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A-Level Physics > Waves and the particle nature of light > Flashcards

Waves and the particle nature of light Flashcards

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1
Q

How is a wave defined?

A

a wave is a means for transferring energy via oscillations

-while energy moves from one place to another, the waves cause no net movement of any matter

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2
Q

How is displacement defined?

A

is the position of a particular point on a wave at a particular instant in time, measured from the mean (equilibrium) position
- symbol: various, often x; units:m

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3
Q

How is Amplitude defined?

A

is the magnitude of the maximum displacement reached by an oscillation in the wave
-symbol (A) units: m

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4
Q

How is frequency defined?

A

is the number of complete wave cycles per second
-symbol (f) units:hertz, Hz

-frequency (Hz) = 1/time period (s)
f = 1/T

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5
Q

How is wavelength defined?

A

is the distance between a point on a wave and the same point on the next cycle of the wave
-symbol (λ) units: m

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6
Q

How is period defined?

A

period (also time period) is the time taken for one complete oscillation at one point the wave
-symbol T units: s

time period (s) = 1/frequency (Hz)
T=1/f
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7
Q

How is phase defined?

A

is the stage given point on a wave is through a complete cycle, measured in angle units, rad
-no standard symbol units: rad

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8
Q

How is wave speed defined?

A

is the rate of movement of the wave (not the rate of movement within oscillation)

  • symbol v or c for the speed of electromagnetic waves
  • units ms^-1
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9
Q

What is a mechanical wave?

A
  • is one if which there needs to be some sort of material medium
  • a substance that oscillates to allow the transfer of energy e.g. sound travelling through air
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10
Q

What is an electromagnetic wave?

A
  • can transfer energy through repeated oscillations of electric and magnetic fields
  • but these fields so not need matter to support them
  • the interaction between electromagnetic waves and matter generally slows their transfer e.g. like travels faster in a vacuum that in water
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11
Q

How do you calculate wave speed?

A 
wave speed (ms^-1) = frequency (Hz) x wavelength (m)
-v = fλ
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12
Q

How do you investigate the speed of sound?

A
  • using a twin beam oscilloscope,a loudspeakers, two microphones and a ruler
  • using the twin beam oscilloscope we can find the extra time a sound takes to travel a short extra distance
  • one beam trace shows a sound picked up by a microphone held 50cm from the loud speaker
  • the other trace shows the same sound picked up by a second microphone held further from the loudspeaker
  • the difference in positions of the peaks on the two oscilloscope traces shows the time take, t, for the sound to travel the extra distance d.
  • then using v=d/t to find the speed
  • it can be difficult to make accurate measurements from the screen of an oscilloscope so we need to synchronize the traces to minimize the effect of random error in taking measurement
  • firstly with both microphones at the same distance from the loudspeaker, the two traces appear in identical phase position (in phase)
  • If we slide the second microphone slowly away from the loudspeaker, we will move the trace out of phase then eventually come back to exact synchronization
  • at this point, the distance between the two microphones is exactly one wavelength (λ). we set the frequency on the signal generator. and so the wave length equation can be used to find the speed v=fλ
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13
Q

how do you measure pulse echo?

A

as the sound has to travel to the object and back it is twice the distance therefore:
2d = v x t
so
d = (v x t )/2

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14
Q

what can pulse echo be used for and why is it useful?

A
  • pulse echo ranging and imaging systems are used in a wide range of technological applications from sonar on ships and submarines to air traffic control radar, medical imaging and the measurement of distance to asteroids and to the Moon
  • this is useful in situations where other methods might be difficult or hazardous e.g. mapping the surface of a planet like Venus
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15
Q

How is a transverse wave defined?

A

a transverse wave is one in which the oscillations occur perpendicular to the direction of movement of the wave energy
-where the movement of the particles or fields in an electromagnetic wave, are up and down or left and right whilst the energy travels forward

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16
Q

How is a longitudinal wave defined?

A

is one in which the oscillations occur parallel to the direction of movement of the wave energy
-happens in fluids and are generated by squashing particles together and then stretching them apart from each other repeatedly

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17
Q

How is compression defined?

A

is an area in a longitudinal wave in which the particle oscillations put them closer to each other than their equilibrium state
-in areas of compression there is higher pressure

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18
Q

How is rarefaction defined?

A

is an area in a longitudinal wave where the particle oscillations put them further apart from each other than their equilibrium
-in areas of rarefaction there is lower pressure

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19
Q

What are Earthquake waves?

A

-also cause seismic waves come in different types primary or P waves and secondary or S waves. These are longitudinal and transverse seismic waves respectively with P-waves travelling faster and arriving first

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20
Q

How are wavefronts defined?

A
  • are lines connecting points on the wave that are at exactly the same phase position
  • diagrams for waves are often drawn as lines, where all the points on a line represent points on the wave that are in the exactly same position, perhaps a wave crest
  • the line showing the direction of travel called a ray must be perpendicular to the wavelength
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21
Q

How is constructive interference defined?

A

-is the superposition effect of two waves that are in phase, producing a larger amplitude resultant wave

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22
Q

How is destructive interference defined?

A

is the superposition effect of two waves that are out of phase, producing a smaller amplitude resultant wave

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23
Q

What is 1 wavelength equivalent to?

A

-1 cycle , 360° or 2π rad

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24
Q

What is wave superposition?

