# Light and Sound

> Physics · 4PH1
> Source: https://www.owlsprep.com/study/edexcel-igcse-physics-s3-light-and-sound/

This guide covers all core and Higher tier content for Edexcel IGCSE Physics Light and Sound, including reflection, refraction, total internal reflection, and properties of sound waves, with exam-aligned worked examples and practical tips.

**Prerequisites:** [Basic wave properties and the wave equation $v = f\lambda$](https://www.owlsprep.com/study/edexcel-igcse-physics-s3-waves-basics/)

## Learning objectives

- Recall light is transverse and sound is longitudinal, and both can be reflected and refracted
- Apply the law of reflection and Snell's law for refractive index calculations
- Draw and interpret ray diagrams for reflection, refraction and total internal reflection
- Explain applications of total internal reflection in optical fibres and prisms
- Calculate critical angle using $\text{sin }c = 1/n$
- For Higher tier: relate sound pitch/loudness to frequency/amplitude, recall human hearing range, and describe sound practicals

## Light Wave Properties & Reflection

**Transverse Wave** — Wave where oscillations are perpendicular to the direction of energy transfer

*Example:* Light waves, all electromagnetic waves

Light is a transverse electromagnetic wave that travels at $3 \times 10^8$ m/s in a vacuum, and can be reflected and refracted. The law of reflection governs all specular (smooth surface) reflection: the angle of incidence equals the angle of reflection, with both angles measured from the normal (a dashed line perpendicular to the reflecting surface at the point of incidence).

**Worked example:** A light ray hits a flat mirror at 20° to the mirror surface. State the angle of reflection, and describe the ray diagram required to show this interaction.

1. 1. Draw a straight line for the mirror, and a dashed normal line perpendicular to the mirror at the point of incidence.
2. 2. Calculate the angle of incidence: 90° - 20° = 70° (angle between incident ray and normal).
3. 3. By the law of reflection, angle of reflection = angle of incidence = 70°.
4. 4. Draw the incident ray with an arrow pointing toward the mirror at 70° to the normal, and the reflected ray with an arrow pointing away from the mirror at 70° to the normal.

> **Exam tip:** Always label the normal, incident ray, reflected ray, and all angles in ray diagrams to gain full marks. Rays must be straight with clear arrows showing direction of travel.

## Refraction of Light & Refractive Index

**Refractive Index** — Ratio of the speed of light in a vacuum to the speed of light in a medium, equal to $\frac{\sin i}{\sin r}$ when light travels from air into the medium.

*Notation:* $n$

Refraction is the bending of light when it travels from one medium to another with a different optical density. When light enters a denser medium (e.g. air to glass), it bends toward the normal; when it enters a less dense medium (e.g. glass to air), it bends away from the normal. You must recall Snell's law for refractive index: $n = \frac{\sin i}{\sin r}$.

**Worked example:** A light ray enters a rectangular glass block from air at an angle of incidence of 50°. The angle of refraction inside the glass is 30°. Calculate the refractive index of the glass, correct to 2 significant figures.

1. Recall Snell's law for refractive index:
2. $$n = \frac{\sin i}{\sin r}$$
3. Substitute values: $i = 50^\circ$, $r = 30^\circ$
4. $$n = \frac{\sin 50^\circ}{\sin 30^\circ} = \frac{0.766}{0.5} = 1.532$$
5. Round to 2 significant figures: $n = 1.5$

> **info**
>
> Practical tip for measuring refractive index of a glass block: trace the incident and emergent rays, draw the normal at the point of entry, measure $i$ and $r$ with a protractor, and repeat for multiple angles to improve reliability.

> **Exam tip:** Make sure your calculator is in degrees mode for all trigonometry calculations in this topic. Using radians will give you completely wrong answers.

*Calculator:* allowed

## Critical Angle & Total Internal Reflection

**Critical Angle** — The angle of incidence in a denser medium where the angle of refraction in the less dense medium is exactly 90°. For angles of incidence greater than $c$, total internal reflection (TIR) occurs if light is travelling from denser to less dense medium.

*Notation:* $c$

The relationship between critical angle and refractive index is $\sin c = \frac{1}{n}$, which you must recall. TIR is used in optical fibres for high-speed data transmission (light bounces repeatedly along the fibre core with very little signal loss) and in prismatic binoculars to reflect light without the image distortion caused by mirrors.

**Worked example:** The refractive index of a type of glass is 1.5. Calculate its critical angle, correct to 1 decimal place. State the two conditions required for TIR to occur in this glass.

1. Recall the critical angle formula:
2. $$\sin c = \frac{1}{n}$$
3. Substitute $n = 1.5$:
4. $$\sin c = \frac{1}{1.5} = 0.6667$$
5. Calculate inverse sine: $c = \sin^{-1}(0.6667) = 41.8^\circ$
6. Conditions for TIR: 1) Light travels from glass (denser) to air (less dense). 2) Angle of incidence is greater than 41.8°.

