3.3 WAVES Flashcards
What is the optimal size of a gap for a wave to diffract through?
One that is similar sized/slightly larger than the wavelength of the travelling wave. Waves bend around the gap, and interfere with each other (light has to bend around sharper corners)
Explain why there is little diffraction when a wave travels through a gap greater than its wavelength
Waves will not be able to combine and produce an interference pattern. This is because the gap is too large for the waves to bend around and interfere with each other
Explain why there is no diffraction when a wave travels through a gap smaller than its wavelength
Waves simply reflected back
Waves do not have to refract much and therefore there is limited interference according to some site
this is wrong app
What determines the resolution of a microscope?
The size of the objective lens relative to the wavelength of light
If the objective lens is much larger than the wavelength of the light, the diffraction pattern will be small and the resolution of the microscope will be high. However, if the objective lens is about the same size as the wavelength of the light, the diffraction pattern will be larger and the resolution of the microscope will be lower
Explain why a light microscope can’t view objects smaller than the wavelength of visible light
The light from the microscope will diffract around the edges of the object, causing the image of the object to blur. As the size of the object decreases, the diffraction of the light increases, causing the image to become even more blurred. This makes it impossible for a light microscope to resolve objects that are much smaller than the wavelength of light because the diffraction of the light causes the image to blur.
What is the optimal size for the wavelength of an electron used to investigate the size of gaps between atoms?
(in electron microscope)
in the order of 10^-10m (ask mrgray)
What makes something exhibit more wave like properties?
Having a longer wavelength
Why do objects travelling at higher speeds diffract less?
Shorter wavelength, less diffraction
λ = h/mv
What is the frequency range of visible light?
650nm (deep red) to 450nm (deep violet)
If i need saving
https://www.youtube.com/watch?v=TqTWSSBcV_4
https://www.youtube.com/watch?v=b6prlN4Fz90
What is a progressive wave?
A (moving) wave that transfers energy without transferring matter
What are examples of how waves transfer energy
- EM waves cause things to heat up
- X rays are ionising
- Source of waves loses energy as
wave propagates
Why can’t longitudinal waves be polarised?
polarisation restricts the vibrations to one
plane by absorbing the vibrations at right angles
to this plane
* longitudinal waves cannot be polarised
because the vibrations have to take place for
energy to be transmitted
The vibrations of a longitudinal wave occur along a single line, it is therefore not possible to confine that to a plane, i.e. a 1D shape cannot be confined within a 2D shape.
How does polarisation provide evidence for the nature of transverse waves?
Polarisation requires the direction of oscillation to be perpendicular to propagation
The reason that only transverse waves can be polarised is that their vibrations can potentially occur in all directions perpendicular to the direction of travel. It is therefore possible to confine the vibrations to a single plane
What is the plane of polarisation of an EM wave defined as?
The plane which the electric field oscillates in
Phase difference in radians
2πd/λ 2πt/T
What are puretone sound waves?
Sound waves of a single frequency
What does LASER stand for? [6]
Light amplification by stimulated emission of radiation
Describe how a standing wave is formed on a taut string
- String is fixed at either ends (to a
weight/wall) [lossless system] - Progressive wave sent along the
string - When wave reaches the end of the string, reflected wave begins to travel in the opposite direction
- Wave must have similar frequency/amplitude
When the two waves meet, they superpose.
Nodes - where 2 progressive waves are always in antiphase, destructive
Antinodes - points where waves are always in phase, constructive
In between is a combo of both
As there is no oscillation at either end of the system, energy is “locked” and can’t be transferred through the standing wave
What are the equations for the nth harmonic frequency?
fn = v/λn = nv/2L
What is the first harmonic also referred to as
The fundamental mode
What is the equation to find the first harmonic frequency of a string?
f1 = (1/2L) * sqrt(T/μ)
where:
f1 is the frequency of the first harmonic mode of vibration (in hertz, Hz)
L is the length of the string (in meters, m)
T is the tension in the string (in newtons, N)
μ is the linear density of the string (in kilograms per meter, kg/m)
assuming the string is under ideal conditions, with negligible damping and a uniform linear mass density. It also assumes that the string is fixed at both ends and is vibrating in a single antinode
What is the principle of superposition?
When two waves meet, the total displacement at that point = the sum of the individual displacements at that point
What makes waves coherent
If they have a constant phase difference
Distance between adjacent node and anti/node
Node + node = 1/2λ
node + antinode = 1/4λ
What do pitch and loudness correspond to in a wave
Pitch - frequency
Loudness - amplitude
What is refraction
The changing of direction of a wave as it passes the boundary between 2 media
What is total internal reflection?
