waves

• a progressive wave (moving wave) carries energy from one place to another without transferring any material
• in transverse waves the oscillations are perpendicular to the direction of energy transfer
• in longitudinal waves the oscillations are parallel to the direction of energy transfer
• plane polarised waves are transverse waves for which the oscillations are in one plane only which is perpendicular to the direction of travel
• polarisation is evidence for the nature of transverse waves
• the principle of superposition states that when two waves meet the total displacement at a point is equal to the vector sum of the individual displacements
• a stationary wave is the superposition of two progressive waves with the same frequency (or wavelength) and amplitude moving in opposite directions
• stationary waves do no transfer energy
• stationary waves: points on the wave at which the amplitude of the vibration is zero are known as nodes
• at a node there is total destructive interference
• antinodes are points of maximum amplitude and there is constructive interference
• the frequencies at which stationary waves are generated are known as resonant frequencies
• refraction is when a wave changes direction as it enters a different medium. The change in direction is a result of the wave slowing down or speeding up
• less dense to more dense = the wave will slow down and therefore bend towards the normal
• more dense to less dense = the wave will speed up and therefore bend away from the normal
• the refractive index of air is approximately 1
• the critical angle θc is the angle of incidence for which the angle of refraction is 90 °
• if the angle of incidence is greater than the critical angle then refraction can't occur. this means that all of the light is reflected back into the material. this effect is known as total internal reflection
• conditions for TIR:

  the medium in which the light is incident to the boundary must be more optically dense than the medium on the other side of the boundary: n1 > n2

  the angle of incidence must be greater than the critical angle: θi > θc
• step-index optical fibres have a high refractive index core which allows EM waves to progress through them. this is surrounded by cladding with a lower refractive index to ensure TIR takes place. the cladding protects the fibre from scratches which could allow light to escape, and also prevents light passing from one fibre to another if two fibres were to come into contact which could result in a cross-over of signals.
• advantages of optical fibres:

  the signal can carry more information as light has a higher frequency

  the light doesn't heat up the fibre - less energy wasted

  no electrical interference

  fibre-optic cables are cheaper to produce

  signal can travel a long way, very quickly and with minimal signal loss
• absorption is where some of the signal's energy is absorbed by the material the fibre is made from, with this energy loss results in the amplitude of the signal being reduced. this is often due to impurities in the material
• using a narrower or thinner core reduces the discrepancy in the distance travelled by different rays of light or infra-red, thus reducing the effect of modal dispersion
• monochromatic light is usually used to avoid material dispersion happening
• using repeaters placed at shorter intervals can ensure that the pulse is reformed before significant pulse broadening has taken place
• Youngs double-slit experiment involved the use of two coherent sources or the use of a single source with double slits to produces an interference pattern
• Youngs double-slit experiment acts as evidence for the wave nature of light
• a laser is a source of monochromatic light and coherent light
• two waves are coherent when they have the same frequency and wavelength, and have a fixed/constant phase difference between them
• the amount by which the path travelled by one wave s longer than the path travelled by the other wave is called path difference
• constructive interference occurs when: path difference = nλ (where n = 0, 1, 2, ...)
• destructive interference occurs when: path difference = (n+1/2)λ
• diffraction is the spreading out of waves as they pass through a gap or around an obstacle
• intensity is the power per unit area
• an optical fibre is a very thin flexible tube of glass or plastic fibre that can carry signals over long distances and round corners using TIR
• single slit diffraction

  the central maximum is twice as wide and is much brighter

  the outer fringes are of the same width

  peak intensity of each fringe decreases with distance
• a diffraction grating is a plate with many closely spaced parallel slits. it produces widely spaced interference patterns as a result of the superposition of waves from the many slits. form brighter and sharper fringes compared to the double slit
• to find diffraction grating split spacing

  $d=$$1/N$

  where N is the number of slits in metres