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Wave Properties Refraction, diffraction and superposition

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The mug trick!

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Today’s lesson Refraction of light

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The mug trick!

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Refraction When a wave changes speed (normally when entering another medium) it may refract (change direction)

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Water waves Water waves travel slower in shallow water

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Sound waves Sound travels faster in warmer air

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Light waves Light slows down as it goes from air to glass/water

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Snell’s law There is a relationship between the speed of the wave in the two media and the angles of incidence and refraction i r Ray, NOT wavefronts

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Snell’s law speed in substance 1 sinθ 1 speed in substance 2 sinθ 2 =

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Snell’s law In the case of light only, we usually define a quantity called the index of refraction for a given medium as n = c = sinθ 1 /sinθ 2 c m where c is the speed of light in a vacuum and c m is the speed of light in the medium vacuum c cmcm

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Snell’s law Thus for two different media sinθ 1 /sinθ 2 = c 1 /c 2 = n 2 /n 1

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Refraction – a few notes The wavelength changes, the speed changes, but the frequency stays the same

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Refraction – a few notes When the wave enters at 90°, no change of direction takes place.

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A practical!

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i r

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Data collection and processing Table of raw results with quantity, unit, uncertainty and an agreement between the uncertainty and precision of measurements Data correctly processed (including graphs and line of best fit Uncertainties correctly propagated (calculated) and error bars on graph (max/min line of best fit)

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Conclusion and evaluation Compare result with actual result (referenced) Discussion of possible systemmatic errors Identification of weaknesses with relevant significance Improvements based on weaknesses No “waffly” terms!

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Diffraction Ripple Tank Simulation

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Diffraction Waves spread as they pass an obstacle or through an opening

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Diffraction Diffraction is most when the opening or obstacle is similar in size to the wavelength of the wave

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Diffraction patterns HL later!

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Diffraction patterns HL b θ n = 1 n = 2 bsinθ = nλ θ = λ/b (radians)

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Diffraction Diffraction is most when the opening or obstacle is similar in size to the wavelength of the wave

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Diffraction That’s why we can hear people around a wall but not see them!

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Diffraction of radio waves

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Superposition

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Principle of superposition When two or more waves meet, the resultant displacement is the sum of the individual displacements

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Constructive and destructive interference When two waves of the same frequency superimpose, we can get constructive interference or destructive interference. + = + =

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Superposition In general, the displacements of two (or more) waves can be added to produce a resultant wave. (Note, displacements can be negative)

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1. Constructive Interference - when the crests (or troughs) of two waves coincide, they combine to create an amplified wave. The two waves are in phase with each other – there is zero phase difference between them.

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2. Destructive Interference - where the crests of one wave are aligned with the troughs of another, they cancel each other out. The waves are out of phase (or in antiphase) with each other – they are half a cycle different from each other.

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Superposition Let’s try adding some waves!

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Standing waves store energy, whereas travelling waves transfer energy from 1 point to another The amplitude of standing waves varies from 0 at the nodes to a max at the antinodes, but the same amplitude for all the oscillations along the progressive wave is constant. The oscillations are all in phase between nodes, but the phase varies continuously along a travelling wave.

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Interference patterns Ripple Tank Simulation

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If we pass a wave through a pair of slits, an interference pattern is produced

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Path difference Whether there is constructive or destructive interference observed at a particular point depends on the path difference of the two waves

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Constructive interference if path difference is a whole number of wavelengths

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antinode

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Destructive interference if path difference is a half number of wavelengths

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node

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