When all incident light reflects after hitting a boundary - Angle of incidence is greater than the critical angle (ray remains in original medium)
- Only possible when ray travels from high to low refractive index
What is the refractive index (n) of a material
The ratio of the velocity of light in a vacuum to its velocity in a specified medium
(The capacity of the material to change the speed of light)
All versions of Snell’s law
n= sini/sinr
c1/c2 =sini/sinr
n1sinθ1 = n2sinθ2
where 1 is 1st medium, and 2 is 2nd medium
Difference between refraction of light vs other waves
Light is changing direction after passing between 2 TRANSPARENT media
What happens when light travels from a material with a high refractive index to a low one
It bends away from the normal
(lower refractive index = higher speed relative to c)
Relate the refractive index of a material (s) to the ratio of the wavelengths of light coming in and going out
Ns = c/cs =λ/λs
As frequency is constant
Do water waves get faster or slower as they travel from deep to shallow water
Slower, as same drag force from the “seabed” acts against a smaller mass of waver, decreasing rate of flow
Wavefronts move closer to the normal, decreasing λ, while f is constant, so v decreases
What is white light?
Light containing a continuous range of all wavelengths
Conditions for light interference
- Waves must be coherent
- Slit separation must be small
- Light waves should have similar
amplitude and intensity
Conditions for greater diffraction
Smaller gap in relation to the wavelength of incident wave
Young’s double slit formula
w = λD/s
Where w is fringe spacing (distance between 2 adjacent maxima or minima)
D is distance from slits to screen
s is distance between centres of each slit
When does single slit diffraction occur
When a wave is incident on a slit approximately the same size of the wavelength
Equation for single slit diffraction
W =λ 2D/a
where a is the size of the slit
W is the width of the central fringe
Consider conditions for first minimum, where rays from end of the slit meet with path difference of λ, as this means pairs of rays can be paired of in a way such that each pair destructively interferes. Angle from 0th order to minimum = angle between slit and shortest path between furthest apart rays. As D»a, angle is very small so sinθ = tanθ
Single slit diffraction patterns
Central fringe is 2x as wide as each outer fringe (measured from minimum to minimum)
Each outer fringe is the same width
Outer fringes are much less intense than central fringe
As you move farther from the center, the path length differences between the waves from the two slits and the screen become larger. This causes the constructive and destructive interference to occur at different points, resulting in the bright fringes decreasing in intensity as you move away from the center
Describe the structure of a fibre optic cable
- Contains a core, highly transparent
to prevent absorption of light which
would reduce amplitude. +
Propagates/guides light. - Cladding protects core from damage
+ prevents cross talk between
touching fibres
Prevents signal degradation through light escaping core, causing info to be lost
n Core > Cladding
What is modal (multipath) dispersion and how is it prevented
Light travelling along the axis of the core travels a shorter distance per unit length than light continuously undergoing TIR. Larger range of path lengths - pulse would become longer than supposed to be, and could merge with next pulse.
Prevent by using narrow fibre + low difference in n between core and cladding
What is chromatic/material dispersion and how can it be prevented
When white light is shone along an optical fibre, different wavelengths of light travel at different speeds. e.g. violet light travels slower than red light in glass. Causes pulse broadening as violet fails to catch up w red
Prevent by using monochromatic light
How are optical fibres used in endoscopy?
Contains two bundles. Endoscope inserted into the body, then illuminated with an incoherent bundle. Lens at other end used to form an image of insides, and light is reflected back through a coherent bundle where the image can be observed.
Coherent bundle - fibres at each end are in same relative position
In the double slit experiment, what would happen if you replaced the volume between the slits and the screen with water?
Maximas would be closer together/ lower fringe spacing, as wavelength of light decreases as it enters water
What happens to a diffraction grating pattern when the number of slits is increased (with same spacing)
Increased intensity + sharper/ more defined maxima at respective angles
No more maxima/ diff in distance as wavelength isn’t changing
Light incident from lots more slits - more waves arrive at a particular point on the screen - so unless dsinθ = nλ, enough waves will be arriving out of phase to result in overall destructive interference.
What increases the chances of overlapping maxima with a non monochromatic source?
A grating with a small number of slits
Why can’t the first and second order visible spectra overlap?
