Waves and Light

What you'll learn

This topic combines wave behaviour with the properties of electromagnetic radiation, forming a substantial portion of Paper 1 and Paper 2 in Edexcel GCSE Physics. Questions regularly test wave calculations, ray diagrams, and applications of different electromagnetic waves. Mastering this material is essential for both foundation and higher tier students.

Key terms and definitions

Wavelength (λ) — the distance from one point on a wave to the equivalent point on the next wave, measured in metres (m)

Frequency (f) — the number of complete waves passing a point per second, measured in hertz (Hz)

Amplitude — the maximum displacement of a wave from its rest position, measured in metres (m)

Transverse wave — a wave where the oscillations are perpendicular to the direction of energy transfer (e.g. all electromagnetic waves, water waves)

Longitudinal wave — a wave where the oscillations are parallel to the direction of energy transfer (e.g. sound waves)

Refraction — the change in direction of a wave when it crosses a boundary between two different media, caused by a change in wave speed

Electromagnetic spectrum — the family of transverse waves that travel at 3 × 10⁸ m/s in a vacuum, ranging from radio waves to gamma rays

Normal line — an imaginary line drawn perpendicular to a surface at the point where a ray meets it, used as a reference for measuring angles of incidence and refraction

Core concepts

Wave properties and equations

All waves transfer energy without transferring matter. The wave equation connects three fundamental properties:

wave speed (m/s) = frequency (Hz) × wavelength (m)

or v = f λ

This equation appears in virtually every waves exam paper. For electromagnetic waves in a vacuum or air, the wave speed is approximately 3 × 10⁸ m/s (the speed of light, often written as c).

Wave properties can be identified from diagrams:

• Wavelength is measured crest-to-crest or trough-to-trough
• Amplitude is measured from the centre line to the peak
• Frequency relates to how many waves pass per second

Period (T) is the time taken for one complete wave to pass a point, measured in seconds. The relationship between period and frequency is:

frequency = 1 ÷ period or f = 1/T

The electromagnetic spectrum

The electromagnetic spectrum consists of seven main regions, listed here from longest wavelength to shortest:

1. Radio waves — longest wavelength (>10 cm), used for communications, television and radio broadcasting
2. Microwaves — wavelengths around 1 mm to 10 cm, used for satellite communications, mobile phones and cooking
3. Infrared — wavelengths around 700 nm to 1 mm, emitted by all warm objects, used in thermal imaging and remote controls
4. Visible light — wavelengths around 400-700 nm, the only part humans can see, ranging from red (longest) to violet (shortest)
5. Ultraviolet — wavelengths around 10-400 nm, causes tanning and skin damage, used for sterilisation
6. X-rays — wavelengths around 0.01-10 nm, used in medical imaging to view bones
7. Gamma rays — shortest wavelength (<0.01 nm), emitted by radioactive materials, used in cancer treatment

All electromagnetic waves are transverse waves that can travel through a vacuum. They all travel at the same speed in a vacuum but have different wavelengths and frequencies. As wavelength decreases across the spectrum, frequency increases (since v = f λ and v is constant).

Dangers and uses of electromagnetic waves

Different electromagnetic waves have different effects on the human body:

Microwaves are absorbed by water molecules in body tissue, causing heating. This is how microwave ovens work but can also cause internal burns.

Infrared radiation is felt as heat. Excessive exposure causes skin burns. Used in heating lamps, night-vision equipment, and optical fibre communications.

Ultraviolet radiation is absorbed by skin cells and can damage DNA, potentially causing skin cancer. It also causes premature skin aging. Small amounts are beneficial as they stimulate vitamin D production. Used for security marking and sterilising water.

X-rays and gamma rays are ionising radiation — they have enough energy to remove electrons from atoms. This can damage or kill cells and mutate DNA, increasing cancer risk. Medical use is carefully controlled with lead shielding and minimum exposure times. Gamma rays are also used to sterilise medical equipment and treat cancer tumours.

Reflection

Reflection occurs when a wave bounces off a surface. The law of reflection states:

angle of incidence = angle of reflection

Both angles are measured from the normal line (perpendicular to the surface). This law applies to all waves including light and sound.

Smooth surfaces produce specular reflection where parallel rays remain parallel after reflection, creating clear images (mirrors). Rough surfaces cause diffuse reflection where parallel rays scatter in different directions — you cannot see a clear reflection, though each individual ray still obeys the law of reflection.

Refraction

Refraction happens when waves travel from one medium into another and change speed. Light slows down when entering denser materials (glass, water) and speeds up when entering less dense materials (air).

When light enters a denser medium:

• It slows down
• The wavelength decreases
• The frequency stays constant (frequency never changes during refraction)
• The ray bends towards the normal

When light enters a less dense medium:

• It speeds up
• The wavelength increases
• The frequency stays constant
• The ray bends away from the normal

If the ray enters along the normal (angle of incidence = 0°), no refraction occurs — the ray continues straight through but still changes speed.

Applications of refraction include:

• Lenses in glasses, cameras and microscopes
• Optical fibres for communications
• Prisms that separate white light into colours (dispersion)

Ray diagrams for lenses

Convex (converging) lenses are thicker in the middle. They refract parallel rays so they converge at the focal point (F). The distance from the lens centre to F is the focal length.

For a convex lens:

• Object beyond 2F: real, inverted, diminished image between F and 2F (camera)
• Object at 2F: real, inverted, same size image at 2F
• Object between F and 2F: real, inverted, magnified image beyond 2F (projector)
• Object inside F: virtual, upright, magnified image on same side (magnifying glass)

Concave (diverging) lenses are thinner in the middle. They refract parallel rays so they spread out (diverge). The rays appear to come from a focal point on the same side as the incident rays. Concave lenses always produce virtual, upright, diminished images.

