Waves and Optics

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Waves - Waves and Polarisation

  • EM waves are oscillating electric and magnetic fields that progress without need for a medium. 
  • Longitudinal waves oscillate parallell to the direction of travel. For example, primary seismic, sound and compression waves. 
  • Transverse waves oscillate perpendicular to direction of propagation. For example, water waves, EM waves and secondary seismic waves.
  • Transverse waves are plane-polarised if the vibrations stay on one plane only, if not, they are unpolarised. longitudinal waves cannot be polarised.
  • A polarising fliter removes all planes of propagation aside from one. If two polaroid filters are places in series, the intensity of the light decreases as the second filter is moved to be perpendicular to the other.
  • Polaroid sunglasses reduce glare in sunglasses as light reflected from water is often horizontally plane-polarised.
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Waves - Measuring Waves

  • Displacement - distance from equilibrium
  • Amplitude - maximum displacement
  • Wavelength - distence between adjacent in phase particles (between crests)
  • Cycle - from max. displacement to next max. displacement
  • Period - time for one complete wave to pass a fixed point
  • Frequency - number of cycles per second
  • The higher the frequency, the shorter the wavelength. c=λf
  • Phase is the fraction of th cycle undertaken from the original position.
  • Phase difference is the fraction of a cycle between two particles = 2πd/λ
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Waves - Reflection, Refraction and Diffraction

  • Reflection - straight waves directed at a certain angle to a surface are reflected at the same angle from the surface.
  • Refraction - when waves cross a boundary, their speed may change, and therefore direction, if at an angle. Bend towards the normal if the speed decreases and away from the normal if speed increases.
  • Diffraction - occurs when waves spread out after passing through a gap.The narrower the gap or the longer the wavelength, the more spread out the waves will be. 
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Waves - Superposition

  • Superposition is the effect where two combine at a point where they meet. When two waves meet, the total displacement at a point is equal to the sum of the individual displacements at that point. 
  • A supercrest is the combination of two crests; a supertrough is the combination of two troughs; and where the waves are completely out of phase, they cancel out.
  • When waves continually pass through each other at a constant phase difference, cancelation and reinforcement occur at fixed positions (for example, double slit) in an effect called interference.
  • Coherent sources of waves produce an interference pattern because they vibrate at the dame frequency with constant phase difference.
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Waves - Stationary Waves

  • A stationary wave is formed when two progressive waves pass each other, or if a progressive wave is reflected back on itself. 
  • Nodes are at fixed positions throughout. 
  • Distance between adjacent nodes = λ/2
  • In general, the amplitude varies from zero displacement at the nodes to maximum displacement at the antinodes.
  • The phase difference between two particles is zero if separated by an even number of nodes and 180 degrees if separated by an odd number of nodes.
  • The fundamental mode of vibration is the first harmonic of a string. It has a node at either end with one antinode.
  • Stationary waves that vibrate freely do not transfer energy to their surroundings. Energy is a maximum at the nodes where there is maximum displacement.
  • All particles vibrate at the same frequency (except at nodes); amplitude varies between nodes and antinodes; phase difference is mπ, where m is number of nodes.
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Waves - Stationary Waves on a String

  • When a string is attached between a frequency generator and a pulley, the first harmonic is seen at the lowest possible frequency that produces a stationary wave with nodes at the frequency generator and the pulley.
  • For first harmonic, λ = 2L; frequency = c/λ = c/2L, where c is the speed of the waves.
  • Second harmonic frequency = c/L = 2f1.
  • Third harmonic frequency = 3c/2L = 3/2f1
  • The time taken for a wave to travel along the string and be reflected at the other end must be equal to a whole number of cycles of the frequency generator. Hence, t=2L/c so 2L/c = kT where T is time period and k is an integer. It can also be written as 2L/c = k/f so f = kc/2L.
  • λ=c/f = 2L/k
  • The pitch corresponds to frequency and this can be altered by changing the tension on the string, or by changing its length. 
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Waves - Oscilloscopes

  • Y-gain and time base
  • 1, 2, 5 and zeros either side (0.1,0.2,0.5,1,2,5,10,20,50)
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Optics - Refraction

  • Refraction is the change of direction that occurs when light passes at an angle across a boundary between two transparent substances. 
  • The light ray bends towards the normal (slows) if it passes into a more dense substance and away from the normal (speeds up) if it passes into a less ense substance.
  • The refractive index of a substance, n = sin i / sin r 
  • For parallel boundaries: sin i1 / sin r1 = sin r2 / sin i2
  • Refraction occurs due to the change in speed of the wave. Therefore the refractive index can also be equated to C/Cs where Cs is speed in substance and C is speed in air.
  • The equation can also be rearranged to n1sinθ1=n2sinθ2
  • FREQUENCY DOES NOT CHANGE, WAVELENGTH CHANGES
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Optics - Refraction at a Boundary

