waves Flashcards
Explain, with reference to refractive index, why the pulse of red light has a shorter transit time than the pulse of blue light
- The refractive index of core for blue light is greater than the refractive index for red
- The speed of the blue light is less than the speed of the red light and travel the same distance
Explain what is meant by modal dispersion in an optical fibre
- Pulse broadening
- Due to different paths through the optical fibre/entering the optical fibre at different angles
- can be prevented by using monomode fibres
Equation to find the wavelength of a stationary wave using length/distance
λ = 2L/n
Equation to find the length of wire used for a stationary wave using the wavelength
L = λn/2
Path Difference
The difference in the distance that to waves have traveled
Phase difference
The amount by which one wave leads or lags behind another measured in degrees or radians
Properties Harmonics
Resonant frequencies occur when an exact number of half wavelengths fit on the string
Resonance f = harmonics
The first harmonic is the lowest possible resonant frequency (f₀)
for the nth Harmonic ->
no. of nodes = n+ 1
no. of anti-nodes = n
frequency = n x f₀
Length =(nλ/2)
wavelength = 2L/n
factors affecting resonant frequencies on a string:
- Length of the string
- extra 1/2 wavelength so lower frequency
- Mass per unit length of the string
- slower travel
- Tension of the string
- slower travel down looser string
F = 1/2π (T/µ)½
Progressive Waves vs Stationary Waves
Progressive Waves
- Amplitude of vibration is the same at every position
- Crests and troughs move along the wave
- All frequencies support progressive waves
- Phase varies continually along the wave
Standing/Stationary Wave
- Amplitude of vibration varies with position
- nodes and anti-nodes do not move along the wave
- only resonant frequencies support stationary waves
- Between adjacent nodes, all points vibrate in phase
ALL KEY WAVE DEFINITIONS
A progressive wave is a mechanism that transfers energy and/or information from one place without the net movement of matter
A mechanical wave is a wave which has oscillations of matter
Longitudinal waves oscillate in the same direction as the wave propagation
Transverse waves oscillate at right angles to the wave propagation
Frequency - the no. of complete oscillations of a wave in one second
Time Period - the time taken to complete one wave cycle
Amplitude of a wave is the max displacement from it’s equilibrium position
wave speed - the speed of which energy is transferred by a wave
Why can radians not be used when doing calculations with practical results involving angles?
You can not convert measured degrees in to radians to calculate angles because it implies a zero level of uncertainty which is not feasibly possible.
Energy of waves at a boundary
The principle of conservation of energy means that, at the boundary between two materials, the energy of the transmitted wave must be equal to the energy of the incident wave.
Diffraction Gratings
- Diffraction Gratings make light fringes brighter and narrower dark fringes which are more intensely dark. Overall making sharper pattern
- With white light it results in a spectrum of colours
Interference
Destructive interference occurs at a path difference of 1/2λ
Constructive interference occurs at path differences multiples of λ
Stationary wave formation & Interference
- The superposition of two progressive waves
- only coherent (waves of a constant phase difference and the same frequency) waves can interfere
-When an oscillator happens to produce an exact no. of waves in the time it takes for a wave to get to the end and back then the two waves reinforce each other
- The frequencies at which this can happen are referred to as the resonant frequencies.
Uses of Polarisers
Light waves that reflect off some surfaces are partially polarised which causes glare that we can filter out using polarising filters.
TV rod signals are polarised by the orientation of the rods on the transmitting aerial
you must align your TV signal aerial to the transmitting aerial or else your signal will be weak because it will be filtered
- same for radio waves
Why may a polarising filter not block out some light?
It hasn’t blocked out all the waves on other planes of light.
How does polarisation show evidence for the existence of transverse waves?
ONLY transverse waves can be polarised.
Diffraction
- For Diffraction to occur the wavelength of the wave source must be similar in size to the gap of the slits
- When white light is shone through a slit, the different wavelengths are diffracted by different amounts ( The longer the wavelength, the greater the diffraction).
Two Source interference
two source interference is when waves fro two different sources interfere with each other to produce a pattern
- to get a clear interference pattern the waves must be monochromatic (must consist of a single frequency and wavelength) and coherent (constant phase difference and same frequency).
At a maxima the path difference is a whole number of wavelengths and have a phase difference of O.
