Light and Sound

Physics· Section 3.14–3.29 (2017 4PH1 specification)· 25 min read

1. Light Wave Properties & Reflection★★☆☆☆⏱ 5 min

📘 Definition

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 $3 \times 1 0^{8}$ 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
1. Calculate the angle of incidence: 90° - 20° = 70° (angle between incident ray and normal).
3
1. By the law of reflection, angle of reflection = angle of incidence = 70°.
4
1. 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.

2. Refraction of Light & Refractive Index★★★☆☆⏱ 7 min

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📘 Definition

Refractive Index

$n$

Ratio of the speed of light in a vacuum to the speed of light in a medium, equal to $\frac{s i n i}{s i n r}$ when light travels from air into the medium.

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: $n = \frac{s i n i}{s i n r}$ .

📐 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: $i = 5 0^{\circ}$ , $r = 3 0^{\circ}$
4
$n = \frac{\sin 50^\circ}{\sin 30^\circ} = \frac{0.766}{0.5} = 1.532$
5
Round to 2 significant figures: $n = 1.5$

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.

3. Critical Angle & Total Internal Reflection★★★☆☆⏱ 6 min

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📘 Definition

Critical Angle

$c$

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.

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.

4. Core Sound Wave Properties★★☆☆☆⏱ 3 min

📘 Definition

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).

5. Higher Tier: Sound Measurements & Properties★★★☆☆HL only⏱ 4 min

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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.

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 $s p ee d = \frac{d i s t an ce}{t im e}$ to calculate speed, repeat multiple times and average to reduce random error.

6. Common Pitfalls

Wrong move:

Measuring angles of incidence/reflection/refraction from the surface instead of the normal

Why:

All wave laws are defined relative to the normal, so incorrect angle measurements produce invalid calculation results and lost marks on ray diagrams

Correct move:

Always draw and measure angles from the dashed perpendicular normal line at the point of incidence

Wrong move:

Stating only one condition for total internal reflection

Why:

Exam mark schemes require both conditions for full credit, and TIR cannot occur if either condition is missing

Correct move:

Always state both: (1) light travels from denser to less dense medium, (2) angle of incidence > critical angle

Wrong move:

Using radians mode on calculators for trigonometric calculations

Why:

All angles in exam questions are given in degrees, so radians mode produces invalid values for $sin i$ , $sin r$ and $sin c$

Correct move:

Check your calculator is set to degrees mode before starting any calculation in this topic

Wrong move:

Confusing the relationship between pitch/amplitude and frequency/loudness

Why:

Higher tier questions frequently test these links, and mixing them up is a common, easily avoidable error

Correct move:

Remember: Pitch = Frequency (higher frequency = higher pitch), Loudness = Amplitude (larger amplitude = louder sound)

Wrong move:

Forgetting that sound cannot travel through a vacuum

Why:

Core multiple choice questions often test the difference between light and sound wave properties

Correct move:

Recall that sound is a mechanical wave requiring a medium, while light is electromagnetic and travels through vacuums

7. Quick Reference Cheatsheet

Concept	Formula/Rule	Key Notes
Law of Reflection	$i = r$	Angles measured from the normal
Refractive Index	$n = \frac{s i n i}{s i n r}$	$i$ = angle in air, $r$ = angle in medium
Critical Angle	$sin c = \frac{1}{n}$	$c$ = angle in denser medium
TIR Conditions	N/A	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

8. Frequently Asked

Do I measure wave angles from the surface or the normal?

Always measure angles of incidence, reflection and refraction from the dashed normal line perpendicular to the surface, not the surface itself. This is one of the most common mark-losing errors in this topic.

When does total internal reflection occur?

TIR only happens if two conditions are both met: 1) light travels from a denser medium (e.g. glass) to a less dense medium (e.g. air), and 2) the angle of incidence is greater than the critical angle of the denser medium.

What is the difference between light and sound waves?

Light is a transverse electromagnetic wave that can travel through a vacuum, while sound is a longitudinal mechanical wave that requires a material medium (solid, liquid, gas) to propagate, so it cannot travel through space.

Going deeper

official_specEdexcel IGCSE Physics 4PH1 SpecificationRefer to Section 3 for full wave content

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.