A

when waves meet, each wave will be trying to cause a wave displacement at the point of intersection, according to its phase at that location

  • the net effect is that the overall displacement will be the vector sum of the displacement caused by the individual waves
  • after the encounter, each wave will continue pass each other, as the energy progresses in the same direction it was originally travelling,
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25
Q

What is an example of a wave superposition?

A

multiple small waves coinciding in the same location can lead to a brief very large displacement
-the graph is of sea surface height at the Drauper North Sea Oil Platform on 1st January 1995, showing a freak 18m wave

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26
Q

How does superposition work in continuous waves?

A
  • rather than a single point along the path of a the wave,we consider the waves superposing over an extended space the outcome is a continuous wave that is the sum of the displacement over time in each location
  • if two waves are in phase (phase difference of 0° or 360° their effect will produce a larger-amplitude resultant wave –> constructive interference
  • if two waves meet and are exactly out of phase (phase difference of 180 °) then the resultant is a zero amplitude wave –> destructive interference (imaging shining two lights at the same place and at that point you see darkness)
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27
Q

How is a stationary wave defined?

A
  • stationary or standing waves consist of oscillations in a fixed space, with regions of significant oscillations and regions with zero oscillations, which remain in the same locations at all time
  • continuous waves travelling in opposite directions will superpose continuously and can set up a stationary wave pattern
  • the waves need to be of the same speed and frequency with similar amplitude and have constant phase relationships –>coherent
  • wave energy does not pass through a stationary wave as it is not moving
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28
Q

How is coherent defined?

A

waves are to be coherent if they have the same frequency and have a constant phase relationship. Coherent waves are needed to form a stable standing wave

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29
Q

How is a progressive wave defined?

A

a progressive wave is a means for transferring energy via oscillation

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30
Q

How are nodes defined?

A

nodes are regions on a stationary wave where the amplitude of the oscillations is zero

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31
Q

How are anti nodes defined?

A

are regions on a stationary wave where the amplitude of the oscillation is at it maximum

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32
Q

What is a sonometer?

A

a sonometer is an apparatus for experimenting with the frequency relationship of a string under tension, usually consisting of a horizontal wooden sounding box and a metal wire stretched along the top of the box

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33
Q

How do stationary waves acted when they constructively interact with their own reflection?

A

-the standing wave pattern that can be set up will have a corresponding wavelength, as the wave equation must still be satisfied
- imagine a string attached at two ends, these must be it nodes:
1 - the fundamental mode (1st harmonic–> looks like a rainbow) has the wavelength of 2L as the length L from each node is reflected back
2- the 1st overtone (2nd harmonic looks line a sine graph) –> has a wavelength of L as it exactly fits one complete wave in the length of the string (λ=L)
3- the 2nd overtone (3rd harmonic) 1.5 cycles therefore wavelength is 2L/3
4- the 3rd overtone (4th harmonic) 2 cycles therfore has the wavelength of L/2
– tip to workout out wavelength could the number of peaks and troughs and divide 2L by that number

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34
Q

How can you calculate String wave speeds?

A

-waves on a stretched spring travel at a speed that is affected by the tension in the spring, T (in newtons) and the mass per unit length of the string μ ( in kgm^-1), The equation for the speed of a wave in a string is:
-v = sqrt(T/μ)
if this equation is combined with the wave equation, we get an equation that tells us how the frequency of vibrations is affected by other factors:
-v=sqrt(T/μ) and v = fλ
-f x λ = sqrt (T/μ)
-f=1/λ x sqrt(T/μ)
in the fundamental mode of vibration, this means the fundamental frequency f(0) depends on the length of the string, its tension and its mass per until length from:
f(0) = 1/2L x sqrt (T/μ)

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35
Q

How can you investigate the factors affecting the fundamental frequency of a string?

A

-we can verify the equation -f(0)=1/2L x sqrt(T/μ) experimentally ,in order to confirm it we need to undertake three separate investigations to verify each part of the relationship, whilst maintaining the other variables as control variable: thus we need to verify F(0)∝ 1/L ; F(0) ∝ sqrt(T) and F(0) ∝ sqrt(1/μ)
we can use a microphone connected to an oscilloscope to monitor the sound produced by a sonometer string and to measure its frequency of vibration, this can be easier if a data logging computer is used instead of an oscilloscope, s the screen can be frozen for close scrutiny

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36
Q

How can you investigate the relationship of f(0)∝1/L?

A

The string support(called bridges) on a sonometer are moveable, so that we can find the frequency with varying lengths, L,whilst keeping the same string (constant μ) and the same hanging mass (constant T) keep the other variables controlled. We can plot a graph to verify F(0) on the y-axis and 1/L on the x-axis which should give us a straight line

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37
Q

How can you investigate the relationship F(0)∝ sqrt(T)?

A

-we can find the fundamental frequency using a fixed length of the same string throughout (constant L and constant μ) for varying masses hung over a pulley i.e. varying T. We can plot a graph to verify F(0) on the y-axis is ∝ to sqrt(T) on the x-axis

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38
Q

How can you investigate the relationship F(0) ∝ sqrt(1/μ)?