At minima complete out of phase( πrad)
and have a path difference of (2n + 1)/2*λ
Laser Safety
- Never shine a laser on a reflective surface
- ## You should wear safety goggles whenever in use-
-
Single Slit
- When a wavelength of light is similar to the size of the slit you get a diffraction pattern
- The central maxima is the brightest part of the pattern because the intensity of the light is the highest at the centre
- For monochromatic light, all photons have the same energy, so this means there is more energy hitting it every second.
- The width of the central maxima varies with the width of the slit and the wavelength of the light
(i.e increase in wavelength = increase in diffraction thus central maximum is wider and intensity is lower
increasing slit width decreases diffraction thus central max is narrower and more intense)
Benefits of Cladding?
- Prevents crossover of signals
- Has a lower refractive index so TIR can occur
- protects core from damage/scratches
Explain what is meant by spectral/chromatic dispersion in an optical fibre
- form of pulse broadening
- the shorter wavelength waves will travel slower in the optical fibre because they are refracted more so different wavelengths of light will reach the ends of the optical fibre at different times
- this can be reduced by using monochromatic light
Two things that affect signals of optical fibres
- Pulse Absorption
- poorly transparent material absorbed light, which would reduce the amplitudes of the pulses progressively
- loss of light reduced amplitude of the pulses
- Pulse broadening
- modal (multipath) dispersion
- core must be narrow rather than wide because transmission via the axis of the optical fibre is a shorter distance to travel than undergoing TIF in the optical fibre.
- spectral (material) dispersion
- must use monochromatic light because if white light is used then due to the differences of wavelengths of rays in the white light, some (larger wavelengths) will travel faster through the core than others (smaller wavelengths)
- the difference in speed will cause longer pulses
- must use monochromatic light because if white light is used then due to the differences of wavelengths of rays in the white light, some (larger wavelengths) will travel faster through the core than others (smaller wavelengths)
- modal (multipath) dispersion
Define superposition
The principle of superposition is that when two waves meet, the total displacement at a point is equal to the sum of the individual displacement at that point
Define superposition
The principle of superposition is that when two waves meet, the total displacement at a point is equal to the sum of the individual displacement at that point
point Y and Z on a stationary wave are separated by 2 nodes what is their phase difference
points separated by an even number of nodes are in phase
point X and Z on a stationary wave are separated by 3 nodes what is their phase difference
points separated by an odd number of nodes are in constant antiphase
Maximum Diffraction
Maximum diffraction of a wave occurs when the size of the gaps/obstacles are equal to the WAVELENGTH of the wave.
What is Coherent light?
light/waves/rays that are monochromatic (of same frequency and wavelength)
- and have a CONSTANT PHASE DIFFERENCE
Why does frequency remain the same during refraction?
This is a consequence of the principle of conservation of energy. The energy of a wave is directly proportional to its frequency, and since energy cannot be created or destroyed, the frequency of the wave cannot change as it moves from one medium to another.
(all other physical quantities of the wave changes to compensate for this: amplitude, wavelength, wave speed etc)
Double Slit vs Single Slit
- fringes in double slit are all the same width
- for single slit the central fringe is double the width of the other fringes
Refraction Definition
- The change of direction that occurs when light passes at an angle across a boundary between two transparent substances
TAGAGA?
light rays bend:
- Towards the normal when it passes from air into glass
- Away from the normal when it passes from glass into air
At the boundary between two transparent substances, the light ray bends…
- towards the normal if it passes into a more dense substance
- away from the normal if it passes into a less dense substance
Partial Reflection
Why do prisms split a beam of white light?
- White light is composed of light with a continuous range of wavelengths (350-650nm)
- the shorter the wavelength in air, the greater the amount of refraction
- ∴ each colour in the white light beam is refracted by a different amount
- this occurs because the speed of light in glass **depends on wavelength
Which has a higher refractive index, Red light or Violet light? Why?
- Violet light
- It travels slower in substances than red light
- because it has a smaller wavelength
How does the speed of light in glass change on increasing the wavelength of light?