The wavelength of red light is greater than 2x the wavelength of violet light
Because the second order maximum value is greater than the third order minimum, those would overlap. The first and second order do not overlap because the maximum of the 1st will never exceed the value for the 2nd order.
Why does red light bend more than blue light in a diffraction grating, but bend less in a prism
Angle of refraction in a grating proportional to wavelength (dsinθ = mλ). Red light has a greater wavelength
n = c/c2 = λ/λs
Red has a greater wavelength so a lower refractive index, so speed is changed less in a prism, and therefore experiences less bending
What could cause polarised light to pass through an analyser at an unexpected angle (badly worded)
If a transparent material is placed between the filters, it could rotate the plane of polarisation
Why are sloping sides used in the ripple tank practical?
To prevent waves from reflecting off the sides
What is a wavefront?
“A line of constant phase” e.g. from joining adjacent peaks
Importance of satellite dish design
Larger dish - stronger signal, as more waves are reflected onto aerial, but a bigger dish reflects waves onto a smaller focus, as waves diffract less, so dish needs to be more carefully aligned due to smaller focus
Why do EM waves lose energy as they propogate?
Waves “spread out” and lose intensity
Difference between emission and absorption spectra
Line emission - sample is heated/given energy and photon excitation causes specific wavelengths of light to be given off (evidence for discrete energy levels)
Absorption -Continuous spectrum passed through sample which absorbs wavelengths of certain frequencies. Light is emitted but not in same direction
Line emission - coloured lines on dark screen
Absorption - Dark lines on coloured screen
What happens when you use a larger wavelength in the single slit experiment?
Wider central fringe, + maxima further apart
(as subsequent fringes are also wider)
Effect of using a range of wavelengths in single slit experiment
Central maximum unchanged in width
Broader maxima/range of angles for each maximum/order
Gradually getting broader/more spread out for greater order maxima
Effect of using a range of wavelengths in single slit experiment
Central maximum unchanged in width
Broader maxima/range of angles for each maximum/order
Gradually getting broader/more spread out for greater order maxima
Polarization by reflection
When unpolarized light reflects off an insulator, the light can become polarized in the plane parallel to the reflecting surface. (common example is glare from water and glass)
Diff light sources
Discharge tubes/ vapour lamps
- Produce dominant colour
Filament/Sun
Produces continuous spectrum (white)
Laser - monochromatic
Pros of diffraction grating
U get sharper fringes - each beam reinforced multiple times more
Multiple slits - fringes are more intense, but at the same angle if wavelength is unchanged
Applications of diffraction gratings
Analysing composition of stars
Chemical analysis
Measure red shift / rotation of stars
Measure the wavelength / frequency of light from a star
Observe the spectra of materials
Analyse the absorption / emission spectra in stars
Diffraction gratings also play a role in x-ray crystallography
X-rays are directed at a thin crystal sheet which acts as a diffraction grating to form a diffraction pattern
This is because the wavelength of x-rays is similar in size to the gaps between the atoms
This diffraction pattern can be used to measure the atomic spacing in certain materials
Assumptions in diffraction eqs
D»s - So rays arriving at a point are virtually parallel - can use similar angles + small angle approximations
Also for double slits assuming that slits are of equal width
First minimum for single slit diff
path lengths differ by 3λ/2 for rays from the top and bottom of the slit. One ray travels a distance λ different from the ray from the bottom and arrives in phase, interfering constructively. Two rays, each from slightly above those two, will also add constructively. Most rays from the slit will have another to interfere with constructively, and a maximum in intensity will occur at this angle. However, all rays do not interfere constructively for this situation, and so the maximum is not as intense as the central maximum
Central max all interfere constructively so more intense
Single slit diffraction pattern for white light
Central fringe white
Each wavelength forms own pattern
Bright fringes now a spectrum
violet at lowest angular separation for a given order, red at the greatest
Wider maxima
Smaller fringe spacing
(Violet/blue closest to central, red furthest)
Effect of slit width + wavelength
Angle of diffraction proportional to wavelength
Width of bright maxima (fringe) proportional to wavelength
Narrower slits reduce intensity + increase fringe spacing
I/sinθ graph for red vs blue shows red wider if that makes senz
Modulation of two slit interference pattern
If light emerging from each slit in two slit experiment may have alr formed its own diffraction pattern. So if light emerging has a minimum at a certain angle, due to OG diffraction, a minimum will also be formed, even if the two slit model predicts a maximum.