To draw ray diagrams accurately:

1. Draw a ray from the object parallel to the axis, refracting through F (convex) or appearing to come from F (concave)
2. Draw a ray from the object through the lens centre, continuing straight
3. Where the rays meet (or appear to meet) is where the image forms

Colour and filters

White light contains all colours of the visible spectrum. A prism refracts different wavelengths by different amounts (dispersion), separating white light into red, orange, yellow, green, blue, indigo, and violet.

Coloured objects work by selective reflection and absorption:

• A red object reflects red light and absorbs all other colours
• A white object reflects all colours
• A black object absorbs all colours

Colour filters only transmit certain colours and absorb the rest:

• A red filter transmits red light and absorbs other colours
• White light through a red filter appears red
• Blue light through a red filter appears black (blue is absorbed, no light passes through)

Worked examples

Example 1: Wave speed calculation

Question: A radio station broadcasts at a frequency of 95.8 MHz. Radio waves travel at 3 × 10⁸ m/s. Calculate the wavelength of the radio waves transmitted. [3 marks]

Solution:

Convert frequency to Hz: 95.8 MHz = 95.8 × 10⁶ Hz [1 mark]

Use v = f λ, rearranged to λ = v ÷ f [1 mark]

λ = (3 × 10⁸) ÷ (95.8 × 10⁶) = 3.13 m [1 mark]

Examiner note: Always convert to standard units first. Show the rearranged equation for method marks even if the final answer is incorrect.

Example 2: Refraction angles

Question: A ray of light travels from air into glass. The angle of incidence is 40°.

(a) State what happens to the speed of the light. [1 mark] (b) State whether the ray bends towards or away from the normal. [1 mark] (c) Explain why the ray changes direction. [2 marks]

Solution:

(a) The speed decreases [1 mark]

(b) The ray bends towards the normal [1 mark]

(c) Light changes speed when entering a different medium [1 mark]. The change in speed causes the direction to change [1 mark].

Examiner note: Part (c) requires an explanation — stating facts without linking them scores only 1 mark.

Example 3: Electromagnetic spectrum

Question: A hospital uses both X-rays and gamma rays.

(a) State one use for X-rays in a hospital. [1 mark] (b) Explain why hospital staff stand behind lead screens when X-ray machines are in use. [2 marks] (c) Compare the wavelengths of X-rays and gamma rays. [1 mark]

Solution:

(a) Medical imaging / viewing broken bones / checking for fractures [1 mark]

(b) X-rays are ionising radiation [1 mark] which can damage cells/DNA and increase cancer risk [1 mark]

(c) Gamma rays have shorter wavelengths than X-rays [1 mark]

Examiner note: Answers must be specific. "Medical purposes" is too vague for (a). In (c), stating "different wavelengths" scores zero — you must specify which is longer/shorter.

Common mistakes and how to avoid them

• Confusing wavelength and amplitude on wave diagrams — Wavelength is the horizontal distance between corresponding points (crest to crest). Amplitude is the vertical distance from rest position to peak. Always check which the question asks for.

• Forgetting to convert units in calculations — MHz must become Hz (multiply by 10⁶), cm must become m (divide by 100), km must become m (multiply by 1000). Write the conversion as a separate line to avoid errors.

• Stating "light bends when it slows down" — This is incomplete. Light bends because it changes speed AND enters at an angle. If light enters along the normal, it slows down but does not bend.

• Thinking frequency changes during refraction — Frequency is determined by the source and never changes. Only speed and wavelength change when waves enter a different medium.

• Muddling ionising and non-ionising radiation — Only ultraviolet, X-rays, and gamma rays are ionising (can remove electrons from atoms). Infrared, microwaves, and radio waves are non-ionising — they can cause heating but do not directly damage DNA.

• Drawing ray diagram rays that don't follow rules — Every ray must follow a specific path. A ray parallel to the axis must refract through the focal point. A ray through the centre continues straight. Drawing random lines scores zero marks.

Exam technique for Waves and Light

• "State" questions (1 mark) — Write a short factual answer with no explanation needed. "State the type of wave" requires just "transverse" or "longitudinal", not a full sentence.

• "Explain" questions (2-3 marks) — Link cause and effect. Use "because" or "this causes" to connect ideas. "Light refracts because it changes speed when entering glass, causing the ray to bend towards the normal" scores full marks. Just stating "light refracts" or "light slows down" separately scores only 1 mark.

• Calculation questions — Always write the equation you're using, substitute values with units, then calculate. This method gains partial marks even if the arithmetic is wrong. Include units in your final answer.

• Ray diagrams (4-6 marks) — Use a ruler and sharp pencil. Draw at least two rays following the correct rules. Label the focal point (F), object, and image. State whether the image is real/virtual and upright/inverted if asked. Untidy or unlabelled diagrams lose marks even if technically correct.

Quick revision summary

Waves transfer energy through oscillations. Use v = f λ for all wave calculations. The electromagnetic spectrum ranges from radio waves (longest wavelength) to gamma rays (shortest). All electromagnetic waves are transverse and travel at 3 × 10⁸ m/s in a vacuum. Refraction occurs when waves change speed entering a new medium — light bends towards the normal when slowing down. High-frequency electromagnetic waves (UV, X-rays, gamma rays) are ionising and damage living cells. Ray diagrams for lenses must show rays following specific paths to locate images accurately.