Waves

• Progressive wave: A wave that transfers energy without transferring material and is made up of particles of a medium oscillating.
• Amplitude: A wave's maximum displacement from the equilibrium position.
• Frequency: The number of complete oscillations passing through a point per second.
• Wavelength: The length of one whole oscillation.
• Modal dispersion can be reduced by making the core very narrow.
• Modal dispersion is caused by light rays entering the fibre at different angles, leading to pulse broadening.
• Material dispersion is caused by using light consisting of different wavelengths, leading to pulse broadening.
• Material dispersion can be prevented by using monochromatic light.
• Both absorption and dispersion can be reduced by using an optical fibre repeater.
• Speed: Distance travelled by the wave per unit time.
• Phase: The position of a certain point on a wave cycle.
• Phase difference: How much a particle/wave lags behind another particle/wave.
• Period: Time taken for one full oscillation.
• X-ray crystallography uses diffraction gratings to measure atomic spacing in certain materials.
• Optical fibers use total internal reflection to carry light signals.
• Total internal reflection can occur when the angle of incidence is greater than the critical angle.
• Refractive index measures how much a material slows down light passing through it.
• Diffraction gratings can be used to split up light from stars and determine the elements present in them.
• Signal degradation in optical fibers can be caused by absorption and dispersion.
• Snell's law is used to calculate the refraction of light.
• 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.
• The speed of a wave is equal to the wave's frequency multiplied by its wavelength.
• The frequency of a wave is equal to 1 over its period.
• The intensity of the fringes decreases from the central fringe, with bright fringes caused by constructive interference and dark fringes caused by destructive interference.
• The greatest diffraction occurs when the gap size is the same as the wavelength.
• The formula for fringe spacing is w = sλD, where w is the fringe spacing, s is the slit separation, λ is the wavelength of light, and D is the distance between the screen and slits.
• Using white light instead of monochromatic light results in wider maxima and a less intense diffraction pattern.
• Transverse waves: Oscillation of particles (or fields) is at right angles to the direction of energy transfer.
• Light fringes occur where the waves interfere constructively, while dark fringes occur where they interfere destructively.
• Sound waves can also demonstrate interference and diffraction, with speakers and a microphone used to measure the intensity of the wave.
• Young's double slit experiment provided evidence for the wave nature of light and disproved theories suggesting light was formed of particles.
• Diffraction is the spreading out of waves when they pass through or around a gap.
• Monochromatic light can be diffracted through a single slit, forming an interference pattern of light and dark fringes.
• Young's double slit experiment: Shine coherent light through two slits, creating a pattern of light and dark fringes.
• The formula for diffraction gratings is sin θ λ d = n, where d is the distance between the slits, θ is the angle to the normal, n is the order, and λ is the wavelength.
• Values of n that give sin θ greater than 1 are impossible.
• Increasing the slit width decreases diffraction and narrows the central maximum, while increasing the light wavelength increases diffraction and widens the central maximum.
• A diffraction grating, with many equally spaced slits, produces a sharper and brighter interference pattern compared to a double slit.
• The diffraction pattern for white light has a central white maximum with alternating spectra, with violet closest to the central maximum and red furthest away.