A
  • this requires different strings (varying diameter metal wires could be used). Maintaining the same length and mass (constant L and constant T) keeps the other variables controlled. Measure the mass of each wire using digit balance, and its full length in order to calculate the mass per unit length for each wire or string used.
  • we can plot a graph to verify F(0) on the y-axis is ∝ to sqrt (1/μ) on the x-axis
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39
Q

What is diffraction?

A
  • diffraction is a spreading of wave energy through a gap or around an obstacle
  • when a wave passes the edge of an obstacle, if there is a space behind the object which is relatively small, the wave energy can pass around both sides of it and continue travelling past the obstacle
  • however if the object is larger there may be a shadow region behind it but there will still be diffraction around each edge
  • if two close obstacles forming a gap then there will be diffraction from each edge of the hap causing the to spread out through the gap
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40
Q

What factors affect diffraction?

A
  • the amount of diffraction around an obstacle depends on the size comparison between the obstacle and the wavelength of the wave
  • as a result there is an optimum size of a gap for maximum diffraction –> usually when the gap is the same size as the wavelength
  • too small –> very little wave energy can pass through
  • too large –> there is little effect off diffraction as the majority of the wave passes through undisturbed
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41
Q

What is the diffraction pattern of light when it goes through a narrow slit?

A
  • the diffraction pattern observed when light passes through a narrow slit, shows a central maximum and then areas of darkness and further maxima of decreasing intensity
  • the gap where there are no lights is an example of an interference pattern from the diffraction –> considering waves bring diffracted from each end of the slit gives us two waves that will meet the screen, at the points the are in phase they will superpose and show light, however when they are out of phase completely there will be no light due to deconstructive superposition
  • the diffraction pattern is an example of a standing wave on a screen where the dark spots are nodes and the light spots are antinodes
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42
Q

In single slit diffraction how does changing the slit size affect the diffraction pattern?

A

a narrower slit widens the central maximum, as well as the further maxima and minima

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43
Q

What is a diffraction grating?

A
  • a diffraction grating is a device that will case ,multiple diffraction patterns which then overlap creating an interference pattern with a mathematically well-defined spacing between bright and dark spots.
  • it is a collection of a very large number of slits through which the wave can pass. these splits are parallel and have a fixed distance between each slit
  • ( CD’s have a series of very close lines marked on them and act as the diffraction grating that reflects. This causes the spectrum of colors that can be seen on the from white light that hits the surface
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44
Q

What is the diffraction grating equation?

A

the pattern produced by each color passing through a diffraction grating follows the equation:

  • nλ=dsinϴ
  • where ϴ is the angle between the original direction of the waves and the direction of a bright spot
  • λ is the wavelength of the light used
  • d is the spacing between the slits on the grating ( normally quoted as a number of lines per meter or millimeter so to find d you need to do the initial calculation d = 1/number per metre OR d = (1 x 10^-3)/ number per millimetre
  • n is called the ‘order’ the order is the bright spot number from the central maximum which is n=0
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45
Q

How can you investigate diffraction with a laser?

A
  • a diffraction grating investigation allows careful study of the light making up the spectrum form any light source, Astronomers use this study the spectra from the start
  • diffraction gratings are manufactured to have a fixed spacing , d, between lines on the grating and this will be printed on the grating
  • by measuring the angle to each maximum brightness spot created by a diffraction grating,you can calculate the wavelength of the light used from the diffraction grating equation
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46
Q

How is interference defined?

A

is the superposition outcome of a combination of waves, an interference pattern will only be observed under certain condition such as the waves being coherent

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47
Q

What is two source interference?

A
  • a wave meeting its own reflection would set up a standing wave pattern, also known as a interference pattern,
  • reflection is a convenient way to generate coherent waves that will produce a standing wave
  • however, any combination of waves that have the same frequency and a constant phase relationship will produce this result
  • e.g. two loud speakers that are generating the same identical sound waves will have constructive and deconstructive interference
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48
Q

What is two-slit interference?

A
  • another interference pattern that can be observed if light is shone into an experimental set-up that causes it to create two coherent wave sources that produce a standing wave pattern
  • this effect was first demonstrated by Thomas Young 1803 using sunlight as the light source
  • Young explained his experiment using a theory that light can behave as a wave, in classical physics, interference is a phenomenon that can only occur with waves
  • Young’s theory was highly controversial at the time, as he was contradicting Newton’s theory that light behaved as a steam of particles
  • despite the experimental evidence he demonstrated, most scientist at the time refused to believe Young’s wave theory of light
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49
Q

How can you investigate two source interference?

A
  • a ripple tank where plane wave are diffracted through two gaps will cause an interference pattern between the two water waves
  • another common experimental demonstration of two-slit interference with a laser light
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50
Q

How do you explain two-source interference?

A
  • each point in a two-source interference pattern will have a superposition result that depends on the phase difference between the waves coming from each source to that point
  • That phase difference will, in turn, depend on the relative distance to the point from each of the slits compared with the wavelength
  • the connection between phase difference and the path difference comes if we remember each complete cycle corresponds to 2π radians.
  • Waves from one slit meeting waves from the other slit at a point will each have had to travel to that point, cycling through wavelengths as they go
  • thus by comparing the path difference this can be converted into phase difference
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51
Q

How do you calculate path difference?

A
  • points where the path difference is equal to nλ exactly, will have a phase difference of 2nπ exactly and will be in phase, producing constructive interference
  • points where the path difference is equal to ((2n + 1)λ)/2 exactly, will have a phase difference of (2n + 1)π exactly and will be in antiphase, producing deconstructive interference
52
Q

How is refraction defined?

