1. Waves
A wave is a vibration (or oscillation) in space that transfers energy.
Two types: transverse and longitudinal.
Transverse: the wave vibrates at 90˚ to the direction it is travelling in (e.g. light waves and water waves).
Longitudinal: the wave vibrates in the same direction it is travelling in (e.g. sound waves and seismic P-waves).
Parts and properties of waves:
Amplitude (A) – Maximum displacement from rest. Unit: metres (m).
Frequency (f) – Number of oscillations per second. Unit: Hertz (Hz).
Period (T) – Time taken to complete one oscillation. Unit: seconds (s). T = 1/f.
Wavelength (λ) – Distance from a point on the wave to the next point that is the same. Unit: metres (m). –

2. Wave Speed & Boundaries
All light waves travel at the same speed: the speed of light (approx. 3x108m/s).
Sound waves travel faster/slower depending on the material (or medium) they are travelling in.
The speed of any wave can be calculated using the wave equation:
At the boundary between two different materials, waves can be absorbed, transmitted or reflected:
Absorption – Material absorbs all energy from the wave. The wave does not pass through it.
Transmission – Material allows the wave to pass through it.
Reflection – Material does not allow the wave to pass through it and sends it back in a different direction (i.e. echo). The angle of reflection is equal to the angle of incidence.
Question: What’s the speed of a wave with f=50kHz and λ=5cm?
v = λ x f = 0.05 x = 2500m/s
v = λ × f
Speed in metres per second, m/s
Frequency in Hertz, Hz
Wavelength in metres, m –

3. Sound Waves Sound waves need a medium to travel through.
The are transmitted by their energy moving from particle to particle. (The particles themselves do not move positions!)
In the ear, sound waves cause the eardrum to vibrate, which is converted to an electrical signal sent to the brain.
The range of normal human hearing is 20Hz to 20,000Hz (i.e. 20kHz). Sounds above this range are known as ultrasound.
Ultrasound waves are partially reflected at boundaries between different materials. The time taken for reflections to reach a detector can be used to determine how far away the boundary is. This allows ultrasound to be used for medical and industrial imaging (e.g. echo sounding to map ocean floors, etc.). –

4. Light Waves
Light that we see is only one type of light wave. There are others, such as x-rays, that we cannot see.
Light waves are also known as electromagnetic (EM) waves.
All types of light are shown on the electromagnetic (EM) spectrum, where they are ordered by wavelength:
Different EM waves can be both useful and hazardous. Some examples:
Radio waves – TV and radio signals (no hazards).
Microwaves – cooking food, mobile phone signals (can heat up body tissue, causing burns).
Infrared – remote controls, heaters (can heat up body tissue, causing burns).
Visible – fibre optic broadband (no hazards). –

5. Colour & Black Body Radiation
The colour of an object is determined by the wavelengths of light it reflects or absorbs.
If all wavelengths are reflected equally, the object appears white.
If all wavelengths are absorbed, the objects appears black.
If an object does not absorb or reflect most light, it will appear transparent or translucent.
All objects (or bodies) emit and absorb infrared radiation (or heat).
The hotter the body, the more infrared radiation it emits in a given time.
A perfect black body absorbs all of the radiation incident on it.
Since a good absorber is also a good emitter, a perfect black body would be the best possible emitter of radiation.
– 4.6.3

6. Lenses
At the boundary between two different materials, waves can be reflected or refracted:
Reflection – Material does not allow the wave to pass through it and sends it back in a different direction (i.e. echo). The angle of reflection is equal to the angle of incidence (i = r).
Refraction – Material allows the wave to pass through it but changes its direction towards the normal by an amount known as the angle of refraction.
A lens forms an image by refracting light.
In a convex (or converging) lens, parallel rays of light are brought to a focus at the principal focus. The distance from the lens to the principal focus is called the focal length.
In a concave (or diverging) lens, parallel rays are focused at a point behind the lens.
Ray diagrams are used to show the formation of images by lenses.

7. Images & Magnification
The image produced by a convex lens can be either real or virtual:
Real image: formed when light rays converge, when an image is on the opposite side of the lens to the object, and can be projected onto a screen.
Virtual image: formed when “imaginary” light rays converge, when an image is on the same side of the lens to the object, and cannot be projected onto a screen.
The image produced by a concave lens is always virtual.
The magnification produced by a lens can be calculated by: Magnification is a ratio and so it has no units.
If the magnification of an image is less than 1 (i.e. a decimal), we say it is diminished.
Magnification = image height object height

8. Drawing Ray Diagrams