Waves & Light
What is a Wave?
A wave is a transfer of energy through oscillations (vibrations) without the bulk movement of matter from place to place. The medium (particles) vibrates and passes energy along, but the particles themselves do not travel with the wave.
Two fundamental types of wave exist based on how particles vibrate relative to wave direction.
Types of Waves
Transverse Waves
Particles vibrate perpendicular (at 90°) to the direction of wave travel.
Examples: all electromagnetic waves (light, radio, X-rays, gamma rays), water surface waves, secondary seismic waves (S-waves).
Features visible on a transverse wave diagram:
- Crest — highest point
- Trough — lowest point
- Amplitude — height from rest position to crest
Longitudinal Waves
Particles vibrate parallel to the direction of wave travel, creating alternating compressions (high pressure) and rarefactions (low pressure).
Examples: sound waves, primary seismic waves (P-waves), ultrasound.
Wave Properties
All waves share four fundamental properties:
| Property | Symbol | Definition | Unit |
|---|---|---|---|
| Wavelength | lambda | Distance between successive crests (or compressions) | metres (m) |
| Frequency | f | Number of complete waves passing a point per second | Hertz (Hz) |
| Amplitude | A | Maximum displacement from rest position | metres (m) |
| Wave speed | v | Distance travelled per unit time | m/s |
The wave equation: v = f x lambda
(wave speed = frequency x wavelength)
Worked Example — Wave Equation
A light wave has a frequency of 5 x 10 to the power 14 Hz. The speed of light in a vacuum is 3 x 10 to the power 8 m/s. Find its wavelength.
lambda = v / f = (3 x 10^8) / (5 x 10^14) = 6 x 10^-7 m = 600 nm (nanometres) — this is in the visible orange/red range.
The Electromagnetic Spectrum
All electromagnetic (EM) waves are transverse waves that travel at 3 x 10^8 m/s (the speed of light) in a vacuum. They do not need a medium — they can travel through empty space.
In order of increasing frequency (and decreasing wavelength):
Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma
| Type | Wavelength range | Key uses | Hazards |
|---|---|---|---|
| Radio waves | 1 mm – 10 km | Broadcasting, communications, radio astronomy | Minimal |
| Microwaves | 1 mm – 10 cm | Cooking food, mobile phones, satellite communications | Internal heating of tissue |
| Infrared | 700 nm – 1 mm | Thermal cameras, remote controls, night vision, heating | Skin burns |
| Visible light | 400–700 nm | Vision, photography, fibre optics | Intense light damages eyes |
| Ultraviolet | 10–400 nm | Sterilisation, banknote checking, phototherapy | Skin cancer, sunburn, eye damage |
| X-rays | 0.01–10 nm | Medical imaging, airport security | Cell damage, cancer risk |
| Gamma rays | <0.01 nm | Cancer treatment (radiotherapy), sterilising equipment | Severe cell damage, cancer |
Visible light covers wavelengths approximately 400 nm (violet) to 700 nm (red). In order: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV) — red has the longest wavelength/lowest frequency; violet has the shortest/highest frequency.
Reflection
When light strikes a smooth surface, it reflects according to the law of reflection:
Angle of incidence = Angle of reflection
Both angles are measured from the normal — an imaginary line perpendicular to the reflecting surface at the point of incidence.
Specular reflection: from smooth, flat surfaces (mirrors) — produces clear images.
Diffuse reflection: from rough surfaces — light reflects in all directions; this is why most objects are visible from any angle (they scatter light).
Refraction
Refraction is the change in direction of a wave when it passes from one medium to another at an angle, due to a change in wave speed.
When light passes from air into glass (or water):
- It slows down (glass is optically denser than air)
- It bends towards the normal (the refracted ray is closer to the normal than the incident ray)
When light passes from glass into air:
- It speeds up
- It bends away from the normal
The greater the change in wave speed, the greater the bending — this is described by Snell's Law: n1 x sin(theta1) = n2 x sin(theta2), where n is the refractive index of the medium.
Total Internal Reflection: if light strikes the glass-air boundary at an angle greater than the critical angle, it reflects completely back into the glass rather than refracting out. Used in optical fibres (telecommunications) and diamond cutting (maximising sparkle).
Lenses
Lenses refract light to converge or diverge rays:
Convex (converging) lens:
- Thicker in the middle
- Causes parallel rays to converge at the focal point
- Used in: magnifying glasses, camera lenses, the eye, telescopes, projectors
- Corrects long-sightedness (hyperopia) — the eye cannot converge light enough on the retina
Concave (diverging) lens:
- Thinner in the middle
- Causes parallel rays to diverge as if from a virtual focal point
- Used in: glasses for short-sightedness (myopia — eye converges light too strongly, focusing in front of retina)
- Spectacles for short-sighted people spread light out before it enters the eye
The Eye and Sight Defects
The human eye is an optical instrument using a converging lens to focus light onto the retina:
- Long-sightedness (hyperopia): eyeball too short; image would focus behind retina → corrected with convex lens
- Short-sightedness (myopia): eyeball too long; image focuses in front of retina → corrected with concave lens
Key Terms
- Transverse wave — wave where particle vibration is perpendicular to wave direction
- Longitudinal wave — wave where particle vibration is parallel to wave direction
- Wavelength — distance between successive equivalent points on a wave (m)
- Frequency — number of complete waves per second (Hz)
- Amplitude — maximum displacement from equilibrium position
- Electromagnetic spectrum — the family of all EM waves ordered by frequency/wavelength
- Reflection — wave bouncing off a surface; angle of incidence = angle of reflection
- Refraction — wave changing direction due to change in speed when entering a new medium
- Total internal reflection — complete reflection of light within a denser medium when angle exceeds the critical angle
Common Mistakes
- Saying light slows down when it moves from glass to air — it speeds up going from dense to less dense medium
- Confusing transverse (e.g., light) with longitudinal (e.g., sound) — the key is direction of vibration relative to wave travel
- Thinking the angle of reflection is measured from the surface — always measure from the normal (the perpendicular line)
- Saying gamma rays and X-rays are identical — they overlap in wavelength but gamma rays come from nuclear decay; X-rays come from electron transitions
Tips and Tricks
- EM spectrum memory: Real Men In Van Use Xtra Gear (Radio, Microwave, Infrared, Visible, UV, X-ray, Gamma)
- Refraction rule: going into a denser medium (air → glass) = bends TOWARDS normal; going into less dense = bends AWAY from normal
- Wave equation triangle: v = f x lambda; cover the unknown to get the formula
- Visible light ROYGBIV: red = lowest frequency, longest wavelength; violet = highest frequency, shortest wavelength