A
  • is a change in wave speed when the wave moves from one medium to another, there is a corresponding change in wave direction. governed by Snell’s law
  • while the speed changed the frequency remains the same, so the change in speed causes a change in wavelength
  • any rays crossing an interface along the normal line does not change direction at all, as the wave fronts are parallel to the edge so their wavelength is equally changed along the length of the wave front
53
Q

How is refractive index defined?

A

n, can be defined in several ways, but it is fundamentally a result of the change in wave speed:

refractive index = speed of light in a vacuum/ speed of light in the medium

n=c/v

54
Q

What is Snell’s law?

A

-whilst it is difficult to measure the underlying change in the speed at least for light waves, the effect on direction can be measured easily. the relationship between direction and refractive index is given by Snell’s law:

n(1)sinθ(1)=n(2)sinθ(2)
-the values of n(1) and n(2) are the refractive indices for each medium and the values of θ(1) and θ(2) are the angles that the ray makes to the normal to the interference between the two media, at the the point the ray meets that interface

55
Q

How does the speed and angle of light waves change with material?

A

when light moves from a less dense material to a more dense it will slow down and move towards the normal
-when light moves from a more dense material to a less dense it will speed up and move away from the normal

56
Q

How can you investigate refractive index?

A

-using a semi circle perspex/acrylic block, a laser and a protractor
-usually we use air and another material as the speed of light in air and in a vacuum is the virtually unchanged therefore n(air) = 1
-place the semi circle block on a piece of paper and draw the normal on the line
-aim the ray to meet the glass at exactly the midpoint of the flat side
-take several different measurement of the angle of incidence θ(1) and the corresponding angle of refraction θ(2)
- then compare the equation we have for refractive index with the equation for a straight line -n(1)sinθ(1)=n(2)sinθ(2)
-n(1) = 1
-sinθ(1)= n(2) sinθ(2)
-sinθ(2) = (n(2))/n(2)
-y=mx +c
a plot of sinθ(2) on the y-axis and sinθ(1) on the x-axis should produce a straight line of best-fit that passes through the origin
-the gradient will be equal to the reciprocal of the refractive index of glass

57
Q

What is dispersion?

A

-one of the most well known phenomena in physics is the splitting of white light into a rainbow colours by a prism
-the ray of white light hitting a prism is shown by:
n(1)sinθ(1)=n(2)sinθ(2)
n=c/v = c/fλ
air to prism therefore n(1) =1 so:
sinθ(1)=csinθ(2)/fλ
OR
sinθ(2)=fλsinθ(1)/c

  • as the frequency stays constant throughout refraction, and the speed of light in a vacuum must be constant, if we keep the same angle of incidence then the sine of the angle of refraction will be proportional to the wavelength
  • so in the glass smaller wavelengths of light will be closer to the normal, red being the furthest
  • the sine of the angle of refraction ( θ(1)on emergence) will now be inversely proportional to wavelength, thus smaller wavelengths of light are now further away from the normal
  • as the angle of incidence on emergence are not all the same, due to dispersion when they first entered the glass, the colour spreading effect is amplified, creating the spectrum or rainbow of colours
58
Q

How is the critical angle defined?

A

the critical angle is the largest angle of incidence that a ray in a more optically dense medium can have and still emerge into less dense medium, Beyond this angle, the ray will be totally internally reflected

  • when the angle in the more dense material (incidence) is less than the critical angle refraction occurs
  • when the angle in the more dense material (incidence) is equal to the critical angle then the ray would emerge at 90° along the edge
  • if the angle in the more dense material (incidence) is greater than the critical ray the ray will emerge inside the dense material (this is not refraction as that involves a change in medium) therefore as the wave energy is reflected inside the more dense medium this is called total internal reflection
59
Q

What is total internal reflection?

A

when wave energy is reflected inside the more dense material

  • requires two conditions:
  • the ray is attempting to emerge from the more dense medium
  • the angle between the ray and the normal to the interface is greater than the critical angle
60
Q

How can we calculate the critical angle?

A 
Snell's law = n(1)sinθ(1)=n(2)sinθ(2)
- if we take medium 1 to be optically more dense material, then θ(2) must be 90° when the light is at the critical angle θ(c) in medium 1
-n(1)sinθ(1)=n(2)sinθ(2)
-n(1)sinθ(c)=n(2)sin90°
sin90°=1
n(1)sinθ(c)=n(2)
n(1)sinθ(c)=n(2)/n(1)
-if the situation involves a light ray emerging into air then the equation becomes:
-sinθ(c)=1/n(1)
-n(1)=1/sinθ(c)
61
Q

How can you investigate total internal reflection?

A

-using a laser, perspex/acrylic block and a ruler
-we can shine the ray through the semi-circle at the midpoint of the flat size
- by increasing the angle of incidence within the glass by moving the laser around the circular edge until the critical angle is reached
-record this angle and we can calculate the refractive index of glass:
n(glass)=1/sinθ(c)

62
Q

What are some applications of total internal reflection?

A
  • periscopes
  • reflective signs
  • fibre optic cables –> uses repeated TIR at the internal edges
  • on a larger scale can be used to guide sunlight to the interior of large buildings
  • Alternatively optical fibres can be used to carry information as light pulses (as in fibre broadband) or as actual images e.g. medical endoscope
63
Q

What is a medical endoscope?

