Waves Flashcards
Total internal reflection
When a ray of light leaving an optically dense material
Travelling into a less dense one
Is not refracted outside
But totally reflected back inside
When is Snells law not applicable
If the angle of incidence is grater than the critical angle
Because total internal relection occurs
Angle of refraction at critic angle
90°
Critical angle
Angle of refraction is 90°
Incident less than means reflection
Incident more than means TIR
Fibre optics
Thin flexible tubes Glass/plastic Carry light signs over long distance Round corners High refractive index Narrow so light says hits at angle bigger than critical for TIR to occur
Cladding
Protects core from scratches and fluid contamination so light can’t escape
Increases critical angle
Lower refractive index than optical fibre allowing for TIR
Modal dispersion
Light enters at different angles so takes different paths
Longer path means longer to reach end than those that travel down middle
Single mode fibre only let’s light take one path
Stopping modal dispersion
Material dispersion
Chromatic dispersion
Light consists of different wavelengths that travel at different speeds
Some reach end before others
Using monochromatic light can stop material dispersion
Uses of fibre optics
Lighting and decoration
Telephones
Microscopy and biomedical research
Computer networking easier and faster
Critical angle formula
Sin¤c=n2/n1
Explain one advantage of having a small core in fibre optics
Less light is lost so better quality signal
Increased probability of total internal reflection
Diffraction
Wave spreading out as it passes through a gap
Condition for max diffraction
Wavelength similar to size of the gap
Waves are either … or …
Longitudinal
Transverse
Longitudinal
The direction of vibration of particles (oscillations) are parallel to the direction in which the wave travels (propagation of wave)
Composed of compressions and rarefactions
Compressions
Regions of high pressure
Due to particles being close together
On a longitudinal wave
Rarefactions
Regions of low pressure
Due to particles being spread further apart
On a longitudinal wave
Transverse
The direction of vibration of particles (oscillations) are perpendicular to the direction in which the wave travels (propagation of wave)
Examples of longitudinal waves
Seismic P-waves
Sound
Springs (left to right)
Ultrasound
Examples of transverse waves
Seismic S-waves
Electromagnetic
Spring (up and down)
Ripples on water
Displacement
How far a point on a wave has moved from the undisturbed position
Vector (+/-)
Measured in metres
Amplitude
The maximum displacement of the wave from the undisturbed position/equilibrium position
Measured in metres
Wavelength
Length of one whole wave oscillation or wave cycle
Measured in metres
Frequency
Number of whole wave cycles (oscillations) per second passing a given point
Measured in Hz
Period
Time taken for one whole wave cycle
Crest to crest/trough to trough
Measured in seconds
Where can amplitude be measured
Crest
Trough
Crest
Point of positive amplitude (maximum positive displacement from the undisturbed position)
Trough
Point of negative amplitude (maximum negative displacement from the undisturbed position)
One oscillation/wave cycle
The point of a wave from crest to crest or trough to trough
Phase
Measurement of the position of a certain point along the wave cycle
Measured in degrees or radians or fractions of a cycle
Phase difference
Amount by which one wave lags behind another
Measured in degrees or radians or fractions of a cycle
1 Hz is equivalent to
Per second
1s^-1
What happens to sound if you increase the frequency
Wave is compressed
Wavelength decreases
Pitch increases
Amplitude stays the same
What happens to sound if you increase amplitude
Wavelength stays the same
Frequency stays the same
Wave is stretched vertically
Sounds louder
What happens to sound if you double the wavelength
Half the frequency
Wave is stretched horizontally
Pitch decreases
Amplitude stays the same
Frequency relation to time period
f=1/T
Wave equation
c=fλ
Deriving the wave equation
Speed=Distance/Time
Time=1/frequency
Speed=Distance/(1/f)
c=fλ
Frequency of sound
20-20000Hz
Order of EM spectrum
Radio Waves Microwaves Infrared Visible Light Ultraviolet X-Rays Gamma Rays
Mechanical waves
Require a medium to transfer energy from one location to another location
Do not transmit energy in a vacuum
Wavelengths of EM spectrum in powers of 10m
R
3
- 2
- 5
- 6
- 8
- 10
- 12
G
Frequencies of EM spectrum in powers of 10Hz
R
4 8 12 15 16 18 20
G
Examples of mechanical waves
Sound waves
Ripples on water
Seismic S and P waves
Radio waves
f
λ
4
3
Microwaves
f
λ
8
-2
Infrared
f
λ
12
-5
Visible light
f
λ
15
0.5x10^-6
Ultraviolet
f
λ
16
-8
X-Rays
f
λ
18
-10
Gamma
f
λ
20
-12
Speed of EM waves in a vacuum
3x10^8
Range of wavelengths of visible light in nm
700 (red)
400 (violet)
Wavelength of green light
495-570nm
Range of frequencies of visible light in THz
430 (red)
750 (violet)
360 degrees is how many radians
2pi
What is polarisation
Restricting a waves vibrational movement to one plane
Only transverse waves
What waves can be polarised
Transverse
They have vibrations in a number of directions
So can filter all out by one
Effect of passing light through two crossed polaroid filters
Polarised light produced after first filter
No light allowed through the second filter
Since perpendicular to the first it blocks the polarised light
Describe the graph for the effect of rotating a polarising filter
A trig graph of either sine or cosine depending on start angles
How can polarisation provide evidence for the nature of transverse waves