Note the separation of the centres of the slits must always be less than the width of each slit
Can be said that single slit pattern modulates double slit pattern (see pg 396 of IB textbook)
Angles for minima of single slit pattern, vs maxima for 2 slit pattern
Minimum - θ = nλ/a (a is slit separation)
Maximum θ = nλ/s (s is distance between centres of slits)
sma θ = sinθ
Which derivations involve sma vs don’t
Single slit + double slit, however diffraction grating u can’t use sinθ = θ as angles are larger
A submarine is using ultrasound of frequency 50 kHz to measure the height of objects on the seabed. The submarine encounters object X. (X is a height hx above the seabed). The phase difference between a signal from the seabed and the returned signal from object X is fraction numerator 2 pi over denominator 3 end fraction radians.
Assuming there is no change of phase when the signals reflect off either the seabed or the object, which of the following heights, A to D, is not a possible height hx of object X?
The speed of sound in water is 1500 m s–1.
The wavelength of the ultrasound can be found using the wave equation:
λ = v / f = 1500 / 50000 = 0.03 m.
Since a phase difference of π radians (or 180º) is equivalent to the waves being separated by λ / 2, 2π / 3 radians is equivalent to a separation of λ / 3,
λ / 3 = 0.01 m or 1 cm.
Therefore the path difference Δx between signals reflected off the seabed and signals reflected off the object must be equal to an integer number of wavelengths (which has no effect on phase) ± one-third of a wavelength:
Δx = nλ ± (λ / 3).
Substituting the value of λ gives
0.03n ± 0.01.
However, because the wave is reflecting and returning to the submarine, the path difference Δx is actually equal to twice the height h𝑥 of the object.
Therefore,
Δx = 2h𝑥 = 0.03n ± 0.01;
h𝑥 = 0.015n ± 0.005
Critical angle for diamonds
The diamond sparkles more than the fake because more light is reflected back out of the front face (there is more internal reflection);
A smaller critical angle will allow more total internal reflection;
This is because there would be more angle of incidences that would be greater than the critical angle to produce TIR
Uses of polarisers
3D Glasses, Sunglasses to reduce glare, Polaroid cameras
Vertically polarised so that plane polarised light is absorbed
Btw in reality light intensity decreases when passing through filter
How polarising filters helps to take picture of underwater fish
Partially plane polarised in vertical plane, light reflected of water polarised in horizontal, blocks glare. Light from fish isn’t reflected but refracted and therefore isn’t plane polarised
Types of waves that can be polarised
EM radiation,Water waves, S(shear) waves
What would cause the displacement of diff particles in phase in a longitudinal wave to be different
If there’s no absorption/spreading out of the wave
Why can’t coherent waves produce constant patterns
They interfere, however the pattern randomly fluctuates as the phase diff is changing
Condition for standing waves
Two waves moving in opposing directions along the same path and in the same plane.
The waves must travel at the same velocity.
The waves must have the same frequency.
The waves should have a similar amplitude (idk y they still produce standing wave but cancellations are diff)
n=ci/cs derivation
Consider horizontal line XY’. Wavefront at angle i from X to point above Y moving a distance ct from Y to Y’. Once inside new wavefront refracted towards normal (angle r) moving distance cst from XY’ to X’Y’. You can form right triangles using the fact that the direction of propagation is ppd to wavefronts, and eliminate XY’, then sub in distances
Angle of incidence for a wavefront vs a ray
Complements of each other, prove to yourself sasageyo
Relationship between wavelength and amount of diffraction
n=l/ls
Smaller l greater n greater diffraction (capacity to change speed)
Why diamonds sparkle in white light
Highest refractive index - separates white light more than other substances, low critical angle - may be TIRd many times before emerging - spreading out colours even more
What can prevent TIR in an optical fibre (bend)
If radius of bend is too small, COULD potentially not refract
Pulse broadening and absorption
Absorption - part of signals energy absorbed by fibre, signal is attenuated, reducing amplitude of signal - loss of info
Pulse broadening caused by modal/chromatic dispersion
Reduce broadening by making core narrow,using monochromatic source, using repeaters so pulse is regenerated before significant broadening has occurred
Measuring fringe width practically
Measure across a few dark fringes, centres of dark easier to find that centres of bright
What determines the “single slit envelope”
Width of single slit
Path difference as
Integer number of wavelengths + path difference (nλ + x)
also to convert from radians to fractions of T/λ divide by 2pi