A

a medical endoscope is used to view the body’s internal organs without cutting the patient open, Light is sent in along one optic fibre, and the reflection is carried away along the other for viewing by medical staff

64
Q

How is convex lenses defined?

A

converge parallel rays to a focus, at the focal length from the lens

65
Q

How is concave lenses defined?

A

diverge parallel rays to appear to have come from a virtual focus, at the focal length back from the lens

66
Q

How is a converging lens defined?

A

will bring light rays closer together

67
Q

How is the focus or focal point defined?

A

the focus, or focal point of a lens is the point where rays incident on the lens and parallel to the principal axis will be made to meet by the refraction on the lens

68
Q

How is a diverging lens defined?

A

will spread light rays further apart

69
Q

How is virtual focus defined?

A

a virtual focus of a diverging lens is the point where rays incident on the lens and parallel to the principal axis will appear to have come from on emergence from the lens
- this virtual focus point has a negative focal length

70
Q

How is the focal length defined?

A

the focal length is the distance from the centre of a lens to its focal point

71
Q

What is optical power?

A

the distance from a lens to its focus is a measure of the strength of the lens

  • more powerful lenses bring the light rays together in a short distance - they have a short focal length
  • the power can be calculated if we know the focal length

-Power (dioptres, D) = 1/focal length(m)

as diverging lens has a negative length its power will be recorded as a negative value

72
Q

What determines the power of a converging lens?

A

the thicker the lens is at the midpoint the more bending occurs

73
Q

What determines the power of a diverging lens?

A

the thinner the lens is at the midpoint the more bending occurs

74
Q

How do you calculate the optical power of lenses in series?

A

if twin lenses are placed one after the other in combination, the overall power of the combination is equal to the sum of the individual powers of the lenses:
P = P(1) + P(2) + P(3)

75
Q

How do you investigate the power of lenses?

A
  • a distant object outside a window will provide parallel rays of light, if we focus an image of this object on a screen, we can easily measure the distance between lens and screen, the focal length
  • by carefully recording the focal length f, of the lens, we can calculate its power;
  • P = 1/f
76
Q

How is a real image defined?

A
  • can be projected onto a screen

- is on the other side of a lens from the object

77
Q

How is a virtual image defined?

A
  • cannot be projected onto a screen

- is on the same side of the lens as the object

78
Q

How is the principle axis defined?

A

a line passing through the center of the surface of a lens or spherical mirror and through the centers of curvature of all segments of the lens or mirror.

79
Q

How can you construct a image through a convex lens?

A
  • ray 1: - move from the top of the image parallel to the lens axis, after it reaches the middle of the lens draw a line straight through the far focal point
  • ray 2:- draw a straight line through the near focal point to the middle of the lens then parallel to the axis crossing with the first ray
  • ray 3:- draw a ray from the top of the object straight through the cross created by the pass two rays, then draw the object on stating its properties
80
Q

How can you construct a image through a concave lens?

A
  • ray 1:- draw a ray parallel to the lens from the top of the object to the lens then once you get to the center of the lens draw a line diagonal in line with the near focal point
  • ray 2:- from the far focal point draw a line in the direction of the top of the object, when you hit the center of the line draw a dotted line parallel to the axis backwards and a arrow parallel to the axis forward
  • ray 3 :-draw a line from the top of the object through the dotted cross created by the dotted lines previously, then draw on the object and state it properties (most images from diverging lenses are upright, virtual and diminished)
81
Q

What are the three different properties of images?

A
  • real or virtual
  • magnified or diminished (or the same size)
  • upright or inverted
82
Q

What is the image calculation?

A

the equation that links the positions of image and object with focal length of a thin lengths
-1/object distance(m) + 1/image distance (m) = 1/focal length (m)
1/u + 1/v = 1/f

-this equation uses a convention known as ‘real is positive’, therefore if a diverging lens is uses it would have a negative focal point and if the virtual image forms on the same side as the real one then the value for image distance would be negative

83
Q

How can you investigate the lens formula?

A

-using a light, an object such as a piece of paper with a black dot on it, a convex lens and a screen
-we can alter the position of the object and measure u
- for each object distance we move the screen back and forth until the clearest possible image is formed on the screen, we then record v
-we plot the reciprocal on a graph: 1/v on the y-axis and 1/u on the x-axis
-comparing the lens formula to y=mx + c:
-1/u + 1/v =1/f
-1/v = -1/u + 1/f
therefore the y-intercept is the reciprocal of focal length

84
Q

How is magnification defined?

A

-is a numerical value given to measure the size comparison between image and original object:
-magnification = image size/object size
m=h(i)/h(o)
- doesnt have any units as it is a ratio of the two heights
-magnification can also be calculated by:
m= image distance/object distance
m=v/u

85
Q

How is polarisation defined?

A

Polarisation refers to the orientation of the plane oscillation of a transverse wave. if the wave (plane) polarised, all its oscillations occur in one single plane

86
Q

What does an electromagnetic wave look like?

A

transverse waves have oscillations at right angles to the direction of motion

  • electric field in the y, magnetic fields in the x, when x is the direction of movement (in this case the electric field is vertically plane polarised)
  • however often many waves travel together, with oscillations in a variety of planes (unpolarised)
87
Q

What is a Polarising filter?