- the speed of light … within a material will be greater than lower wavelength light
How is frequency affected when light travels through optically dense material
- Frequency does not change when light travels through an optically dense material even though the wave speed decreases
- Wavelength does affect the speed of light in optically dense material
c = f λ
- to maintain their frequencies lower wavelength light will move slower in optically dense material even
- to maintain their frequencies lower wavelength light will move slower in optically dense material
A red light ray had an angle of refraction of 20° upon entering a material and a blue light ray had an angle of refraction of 18° upon entering the same material. Explain how this proves blue light travels slower than red light in a material
- a smaller angle of refraction -> closer to the normal
- ∴ according to Snell’s law nsinx=n’sin’x, given the angle of incidence does not change:
- the refractive index is greater for blue light > refractive index of red light
- c/c’ = r where c’ = speed of light in a material, r = refractive index
- a greater refractive index means a slower speed of light in a material ∴ blue light must have a slower speed of light than red light in a material.
Total internal reflection can only take place if…
- the incident substance has a larger refractive index than the other substance
- the angle of incidence exceeds the critical angle
where sinx (c) = n2/n1 (n1>n2)( if it’s at the critical angle it will cause an angle of refraction of 90° and the light ray will emerge along the boundary) - this is not the same as partial reflection
Why do diamonds sparkle when white light is directed at them?
- the high refractive index of diamond gives it a critical angle of 24.4° ( sin^-1(1/2.417) )
- so a light ray in a diamond will be total internally reflected many times before it emerges
- the white light will ( due to the nature of it containing light of continuous wavelengths) also separate in to the colours of the spectrum
(more than any substance does)
Uses of Optical Fibres
- medical endoscopes
- communications ( by carrying light signals)
- small radius of bend -> encourages refraction and escape through the cladding
- refractive index
Medical Endoscopes
- Make use of Optical Fibres to do medical imagining within the body
- they consist of two bundles of fibres
- one fibre bundle works to illuminate the body cavity
- the other allows reflected light to travel through to be observed
- a fibre bundle needs to be a coherent bundle, meaning the fibre ends at each end are in the same relative position ( so an image can be produced)
What occurs during Young’s Double slit experiment if the first single slit is too wide?
- each part of it produces a fringe pattern which is displaced slightly from the pattern due to adjacent parts of the single slit
- As a result, the dark fringes of double slit pattern become narrower than the bright fringes, and contrast is lost between the dark and the bright fringes.
( simply - wider slit means light could be hitting the double slits at multiple different directions, each direction gives rise to its own diffraction pattern, the sum of these patterns reduce the contrast, see pic)
What is a Coherent Source?
- A source which emits light waves with a constant phase difference and the same frequency
At bright fringes
- the light from one slit reinforces the light from another, the light waves from each slit arrive in phase
where P,path difference S1 and S2 are waves at each slit
S1P - S2P = m λ <- reinforcement
At dark fringes
- the light from one slit cancels the light from the other slit, the light waves from the two slits arrive 180° out of phase
S1P - S2P = (m + 1/2) λ
Derive the Formula for fringe separation
- This equation is only valid when the fringe separation is much smaller than the distance D from the slits to the screen
- this ensures that the triangles used in ur derivation are similar in shape
(aka for small angle approximations)
How do Loud Speakers demonstrate the results of Young’s Double slit Experiment?
- two loudspeakers connected to the same signal generator can be used to demonstrate interference as they are coherent sources of sound waves
- there will be detectable points of cancellation and reinforcement (you can hear by ear)
How is a Coherent source formulated when using a single slit before a double slit in a double slit experiment?
- each wave crest and wave trough from the single slit always passes through one of the double slits a fixed time after it passes through the initial single slit
- the double slits therefore emit wavefronts with a constant phase difference
Why can’t light from two nearby lamp bulbs produce an interference pattern?
- the two light sources are not coherent
- they emit light waves at random
- the points of cancellation and reinforcement would change at random, so no interference pattern is possible
What is white light composed of?
- ## white light is composed of a continuous spectrum of colours, corresponding to a continuous range of wavelengths
Explain why blue light has a larger fringe spacing for it’s interference pattern than red light
- w = λD/s
- red light has a larger/longer wavelength than blue light
- so a larger fringe spacing is observed for red light than blue light
Examples of Light Sources
- Vapour lamp and discharge tubes
- e.g sodium vapour lamp, composed of primarily wavelengths around 590nm, yellow/orange
- acts as a monochromatic light source because spectrum is dominated by light of a certain colour - Filament/Sun
- continuous spectrum
- Laser
- monochromatic source
- wavelength dependent on source
- risk to the eyes because the beam is almost perfectly parallel and monochromatic, when lens is used against it, it can concentrate its power in a very small area
( this can destroy the retina)
How does a double slit diffraction pattern appear for white light?