Polarisation can only occur if the waves oscillations are perpendicular to the propagation
Application of polarisation
Polaroid sunglasses
TV and radio signals
How do polaroid glasses work
They reduce glare By blocking partially polarised light Reflected from water and tarmac As they only allow oscillations in the plane of the filter Making it easier to see
How do TV and radio signals make use of polarisation
Usually plane-polarised by the orientation of the rods on the transmitting aerial
So the receiving aerial must be aligned in the same plane of polarisation
So receive the signal at full strength
What is a progressive wave
A travelling wave that transfers energy without the matter carrying the wave being translated
Example of a progressive wave
Mexican wave
All people have the same amplitude and frequency of oscillation
Each person is out of phase
4 key features of progressive waves
Adjacent oscillating particles have a phase difference
Amplitude is the same for all particles in path of wave
All particles vibrate with the frequency of the wave
Crests and troughs travel with the waves velocity
When does a stationary wave occur/what is a stationary wave
A progressive wave is reflected
Reflected wave and initial wave superpose and combine
Giving a stationary wave with no net energy transfer
Because the two progressive waves have the same amplitude, frequency and speed
But are travelling in the opposite direction
Nodes
Position of zero displacement on a stationary wave
Formed when two progressive waves combine out of phase
So destructively interfere
Antinodes
Position of maximum displacement (either positive or negative) on a stationary wave
Formed when two progressive waves combine in phase
So constructively interfere
Distance between nodes and antinodes on a stationary wave
Quarter of a wavelength
Distance between adjacent nodes
Distance between adjacent antinodes
Half a wavelength
Do stationary waves transfer energy
No
What is the phase relationship for particles between two adjacent nodes on a stationary wave
No phase difference
They are in phase
Phase relationship for particles either side of a node
180°
Out of phase
How does the amplitude change in a stationary wave
Varies from zero at the nodes to maximum at the antinodes
How does the frequency change on a stationary wave
All particles vibrate with the frequency of the wave
Except the nodes which are stationary
Stationary wave vs progressive wave
P transfers energy/S does not
P has same frequency for all particles/S has the same for all particles except at the nodes which is 0
P is a travelling wave/S is not
P all particles have the same amplitude/S varies from 0 at nodes to maximum at antinodes
Node vs antinode
N has 0 amplitude or displacement/A has maximum
N formed from progressive waves combining out of phase and interfering destructively/A formed from progressive waves combining in phase and interfering constructively
How can you tell if a particle is moving up or down on a wave
Draw a tangent at the particle of interest
If the gradient is negative then it is moving upwards
If the gradient is positive then it is moving downwards
Where does the sound come from for a vibrating string
Air around the string vibrates at the same frequency
So a progressive sound wave moves away from the string
Most sound energy comes from resonating soundboard of instruments and not the string
Wavelength of first harmonic
λ/2
Wavelength of second harmonic
λ
Harmonic frequency formula
fn=
n/2L x root(T/u)
L=length
T=tension
u=mass per unit length
Derive the formula for harmonic frequency
c=root(T/u)
T=Tension (ma)
u=Mass/Length
λ=n/2L
c=fλ
Sub in and you will get the harmonic formula
What is the normal
A line perpendicular to a surface or boundary
Reflection
Wave is bounced back when it hits a boundary
What is the incident ray
The ray approaching a boundary
What is the reflected ray
They ray moving away from the boundary
Angle of incidence
Angle the ray of incidence makes with the normal at the boundary
Angle of reflection
Angle the ray of reflection makes with the normal at the boundary
Law of reflection
Angle of incidence = Angle of reflection
If the incident ray, reflected ray and normal all lie in the same plane
Refraction
Wave changes direction as it enters a different medium
Resulting in the wave speeding up or slowing down
What happens to light as it enters a glass block
Glass is more optically dense than air So it slows down and bends towards the normal (refraction) Wavelength decreases Frequency stays the same
What happens to light as it leaves a glass block
Air is less optically dense than air So it speeds up and bends away from the normal (refraction) Wavelength increases Frequency is the same
How does light entering a glass block compare to light leaving a glass block
Returns parallel to its original path
Frequency, wavelength and wave speed all the same
What happens if light enters a glass block at 90 degrees
Slows down
Remains along the same path
Wavelength decreases
Frequency stays the same
In terms of refraction, what does it mean if a material is more optically dense
Wave slows down
Wavelength decreases
Refracted towards the normal
Angle of incidence is greater than the angle of refraction
How can filling a cup with a coin in with water make the coin visible
Without water, coin can’t be seen
There is no reflected lines of light that make it to the eye
With the water, some of the light that would have previously passed the eye is now refracted into it
What is the absolute refractive index
Ratio of speed of light in a vacuum to the speed of light in the material
Formula to work out the absolute refractive index of a material
n=Speed of light in a vacuum/speed of light in material