A
  • for waves on a string is it a simple as a card with a slit in it to only allows waves to go in one direction
  • for light waves, the polariser is a piece of plastic impregnated with chemicals with long chain molecules, called a Polaroid sheet
88
Q

How do Polaroid sheets work?

A
  • the polaroid filter will only allow light waves to pass if their electric field oscillations are orientated in one direction
  • e.g. if the filter is of vertical orientation only vertical oscillations of electric field will pass through, making them vertically plane polarised
  • to check the light is polarised you can use another filter after it in the same orientation –> this is called an analyser
  • a filter after this at 90° will block all light out
  • when two filter at 90° to each other they are called crossed Polaroids
89
Q

How can you investigate structural stresses?

A
  • we can use crossed Polaroids to observe stress concentrations in clear plastic samples
  • the first Polaroid produces polarised light, which passes into the plastic sample, Stressed areas have their molecules in slightly different orientations, and this will affect the passage of the light through the plastic
  • this effect varies with the colour of the light
  • When the second Polaroid acts on the emerging light some of the light with have travelled slightly more slowly through the plastic and will destructively interfere with other light waves of the same colour
  • Thus, depending on the degree of stressed areas appear as different colour through the second Polaroid
  • changing the stresses on the plastic will alter the internal stresses, and the interference pattern will change
  • engineers use this to see stress concentrations in models of structure, and to observe how the stress concentration change when the amount of stress changes, This allows them to alter the design to strengthen a structure in regions of highest stress
90
Q

How can polarisation occur from reflection and refraction?

A
  • when unpolarised light reflects from a surface, such as a road, the waves will become polarised, the degree of polarisation depends on the angle of incidence but it is always tending towards horizontal plane polarisation
  • light waves incident on a surface into which they can refract such as a pond, will reflect partially horizontally polaised light, but will also transmit partially vertically polarised light into the new medium
91
Q

What is Brewster’s angle?

A

-at a certain angle of incidence no light passes through the analyser showing that reflected light is plane polarised
-this angle is called the polarizing angle , ip, or Brewster’s angle
-later Brewster discovered that the polarising angle that the reflected and refracted rays an separated by is 90°
-n=sin(p)/sin(r) but r=90-ip
n= sin(ip)/sin(90-ip)
n=sin(ip)/cos(ip)=tan(ip)

92
Q

How can polarization occur by chemical solution?

A
  • the analysis of stress concentrations investigated above works because different parts of the plastic model have different effects on polarised light
  • this is also the case with some chemicals,such as sugar solution
  • the amount of the concentration of the sugar solution varies the angle to which it rotates the polarisation of the light
  • we can use Polaroid filters to analyse the strength of the sugar solution, by measuring the angle at which the light polarization emerges after passes through the chemical solution
93
Q

How is a photon defined?

A

photons are ‘packets’ of electromagnetic radiation energy where the amount of energy E=hf, which is Planck’s constant multiplied by the frequency of the radiation: the quantum unit that is being considered when electromagnetic radiation is understood using a particle model

94
Q

How is quantisation defined?

A

is the concept that there is a minimum smallest amount by which a quantity can change: infinitesimal changes are not permitted in a quantum universe, The quantisation of a quantity is analogous to the idea of the precision of a an instrument measuring it

95
Q

How is wave-particle duality defined?

A

is the principle that the behaviour of electromagnetic radiation can be described in both waves and photonss

96
Q

Who was Christiaan Huygens?

A
  • A dutch scientist who can up with the principle of predicting the future movement of waves if we know the current position of the wavefront -Huygens’ principle
97
Q

What is Huygens principle?

A

the basic idea to consider that any and every point on a wavefront is a new source of circular waves (also called secondary wavelets) travelling forward from that point.

  • when the movement of these myriad circular waves is plotted, and then their superposition considered, the resultant wave will be the new position of the original wavefront
  • so after time ‘t’ the new position of a wave front is the surface tangent to these secondary wavelets therefore distance is c x Δt
  • also according to huygens’ principle the angle of the incoming rays during reflection, is the same angle that the out going rays go out at
98
Q

what is the evidence that light is a wave?

A
  • the interference pattern produced by diffraction and Young’s two-slit experiment both requires the superposition of wave displacement to generate the standing wave pattern seen.
  • this is only possible if light is behaving as a wave and has the appropriate repeating cycles of displacement that cause this ongoing superposition to maintain constructive and destructive interference that produces nodes and anti-nodes
  • particles cannot superpose in this was
  • Polarisation is another phenomenon exhibited by electromagnetic waves, including light, that can only be explained in classical physics by using the ideas of waves
99
Q

What is the evidence that light is a particle?

A

-photoelectric elect –> first observed by heinrich hertz
-max planck–> suggested that light could exist as quantised packets of energy called photons
einstein –> wrote a paper explaining the photoelectric effect –> he explained that photoelectric effect cannot be explained using a wave theory for light however, the idea that light travels as particles, or photons whos energy is proportional to the frequency it would have when considered as a waves fits all observations

100
Q

How can you calculate the energy for electromagnetic radiation?

A

-the energy of the photon can be calculated by multiplying frequency by planck’s constant
-photon energy (Js) = Planck’s constant (h) x frequency (hz)
E=hf

101
Q

What is Planck’s constant?