  • Light can be refracted through a prism to produce a spectrum because white light is composed of different wavelengths which diffract by differnet amounts. 
  • The shorter the wavelength, the greater the amount of refraction, so blue refracts the most and red the least.
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Optics - Total Internal Reflection

  • If the angle of incidence exceeds a particular value, it refracts along the boundary as it would not be able to bend away from the normal. This is called the critical angle.
  • If the incident rays are at an angle of incidence greater than the critical angle, they will be totally internally reflected.
  • TIR can only take place if the first medium has a greater refreactive index than the one it shares the boundary with; and if the angle of incidence exceeds the critical angle.
  • At the critical angle the angle of refraction, is 90 degrees. sin 90=1, so sin θc = n2/n1
  • A diamond has a very high refractive index meaning it is totally internally reflected a number of times before it leaves the diamond again, this disperses the colours of the light.
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Optics - Optical Fibres

  • Optical fibres are used in endoscopes to see inside the body and carry light signals. 
  • The light ray is totally internally reflected each time it reaches a boundary. This allows pulses of light entering at one end reach a reciever at the other end.
  • The fibres must be highly transparent to avoid absorbtion of light and must have cladding of a lower refractive index to reduce light loss and increase the critical angle.
  • Fibres must be separated to avoid transfer of light between fibres. 
  • The core must be narrow to avoid modal dispersion. This occurs when the path difference between rays of light is too great.
  • Material dispersion is caused due to different wavelengths travelling at different speeds, hence monochromatic light must be used.
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Optics - Double Slit Interference

  • Young's experiment was used to show the wave form of light by interference. 
  • To do this, light was passed a single slit then through two parallel slits, acting as coherent light sources, forming alternating dark and bright fringes on the screen behind.
  • The fringes are formed through the interference of light. A bright fringe wherethe light arrives in phase; a dark fringe where the light waves arrive 180 degrees out of phase. 
  • The fringe separation is the distance from the centre of one bright fringe to the next. This depends on the slit spacing, distance from the screen and wavelength of light, giving rise to the equation: w=λD/s.
  • Fringes are formed at the points where the waves have an integer wavelength path difference from their respective slits; likewise destructive interference takes place where the paths are a half integer wavelength difference. 
  • it is easier to measure from the centre of dark fringes across multiple fringes, as they are easier to see and by taking multiple into account and averaging, there is a greater degree of accuracy.
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Optics - Interference

  • Coherence - same frequency and constant (or the same) phase difference. 
  • Blue light has narrower fringes because the wavelength is smaller. Red has greater fringe separation because it has a larger wavelength.
  • Vapour lamps and discharge tubes emit light of a dominant colour, for example sodium vapour lamps emit predominantly yellow or orange.
  • Light from a laser is monochromatic and because the beam is also parallel, it can be concentrated to a point, meaning all its power is also concentrated, making it dangerous as the eye lens would focus the light on the retina, destroying the retina.
  • White light fringes show a spectrum of colours when used in the double slit experiment, with blue on the inside edges and red on the outer edges, the fringe in the middle is white.
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Optics - Diffraction

  • Diffracted waves spread out more if the gap is made narrower or if the wavelength becomes larger.
  • Diffraction through a single slit forms a central fringe with further fringes of decreasing intensity either side of the central fringe. The central fringe is twice as large as the outer fringes, each of the outer fringes are the same width, outer fringes are much less intense.
  • Width of central fringe, W = 2D*λ/a (where a is the width of the single slit and D is the distance from the screen. Therefore fringe width is proportional to λ/a.
  • A higher wavelength of monochromatic light results in wider fringes.
  • The narrower the slit, the wider the fringes.
  • For Young's double slit to work, the slits must be close so the diffracted waves overlap and each slit must be narrow enough to diffract the light sufficiently.
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Optics - Diffraction Grating

  • A diffraction grating consists of a plate with a high number of slits. When a parallel beam of light is passed through, light is transmitted in certain directions only. This is because each slit diffracts the light and superposition and cancellation occur in specific directions.
  • The central beam (zero order beam) is the same direction as the incident beam, other beams are numbered outwards from the zero order beam.
  • The beams are at a higher angle from the centre beam if a longer wavelength is used, or if a grating with closer slits is used.
  • dsinθ=nλ (where d is the grating spacing, θ is the angle of diffraction, n is the nth order beam and λ is the wavelength)
  • The number of slits per metre, N = 1/d. The larger the number of slits per meter, the grater the angle of diffraction.
  • To find the maximum number of orders produced, substitute θ with 90 and calculate n  =d/λ. Round down to nearest integer. 
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Optics - Spectra

  • Continuous spectra - white light , by measuring the wavelength of he brightest part of the spectrum, the temperature of the light source can be determined.
  • Line emission spectra - a glowing light emits certain wavelengths of light so narrow lines of these wavelengths are formed.
  • Line absorbtion spectra - shows the wavelengths of light absorbed by a certain element so the transmitted light is missing these wavelengths.
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