wave properties refraction, diffraction and superposition
TRANSCRIPT
Wave Properties
Refraction, diffraction and superposition
The mug trick!
Today’s lesson
• Refraction of light
The mug trick!
Refraction
When a wave changes speed (normally when entering another medium) it may refract (change direction)
Water waves
Water waves travel slower in shallow water
Sound waves
• Sound travels faster in warmer air
Light waves
Light slows down as it goes from air to glass/water
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
Snell’s law
speed in substance 1 sinθ1
speed in substance 2 sinθ2
=
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 = sinθ1/sinθ2
cm
where c is the speed of
light in a vacuum and cm is the speed of light in the medium
vacuum
c
cm
Snell’s law
Thus for two different media
sinθ1/sinθ2 = c1/c2 = n2/n1
Refraction – a few notes
The wavelength changes, the speed changes, but the frequency stays the same
Refraction – a few notes
When the wave enters at 90°, no change of direction takes place.
A practical!
ir
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)
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!
Diffraction
Waves spread as they pass an obstacle or through an opening
Diffraction
Diffraction is most when the opening or obstacle is similar in size to the wavelength of the wave
Diffraction patterns HL later!
Diffraction patterns HL
bθ
n = 1
n = 2
bsinθ = nλ
θ = λ/b (radians)
Diffraction
Diffraction is most when the opening or obstacle is similar in size to the wavelength of the wave
Diffraction
That’s why we can hear people around a wall but not see them!
Diffraction of radio waves
Superposition
Principle of superposition
When two or more waves meet, the resultant displacement is the sum of the individual displacements
Constructive and destructive interference
When two waves of the same frequency superimpose, we can get constructive interference or destructive interference.
+ = + =
Superposition
In general, the displacements of two (or more) waves can be added to produce a resultant wave. (Note, displacements can be negative)
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.
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.
Superposition
Let’s try adding some waves!
• 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.
If we pass a wave through a pair of slits, an interference pattern is produced
Path difference
Whether there is constructive or destructive interference observed at a particular point depends on the path difference of the two waves
Constructive interference if path difference is a whole number of wavelengths
Constructive interference if path difference is a whole number of wavelengths
antinode
Destructive interference if path difference is a half number of wavelengths
Destructive interference if path difference is a half number of wavelengths
node