A
  1. 626 x 10^-34 Js
    - this constant is so small because it represents the fundamental minimum possible step in energy
    - photons cannot have an energy value that differ by less than the Planck constant
    - this means that there are some energy values that are impossible in our universe, such a system of minimum sized steps is called quantisation
102
Q

What evidence is there to show electrons are particles?

A
  • experiments that produce ions can demonstrate electrons behaving as particles because a fixed lump of mass and charge is removed from the atom in order to change the atom into an ion
  • the charge mass ratio is a uniquely identified property of particles, and was first demonstrated for the electron by J.J. Thomson in 1970
  • Robert, Milikan in an experiment published in 1913 took this one stop further to find the electron charge itself, the fact that electrons hold a fixed amount of charge and a fixed mass indicated they are localised particles
103
Q

What was wrong with Robert Milikan’s value for the charge of an electron?

A
  • Robert Milikan’s oil drop apparatus showed that electrons have a fixed charge of 1.5924 x 10^-19 coulombs
  • the difference with the current accept value is caused by a mistake in MIlikan’s calculations, because he used a slightly incorrect value for the viscosity of air
104
Q

What evidence is there to show that electrons are waves?

A
  • if electrons are made to travel at very high speeds,they will pass through gaps and produce a diffraction pattern, they will similarly interact with a double slit-apparatus to produce the interference pattern seen when waves pass through two slits
  • diffraction and interference are not expected by classical particles as they should simply travel straight through the observation of these experimental result proves electrons can behave as waves
105
Q

How is a photoelectron defined?

A

photoelectrons are electron released from a metal surface as a result of its exposure to electromagnetic radiation
-e.g. if ultraviolet light is shone onto a negatively charged zinc plate, the plate loses its charge, the explanation for this is that the light causes electrons to leave the metal removing the negative charge, the electrons released as called photoelectrons

106
Q

How is work function defined?

A

work function is the minimum energy needed by an electron at the surface of a metal to escape from the metal

107
Q

how is the threshold frequency defined?

A

-the threshold frequency for a given metal is the minimum frequency of electromagnetic radiation that can cause the emission of photoelectrons from the metal

108
Q

How is the stopping voltage defined?

A

the stopping voltage in an appropriately illuminated photoelectric cell is the minimum voltage needed to reduce the photoelectric current to zero

109
Q

How does the wave theory of light link to photoelectrons?

A
  • the wave theory of light would allow some of the wave energy to be passed to the electron to enable them to gain the work function and escape
  • in the wave theory, the energy carried by a wave depends on its amplitude –> the brightness of the light
  • this leads us to believe that any colour of light, if made sufficiently bright should enable that release of photoelectrons, alternatively if it was shone for long enough it could also give the electrons enough energy to gain the work function
  • however this isnt the case as the zinc plate does not release electrons when red light is shone on it
  • this shows there is a maximum ave length for the light, above which no photo electron are ever emitted
  • this minimum frequency for the light that is needed is called the threshold frequency
110
Q

How can you investigate photoelectrons?

A
  • if you charge a gold lead electroscope then it will show a deflection on the gold leaf
  • if you place a zinc plate on top of the electroscope the photoelectric effect will allow the electroscope to be discharge if it held a negative charge
  • if you shine UV light onto the zinc plate the gold leaf will fall immediately
  • this observation shows that electrons on the zinc plate have escaped
  • those electron remaining on the gold leaf and electroscope stalk spread out more so tat there is no long enough mutual repulsion to hold up the gold lead
  • you may need to clean the surface of the zinc, as it oxidizes quite easily in air, o there may be a layer of oxide on top of the pure metal stopping light absorption
111
Q

What explanations can be drawn for investigating photoelectrons?

A
  • light travels as photons, with a photons energy proportional to the frequency
  • when a photo encounters an electron, it transfers all its energy to the electron (the photon ceases to exist)
  • if an electron gain sufficient energy - more than the work function - it can escape the surface of the metal as a photoelectron
  • Brighter illumination means more photons per second, which will mean a greater number of photoelectrons emitted per second
  • if an electron does not gain sufficient energy from an encounter with a photon to escape the metal surface, it will transfer the energy gained from the photon to the metal as whole before it can interact with another photon, thus, if the photons energy is too low, no photoelectrons are observed
112
Q

What is the photoelectric equation?

A
  • an electron gaining energy from a photon will have to use up the amount of energy equal to the work function in order to escape the metal, to get from inside the metal additional energy along the way must be used
    -only the remaining energy is available as kinetic energy, to fly away, thus kinetic energy that the electron can have on departure from the metal surface is less than or equal to the difference between the photon energy and the work function
    -the maximum possible kinetic energy 1/2mv^2(max) determines the maximum velocity v(max) of the photon electron
    1/2mv^2(max)=hf - Φ
  • or in direct conservation of energy terms, the photo energy is used by the electron partly to escape the metal surface and partly as it kinetic energy therefore:
    -hf =Φ + 1/2 mv^2(max)
    -SI unit of the photoelectric equation are all in Joules, but is often used in units of electronvolts (eV)
113
Q

What is the photoelectric cell experiment?