> **Exam tip:** Never omit the two conditions for TIR in exam answers: you will lose marks if you only state one.

*Calculator:* allowed

## Core Sound Wave Properties

**Longitudinal Wave** — Wave where oscillations are parallel to the direction of energy transfer, made of alternating compressions and rarefactions of the medium

*Example:* Sound waves

Sound is a longitudinal mechanical wave that requires a medium (solid, liquid, gas) to travel, so it cannot pass through a vacuum. Like light, sound can be reflected (producing echoes) and refracted (e.g. sound bending over cold water because cold air is denser than warm air).

## Higher Tier: Sound Measurements & Properties

For Higher tier only, recall the human hearing range is 20 Hz to 20,000 Hz (20 kHz). Frequencies above 20 kHz are ultrasound, below 20 Hz are infrasound, neither of which humans can hear. An oscilloscope connected to a microphone can display sound waves as transverse traces: the horizontal time-base setting lets you measure the period $T$ of the wave, so frequency $f = \frac{1}{T}$.

**Worked example:** An oscilloscope trace of a sound wave shows one full wave covers 4 divisions on the horizontal axis. The time-base is set to 1 ms per division. Calculate the frequency of the sound, and state if a human can hear it.

1. Calculate period $T$: 4 divisions × 1 ms/division = 4 ms = 0.004 s
2. $$f = \frac{1}{T} = \frac{1}{0.004} = 250 Hz$$
3. 250 Hz is between 20 Hz and 20 kHz, so a human can hear this sound.

> **tip**
>
> Pitch of a sound is determined by frequency: higher frequency = higher pitch. Loudness is determined by amplitude: larger amplitude = louder sound.

Practical to measure speed of sound in air: Set two microphones connected to a timer 100 m apart in a large open space. Fire a starting pistol next to the first microphone, record the time difference between the signal reaching the first and second microphone. Use $speed = \frac{distance}{time}$ to calculate speed, repeat multiple times and average to reduce random error.

*Calculator:* allowed

## Common pitfalls

- **Wrong:** Measuring angles of incidence/reflection/refraction from the surface instead of the normal
  - Why it fails: All wave laws are defined relative to the normal, so incorrect angle measurements produce invalid calculation results and lost marks on ray diagrams
  - Correct: Always draw and measure angles from the dashed perpendicular normal line at the point of incidence
- **Wrong:** Stating only one condition for total internal reflection
  - Why it fails: Exam mark schemes require both conditions for full credit, and TIR cannot occur if either condition is missing
  - Correct: Always state both: (1) light travels from denser to less dense medium, (2) angle of incidence > critical angle
- **Wrong:** Using radians mode on calculators for trigonometric calculations
  - Why it fails: All angles in exam questions are given in degrees, so radians mode produces invalid values for $\text{sin }i$, $\text{sin }r$ and $\text{sin }c$
  - Correct: Check your calculator is set to degrees mode before starting any calculation in this topic
- **Wrong:** Confusing the relationship between pitch/amplitude and frequency/loudness
  - Why it fails: Higher tier questions frequently test these links, and mixing them up is a common, easily avoidable error
  - Correct: Remember: Pitch = Frequency (higher frequency = higher pitch), Loudness = Amplitude (larger amplitude = louder sound)
- **Wrong:** Forgetting that sound cannot travel through a vacuum
  - Why it fails: Core multiple choice questions often test the difference between light and sound wave properties
  - Correct: Recall that sound is a mechanical wave requiring a medium, while light is electromagnetic and travels through vacuums

## Cheatsheet

| Concept | Formula/Rule | Key Notes |
| --- | --- | --- |
| Law of Reflection | $i = r$ | Angles measured from the normal |
| Refractive Index | $n = \frac{\sin i}{\sin r}$ | $i$ = angle in air, $r$ = angle in medium |
| Critical Angle | $\sin c = \frac{1}{n}$ | $c$ = angle in denser medium |
| TIR Conditions | N/A | 1. Denser → less dense medium 2. $i > c$ |
| Sound (Higher) | $f = 1/T$ | Hearing range: 20 Hz – 20 kHz; Pitch = frequency, Loudness = amplitude |
| Speed of Sound | $v = d/t$ | Use for practical calculations, no need to memorise exact speed of sound |

## What's next

Now that you have mastered light and sound properties, you are ready to move on to other wave topics in the Edexcel IGCSE Physics specification. Next, revise the electromagnetic spectrum, which covers other types of transverse electromagnetic waves similar to light, and practice past paper questions on wave phenomena to consolidate your understanding. Make sure you practice drawing ray diagrams under timed conditions, as these are high-mark questions that often trip students up with small errors like missing labels or incorrect angles. For Higher tier students, focus on practical questions related to sound measurements, as these are frequently assessed in Paper 2.

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/edexcel-igcse-physics-s3-light-and-sound/