Light can be modelled using rays or wavefronts. which are perpendicular to the direction of wave motion. Wavefronts have curvature, unless they come from a very distant source, in which case they are plane wavefronts.
Curvature is given by:
As the radius approaches infinity, the curvature approaches zero.
Converging lenses focus light onto a point behind them, called the principal focus. The principal focus lies a distance
The Lensmaker's Equation shows how a converging lens works:
Where
Lenses can also magnify objects. Linear magnification is given by:
Digital cameras contain a microchip called a CCD (charge-coupled device). The CCD has a screen with millions of pixels, which store charge when light falls on them, storing an amount of charge proportional to the intensity of incident light. The charges are converted to an array of numbers which represents an image.
Information is stored in binary, using bits with one of two values: 0 and 1. The number of bits,
The resolution of an image is the smallest distance between two points which can be distinguished:
The amount of information in an image (in bits) is given by:
Computer images are stored as an array of numbers. They can be manipulated
in the following ways to enhance the image:
Analogue signals continuously vary between values, whereas digital signals can only take discrete values. Analogue signals are converted to digital signals by sampling. The signal is sampled at regular intervals, with a measurement of the amplitude taken and rounded to the nearest quantisation level. This produces a quantisation error equal to the difference between the actual value and the quantisation level.
Advantages of digital signals:
Disadvantages of digital signals:
The maximum number of useful quantisation levels is given by:
The number of bits required is given by:
When sampling, the minimum sampling rate must be at least twice the highest frequency in the signal (Nyquist's Theorem), otherwise aliasing will occur, producing spurious low frequency signals.
Bit rate is the rate of transmission of digital information. It is given by:
Electromagnetic waves are transverse waves, consisting of oscillating magnetic and electric fields at right angles to each other. Transverse waves can be polarised, which means they oscillate in only one plane[2].
Footnote on the Cartesian sign convention
This is mentioned explicitly in the specification.↩︎
Footnote on wording of polarisation
This wording is mildly confusing. In a polarised EM wave, each field of the wave oscillates in only one plane; the magnetic field oscillates in only one plane and the electric field oscillates in only one other plane (at right angles still)↩︎