A

we could use the photoelectric effect equation to measure Plank’s constant and the work function for a metal

  • in a vacuum, we place the metal as the anode in the that has a gap to the cathode
  • when we shine light of a know frequency onto the anode photo electrons will be emitted and the current registered on the ammeter
  • if we slowly increase the pd across the photoelectric cell eventually the anode will become sufficiently positive that all photoelectric will be stopped and attracted back to it, so the photoelectric current will be zero
  • this stopping voltage V(s), will give us the maximum kinetic energy of the photo electrons from the definition of voltage
  • 1/2mv^2(max) = e x Vs
  • if we use a range of frequencies and find the stopping voltages, we can photo a graph of maximum kinetic energy against frequency
  • 1/2mv^2(max) = hf - Φ
  • where the y -intercept represents the value of the work function and the x intercept is the threshold voltage
114
Q

What experiment did Davisson and Germer in 1927?

A
  • tried to detect diffraction of electron ‘waves’ when they reflected from a crystal of nickel
  • they measured the intensity of the beam at different angle for various accelerating voltages, and plotted a graph of their results
  • not only did they prove electrons can behave as waves but their results also allow calculation of the distance between atoms in the nickel crystal
  • this has given rise to advances in the study of atomic structures using electron beam crystallography
115
Q

What is de Broglie equation?

A
  • in 1924, a french prince called Louis de Broglie suggest electrons could behave as waves and proposed an equation to calculate their wave length
  • their wavelength is inversely proportional to the momentum they have when considered as particles
  • electrom wavelength (m) = Planck’s constant (Js)/ momentum (kgms^-1)
  • λ = h/p
116
Q

how can you investigate electron diffraction?

A
  • using electron beam diffraction tubes
  • this accelerates a beam of electrons through a high voltage, and then passes the beam through a sliver of graphite
  • this array of carbon atoms in the graphite acts, as a diffraction grating in two dimensions, which produces a circular diffraction pattern
  • the front end of the tube has a phosphorescent screen that will show up the diffraction pattern
  • if we make careful measurements of the dimensions of the tube and the diffraction pattern produced with different accelerating voltages,we can carry out an approximate calculation of the atom spacing in graphtie
117
Q

What is two-slit electron interference?

A
  • in 1965, Richard Feynman suggested the electron that electrons should also be able to produce the two-slit interference pattern seen with light, as they can behave as waves, Recently, this has been shown to be the case, giving further evidence for the wave nature of electrons
  • however the latest research has allowed scientist to observe that the interference pattern is built up by the movement through the apparatus of the individual electrons
  • they behaving as both individual particles and waves at the same time
  • they are showing wave-particle duality
118
Q

What is electron microscopy?

A
  • using the wave nature of electrons to study objects at very small scales
  • an electron beam can work like a beam of light but with some different properties that can make the electron beam, much more useful for microscopy
  • the main advantage of an electron beam can be controlled by altering the voltage applied to accelerate the electron
  • as they are the same size as an atom they can produce images of object 1000 times smaller that visible light
119
Q

How is ground state defined?

A

is the lowest energy level for a system, for example when all the electrons in an atom are in the lowest energy levels they can occupy, the atom is said to be in its ground state

120
Q

What is excitation and de-excitation?

A

is an energy state for a system that is higher energy that the ground state. for example in an atom if an electron is in a higher energy level than the ground state, the atom is said to be excited

  • this can occur if the atom collides with another particle, alternatively if the electrons absorbs a photon that has the correct amount of energy, the electron can jump to a higher energy level
  • an incident photon that does not have the energy exactly equivalent to a jump between the current position of the electron and the one of the higher levels will not be absorbed
  • if the gas atoms are illuminated by ranges of frequencies (colours), those with the correct frequency values will be absorbed, so there will be some colours missing from the light after it passes through the gas
  • after a random amount of time the electron will deexcite, this may involve dropping to ground level or to the level below –> conservation of energy, when they drop down the they have less energy therefore a photon is released with the same energy they lost
121
Q

How is ionization energy defined?

A

is the minimum energy required by an electron in an atom’s ground state in order to remove the electron completely from the atom

122
Q

How is line spectrum defined?

A

is a series of individual lines of colour showing the frequencies present in a light source

123
Q

What is a line spectra?

A
  • using a diffraction grating we can split up light dependent on it wavelength, so the various colours will spread different amounts
  • the resulting spectrum will often be a series of individual lines, if the original light contained only a select few wavelength
  • this is done by passing electricity through a gas, which excites the atoms, each coloured line is a wavelength of light given off as a result of an electron dropping between levels
  • depending on the energy lost depends on the wavelength of colour let off
124
Q

How do we investigate gas discharge spectra?

A
  • a high voltage will cause an electric current to pass through a gas in a discharge tube
  • the electrical energy excites the electron in each atom of the gas, and they then drop energy levels at random times, giving off a photon for each energy level transition
  • as there are so many atoms it appears as if the gas is continuously emitting light and of all the possible colours - all the possible transitions within its energy level ladder
  • using a diffraction grating we can analyse the light emitted from the tube to detect the separate colours , or wavelengths being emitted, we observe a line spectrum
125
Q

How can we calculate the intensity of radiation?

A

-it is the amount of energy it carries per, unit area, per unit time, if power is the rate of transfer of energy the equations is:
intensity (Wm^-2) = power (W)/area(m^2)
I=P/A

A-Level Physics (5 decks)

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