n=c/cs
Key points for refractive index
No units because its a ratio
Never smaller than 1
Bigger refractive index means more optically dense
Snells law
Of refraction
sinθ1/sinθ2 = c1/c2 = λ1/λ2 = n2/n1
What is total internal reflection
A ray of light leaving an optically dense material travelling into a less optically dense material
Is not refracted out of the dense material
But totally reflected back inside
Angle of incidence is less than the critical angle
Refraction
Angle of refraction greater than incidence
When is Snells law not applicable
When the angle of incidence is greater the critical angle
How do you find the critical angle
Sin-¹(n2/n1)
Explain the change from refraction to reflection
Not sudden
Some light always reflected inside the block
As angle of incidence increases more and more light is reflected
Angle of refraction at the critical angle
90
Angle of incidence greater than critical angle
All light totally internally reflected
What is an optical fibre
Thin flexible tube of glass/plastic That carries light signals over long distances And round corner High refractive index Narrow so light always hits a boundary between fibre and cladding at a bigger angle than critical angle So all light is totally reflected From boundary to boundary Until it reaches the end
Why is cladding used with optical fibres
Protects core from scratches light could escape from and contacts with fluids
Increases the critical angle to increase the chance of total internal reflection
Advantage of using optical fibres as opposed to standard copper wires to transmit information
Faster: light travel faster than electrons in copper
Electrons and copper can only transmit one signal at once whereas light can transmit many at once by using a different angle
What is an interference pattern
If coherent waves overlap, superposition gives reinforcement of the waves at some points and cancellation at other points
Crest meets crest means constructive interference
Crest meats trough means destructive interference
Coherent sources
Same frequency and a constant phase relationship
Equipment for Youngs Double Slit Experiment
Monochromatic light (coherent)
Placed behind a single slit
Second barrier with two parallel slits
A screen to show bright and dark interference fringes
Explain Youngs Double Slit experiment
Light passing through the first slit spreads out by diffraction
This light is incident on the second two slits
Light from these two slit spreads out by diffraction
When these waves overlap and superpose, interference occurs
Resulting in an interference pattern
Bright fringes/maxima where constructive interference has occurred
Dark fringes/minima where destructive interference has occurred
Youngs Double Slit Formula
w=λD/s
w; Fringe separation in meters, one minima to next
D; Slit to screen distance in meters
s; Slit separation in metres
What is the result of allowing both yellow and blue light through young’s double slit experiment
Central maxima is green
Moving outwards there are separate colours of blue and yellow but some overlap producing green
Result of allowing white light through young’s double slit experiment
Central maxima is white
Moving outwards separate fringes with different colours
Blue on the inside and red on the outside
Path difference
Phase difference
Interference type
Maxima
nλ
0/In phase
Constructive
Path difference
Phase difference
Interference type
Minima
(n+0.5)λ
180/Antiphase
Destructive
Key points for intensity against fringe separation in diffraction
Width of central maxima is twice that of other maxima
Central maxima much brighter/intense and may be the only one visible in practice
W proportional to λ
W inversely proportional to s
As W increases amplitude decreases because energy is being spread over a greater area
Area under graph stays the same
Conditions for an interference pattern to be produced
Coherent source
Slit gap distance must be small enough so light can interact as it passes through/diffract
Difference for W in double and single slit
Double; W constant
Single; W decreases
What is the effect of increasing the gap width for single or double slit
Less diffraction occurs
Smaller fringe width
What is a diffraction grating
Series of very narrow gaps scratched onto a surface
When light is shone through a diffraction grating it makes an interference pattern
Diffraction grating equation
dsinθ=nλ
Number of orders obtained
n=d/λ
Effect of increasing wavelength of diffraction
Increases the amount of diffraction
Central maxima width wider but intensity lower
Applications of diffraction gratings
Analysing spectra of stars to find their composition
Analysing spectra of certain materials to see what elements are present
X-Ray crystallography
Explain X-Ray crystallography
Average wavelength of x-rays is a similar scale to the spacing between atoms in a crystalline solid
When directed at a thin crystal soidi diffraction pattern forms
Crystal acts like a diffraction grating and the spacing between atoms (s) can be found from diffraction pattern
Used to discover the structure of DNA
Approximation for youngs single slit
Distance between the slit is much less than the distance to the screen
So they are effectively parallel
Can only use the formula if this applies
Approximation for youngs double slit
Distance between the slits is much less than the distance so screen
So approximately parallel
Can only use the equation if this occurs
How is light from a diffraction grating able to form a maxima on a screen
Lights from slits overlap
Undergoing diffraction
Path difference is a whole number of wavelengths/arrive in phase with 0 phase difference
So meet and undergo superposition