- white light central fringe because ever colour contributes at the centre
- the inner fringes
- inner side are the low wavelength light (ie blue)
- outer side are large wavelength light (ie red)
- the outer fringes merge of a spectrum of the rest of the colours overlapping each other
Why must the two slits in double slit experiment be close together?
- If two slits are two far apart no interference can occur because the waves are too far apart to be able to interfere
Why are the fringe widths of blue light more narrow than red light
- the width of each fringe is proportional to λ/a
- blue light has a shorter wavelength than red light so the width of each fringe are narrower
where W = 2λD/a (D is slit screen distance, W front width, a, width of the single slit)
Why is light only transmitted in certain directions when a diffraction grating is used on a parallel beam of monochromatic light?
- the light passing through each slit is diffracted
- the diffracted light waves from adjacent slits reinforce each other in certain directions only, and cancel out in all other directions
Derivation of the Diffraction Grating equation
(fill this in later icl, no that relevant for rn we hope anyways)
N = 1/d
N, number of slits per metre
d, the grading spacing
Types of Spectra and some uses
- Continuous spectra
- continuous spectrum of colour from violet to red, the most intense part if the spectrum is dependent on the temperature of the light source.
the hotter the light source the more intense the shorter λ is and vice versa
we can use it to measure the temperature of a light source - Line emission spectra
- emission of waves of particular wavelengths from gases, forming lines of spectra in an other wise dark spectrum, elements all have specific line spectra and we can identify specific elements using it - Line absorption spectra
- continuous spectrum with dark lines at certain wavelengths
the dark line patterns are due to elements (typically gases) absorbing light at specific wavelengths while subsequently emitting light in alternate directions.
Define the Principal of Superpostion
- When two waves meet, the total displacement at one point is equal to the sum of the individual displacements at that point
- crest + crest -> super crest
- trough + trough -> super trough
- crest + trough -> 0 (minimum)
When do resonant frequencies occur in a pipe?
- When there is an antibody at the open end and a node at the other end
How to use an Oscilloscope
To display a waveform:
- the X-plates are connected to the time base circuit which makes the light spot move at a constant speed across the screen
- calibrated in milliseconds or microseconds per centimetre (∵ constant speed) - the pd to be displayed is connected to Y-plates via the Y-input/sensitivity so that the spot moved up-down the screen
- calibrated in volts per centimetre (or per division on screen) - as the spot moves up and down the screen as it moves horizontally at a constant speed a waveform is produced on screen
- to calculate frequency of the alternating pd applied:
- find time period using time base circuit and x measurement
- f = 1/T
What is an Oscilloscope and what do we use it for?
- an oscilloscope is made up of an electron tube and control circuits
- Can be used to measure the speed of ultrasound
- The time base circuit of an oscilloscope can be used to trigger an ultrasonic transmitter so it sends out a short pulse of ultrasonic waves
- an ultrasonic receiver detects the transmitted pulses- if the receiver signal is applied to the Y-input of the oscilloscope, the wave form of the received pulse can be seen on the oscilloscope screen
- by using the horizontal distances and time-base control you can calculate the speed of the ultra sound via s = vt
Why are we able to use the Y-gain and Time base circuit to find the Potential Difference (and it’s frequency) applied on an Oscilloscope?
- The displacement of the spot on the oscilloscope screen is proportional to the applied P.D
- for both the X-plates and Y-plates
Explain why a Single slit should be narrow
- The narrow slit produced wide diffraction of the light
- To ensure that both S1 and S2 are illuminated
( where S1 and S2 are the pair of slits of the double slit)
Why do the slits S1 and S2 act as a coherent sources?
- (Slit S acts as a point source)
- S1 and S2 are illuminated by the same source, giving monochromatic light of the same frequency
- The path from S to S1 and from S to S2 are of constant length, giving a constant phase difference between the waves
