Waves

• Progressive waves transfer energy without transferring material and are made up of particles of a medium (or field) oscillating, for example, water waves are made of water particles moving up and down.
• The amplitude of a wave is its maximum displacement from the equilibrium position, measured in units of m.
• The frequency of a wave is the number of complete oscillations passing through a point per second, measured in units of Hz.
• The wavelength of a wave is the length of one whole oscillation, measured in units of m.
• The speed of a wave is the distance travelled by the wave per unit time, measured in units of m/s.
• Modal dispersion can be reduced by making the core very narrow, making the possible difference in path lengths smaller.
• Both absorption and dispersion can be reduced by using an optical fibre repeater, which regenerates the signal during its travel to its destination.
• Material dispersion is caused by using light consisting of different wavelengths, meaning light rays will travel at different speeds along the fibre, which leads to pulse broadening.
• Modal dispersion is caused by light rays entering the fibre at different angles, taking different paths along the fibre, which leads to pulse broadening.
• Material dispersion can be prevented by using monochromatic light.
• The phase of a wave is the position of a certain point on a wave cycle, measured in units of radians, degrees or fractions of a cycle.
• The phase difference between two points on a wave is how much a particle/wave lags behind another particle/wave, measured in units of radians, degrees or fractions of a cycle.
• The period of a wave is the time taken for one full oscillation, measured in units of s.
• Two points on a wave are in phase if they are both at the same point of the wave cycle, they will have the same displacement and velocity and their phase difference will be a multiple of 360° (2π radians), they do not need the same amplitude, only the same frequency and wavelength.
• Two points are completely out of phase when they’re an odd integer of half cycles apart, for example, 5 half cycles apart where one half cycle is 180° (π radians).
• The speed of a wave is equal to the wave’s frequency multiplied by its wavelength: λ c = f.
• The frequency of a wave is equal to 1 over its period: f = 1/T.
• A diffraction grating is a slide containing many equally spaced slits very close together.
• The maximum value of sin θ is 1, therefore any values of n, which give sin θ as greater than 1 are impossible.
• White light is made up of all colours, therefore all different wavelengths of visible light, and the different wavelengths of light are all diffracted by different amounts, resulting in a spectrum of colour in the diffraction pattern.
• The formula associated with diffraction gratings is sin θ λ d = n, where d is the distance between the slits, θ is the angle to the normal made by the maximum, n is the order and λ is the wavelength.
• Increasing the slit width decreases the amount of diffraction so the central maximum becomes narrower and its intensity increases.
• Increasing the light wavelength increases the amount of diffraction as the slit is closer in size to the light’s wavelength, therefore the central maximum becomes wider and its intensity decreases.
• The diffraction pattern for white light has a central white maximum with alternating bright fringes which are spectra, violet is closest to the central maximum and red furthest away.
• When monochromatic light is passed through a diffraction grating, the interference pattern is much sharper and brighter than it would be after being passed through a double slit like in Young’s double slit, due to the increased number of rays of light reinforcing the pattern.
• As λ increases, the distance between the orders will increase because θ is larger due to the increase in diffraction as the slit spacing is closer in size to the wavelength, this means the pattern will spread out.
• The ray of light passing through the centre of a diffraction grating is called the zero order line, lines either side of the zero order are the first order lines, then the lines outside the two first order lines are the second order lines, and so on.
• Transverse waves are waves where the oscillation of particles (or fields) is at right angles to the direction of energy transfer, all electromagnetic (EM) waves are transverse and travel at 3 x 10 8 ms-1 in a vacuum.
• Transverse waves can be demonstrated by shaking a slinky vertically or through the waves seen on a string, when it's attached to a signal generator.
• As the light moves across the boundary of the 2 materials its speed changes, which causes its direction to change.
• Snell’s law is used for calculations involving the refraction of light: sin θ sin θ n 1 1 = n 2 2 ➔ n 1 is the refractive index of material 1,➔ n 2 is the refractive index of material 2,➔ θ 1 is the angle of incidence of the ray in material 1,➔ θ 2 is the angle of refraction of the ray in material 2.
• Refraction occurs when a wave enters a different medium, causing it to change direction, either towards or away from the normal depending on the material’s refractive index.
• A material with a higher refractive index can also be known as being more optically dense.
• Signal degradation can also be caused by absorption where part of the signal’s energy is absorbed by the fibre, reducing the amplitude of the signal, which could lead to a loss of information, and dispersion which causes pulse broadening, where the received signal is broader than the original transmitted signal.
• Optical fibres are flexible, thin tubes of plastic or glass which carry information in the form of light signals, with an optically dense core surrounded by cladding with a lower optical density allowing TIR to occur, this cladding also protects the core from damage and prevents signal degradation through light escaping the core, which can cause information to be lost.
• Diffraction gratings are used in several applications such as splitting up light from stars to get line absorption spectra, and in X-ray crystallography where x-rays are directed at a thin crystal sheet which acts as a diffraction grating to form a diffraction pattern.
• The refractive index (n) is a property of a material which measures how much it slows down light passing through it, calculated by dividing the speed of light in a vacuum (c) by the speed of light in that substance (c s ).
• Total internal reflection (TIR) can occur when the angle of incidence is greater than the critical angle and the incident refractive index (n 1 ) is greater than the refractive index of the material at the boundary (n 2 ).
• Longitudinal waves are waves where the oscillation of particles is parallel to the direction of energy transfer, these are made up of compressions and rarefactions and can’t travel in a vacuum.
• Sound is an example of a longitudinal wave, and they can be demonstrated by pushing a slinky horizontally.