarefactions moving through air, like a slinky pushed and pulled.

Amplitude is the maximum displacement from the rest position — it determines a wave's energy (and for sound, its loudness; for light, its brightness). Amplitude is NOT the same as wavelength — this confusion costs marks constantly.

Period $T$ is the time for one complete wave, linked to frequency by:

$$T = \frac{1}{f}$$

2.2 Reflection and Refraction

Reflection follows one unbreakable rule: the angle of incidence equals the angle of reflection, both measured from the normal — an imaginary line drawn perpendicular to the surface at the point of contact. Never measure from the surface itself; examiners penalise this immediately.

Refraction happens when a wave changes speed crossing a boundary between two media, which bends its direction (unless it hits the boundary at exactly 90°, in which case it slows/speeds up but doesn't bend). Light slows down entering a denser medium (like glass or water) and bends towards the normal. It speeds up leaving a denser medium and bends away from the normal.

The refractive index $n$ links speed, angles, and bending:

$$n = \frac{\sin\theta_1}{\sin\theta_2} = \frac{c}{v}$$

where $\theta_1$ is the angle in air (or vacuum), $\theta_2$ is the angle in the denser medium, $c$ is the speed of light in vacuum ($3\times10^8$ m/s), and $v$ is the speed in the medium.

Total internal reflection (TIR) occurs when light tries to leave a denser medium at an angle greater than the critical angle $C$, where:

$$\sin C = \frac{1}{n}$$

Beyond $C$, all light reflects back inside the denser medium instead of refracting out. This is exactly how optical fibres carry data — light bounces along the inside of the glass fibre via repeated TIR, barely losing any energy, which is why fibre-optic cables beat old copper wires for carrying internet signals.

flowchart TD
    A["Light hits boundary inside denser medium"] --> B{"Angle of incidence vs critical angle C?"}
    B -->|"angle < C"| C["Light refracts out — partial reflection + refraction"]
    B -->|"angle = C"| D["Refracted ray travels along the boundary at 90°"]
    B -->|"angle > C"| E["Total internal reflection — all light reflects back inside"]
    E --> F["Used in optical fibres and periscope prisms"]

2.3 The Electromagnetic Spectrum and Sound

All EM waves travel at the same speed in a vacuum — $3\times10^8$ m/s — but differ in frequency and wavelength, which is why they behave so differently. In order of increasing frequency (decreasing wavelength): radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.

Sound is different in kind: it's a longitudinal mechanical wave, meaning it needs a medium (solid, liquid or gas) and cannot travel through a vacuum — a classic "explain why" exam question. Human hearing range is roughly 20 Hz to 20,000 Hz; anything above that is ultrasound, used in medical scanning and cleaning because it reflects off boundaries between tissues of different density, letting equipment build an image from the reflected echoes (same principle as an echo: distance = speed × time, divided by 2 because the sound travels there and back).

3. Worked Example

Question: A sound wave travels through water at 1500 m/s. It has a frequency of 300 Hz. Calculate its wavelength. Then, if a ship sends an ultrasound pulse downward and the echo returns after 0.8 seconds, calculate the depth of the water.

Part 1 — wavelength:

Rearrange $v = f\lambda$ to solve for $\lambda$:

$$\lambda = \frac{v}{f} = \frac{1500}{300} = 5\text{ m}$$

Part 2 — depth using echo time:

The 0.8 s includes the journey down and back up, so the one-way time is $0.8 \div 2 = 0.4$ s.

$$\text{distance} = \text{speed} \times \text{time} = 1500 \times 0.4 = 600\text{ m}$$

So the water is 600 m deep. The trap here: forgetting to halve the time is the single most common error in echo-sounding questions — always check whether the given time is "there" or "there and back."

4. Examiner's Breakdown

4.1 What Examiners Actually Reward

1. "The angle of incidence is measured between the incident ray and the normal, not the surface."
2. "Frequency is the number of waves passing a point per second, measured in hertz (Hz)."
3. "Light slows down and bends towards the normal when entering a denser medium."
4. "Total internal reflection occurs when the angle of incidence exceeds the critical angle and the ray is travelling from a denser into a less dense medium."
5. "Electromagnetic waves are transverse waves that transfer energy without transferring matter, and all travel at the same speed in a vacuum."
6. "Sound cannot travel through a vacuum because it requires particles of a medium to vibrate and transfer energy."

4.2 Trapdoor Mistakes

1. MISTAKE: Measuring angles from the surface of the mirror or glass block. → FIX: Always draw the normal first (perpendicular, dashed line) and measure every angle from it.
2. MISTAKE: Saying amplitude and wavelength are "basically the same thing" when asked what affects loudness/brightness. → FIX: State clearly — amplitude relates to energy/loudness/brightness; wavelength relates to pitch/colour, and they're independent properties.
3. MISTAKE: Forgetting to halve the time in echo/ultrasound depth calculations. → FIX: Always write "time for one-way journey = total time ÷ 2" explicitly as a working line, even if it seems obvious.
4. MISTAKE: Claiming all EM waves "are dangerous" or "all cause cancer" in a blanket statement. → FIX: Match the specific hazard to the specific wave — UV causes skin cancer/skin damage; X-rays and gamma rays cause cell mutation; microwaves cause internal heating, not mutation.

4.3 Score-Boosting Comparisons

5. Now Try It

Exam-style question: "A ray of light travels from air into a glass block at an angle of incidence of 40°. The refractive index of the glass is 1.5. (a) Calculate the angle of refraction. (b) Calculate the critical angle for this glass. (c) Explain what would happen if light inside the glass hit the glass-air boundary at an angle of 50°."

A top-band answer must: show the rearranged formula $\sin\theta_2 = \sin\theta_1 / n$ with substituted numbers before giving a final angle to 1 decimal place; use $\sin C = 1/n$ correctly and state the critical angle in degrees; and in part (c), explicitly compare 50° to the critical angle to justify whether total internal reflection occurs, naming the phenomenon correctly.

Work through all three parts now, showing every substitution step.

Success looks like: you get angle of refraction ≈ 25.4°, critical angle ≈ 41.8°, and correctly state that at 50° (greater than 41.8°) total internal reflection occurs.

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