As Physics Notes

7/30/2019 As Physics Notes

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AS Physics Notes


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Chapter 1 - Imaging


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1.1 Seeing Invisible Things

Although as humans we can only see the visible spectrum of electromagneticradiation we can use machines to see UV and infrared radiation, they can also

make an image from sound.

Ultrasound used for seeing inside the body uses high frequency sound waves

to make an image, a much higher frequency than human ears can detect.

Resolution is the smallest size object a sensor can detect. For pictures this thesize of the pixels, if you zoom in to far the image becomes pixelated.

In order for a sensor to show a decent image the wavelength has to be much

smaller than the object being detected, as this affects the resolution.

Formulae for waves used in imaging:

T = 1 = vT = vf f T = time of oscillation

v = velocity

f = frequency

= wavelength


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To see very small things, suchas atoms, we would need touse a wave with an extremelyshort wavelength. Muchshorter than any of theelectromagnetic spectrum, so

instead we use electrons. Anscanning tunnelling microscope is a ultra sharp needlepoint held just above a surfaceso atoms, so close theelectrons can tunnel across

the gap, this creates a currentand the smaller the gap thelarger the current, and thisdata can be used to create animage of electrons.

1.1 Seeing Invisible Things


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1.2 Information in images

Bits and Bytes

Information is stored digitally in binary form, this is a series of 0s

and 1s, one digit is called a bit. But in images we use 256 shades

of colour so we need 8 bits to store each pixel, 8 bits is 1 byte.

N = 2I

and log2(N)=I

So N = 28 = 256

This is normally shown on a logarithmic scale, one which equal

distances correspond to equal multiples

Each shade of a colour is given a number given to each shade a

colour of either grey (for black and white) or RGB (for colour

pictures). The higher the number the darker the shade.

This is pictures are stored and sent to people as the each pixel uses

3 bytes of storage

N = Number of alternativesI = Amount of bit


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Image Processing

Most images contain noise which distorts the image, so changes the

data you can collect form it.

To solve these problems we use of image processing

Smoothing sharp edges: - replace each pixel by the mean of thosearound it, (mean method).



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Image Processing

Removing noise: - Replace each pixel with the median of those of its

neighbours

Finding edges: Subtract the N,S,E and W from 4 times the value of

each the pixel



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1.3 Lenses

Introduction

Lenses bend light to either focus it on a point, concave, or spread it

out, convex. We only need to learn about concave lenses. Lenses

bend light using refraction, as the light enter the glass it changes

median so it slows down, so it refracts toward the median and as itleaves it bends away from the median.

As you can see the shape of the lens causes the light to bend.


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The Eye

In the eye there are two main lenses the cornea and the lens.Although the lens is much more curved than the cornea, it bends thelight less. This is because in order for the light to bend it needs topass through a change in median to refract. As the light passes fromthe air into the cornea, there is a large change in refractive index,similar to that of a glass lens, this causes the light to bend on thesteep angle. But the before the light enters the second lens, it is inthe aqueous humour, and this has a similar refractive index the lensmeans the light doesnt bend very much.

1.3 Lenses


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The Focal Length

When the light is from a very distant source the waves have no

curvature, they are parallel. When this is the case it will cause an

image at the focal length (f). 1/f is the power of the lens in dioptres

(D) when the focal length is meters.

1.3 Lenses


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The Formula

1.3 Lenses


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The Formula

1/u is the curvature of the waves before(negative), and 1/v is the curvature of the wavesafter the lens.

1/v = 1/u + 1/f So the curvature of the waves after the lens

equal the curvature before the lens plus thecurvature added by the lens.

This works with parallel waves from far away,because 1/infinaty = 0, and so 1/v = 1/f, so v = fand the image is at the focal point.

1.3 Lenses


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Image

The further the source is away from the lens the closer the image will be, so to createan image that is in focus you have either move the lense or the image, but in themuscles contract and relax, to strengthen or weak the power of the lens so the imageis always in focus on the retina.

Example

If source 1 is 2m away from the lens the waves have a curvature of -0.5D and say thelens has a power of 2D the curvature afterwards is 1.5D so the image is 0.66m awayfrom the lens.

But say source 2 is 4m away from the lens the waves have a curvature of -0.25D,

and with the same power lens the afterwards is 1.75D so the image is only 0.57maway from the lens.

1.3 Lenses


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Magnification and Inversion Lenses can be used to magnify stuff, for example in magnifying glass, this is

when the image is in focus after the waves have spread out causing the

image to appear larger than the initial source. But they also turn the image

upside-down, as you can see in the diagram the waves from the top of the

source are projected to the bottom of the image, and the bottom to the top.

1.3 Lenses


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Chapter 2 - Sensing


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2.1 Making very small things

Small things

Very tiny things have to be produced in order to make sensors, forexample circuit boards in mircosensors, which are then used in veryday items, a car for example has hundreds of mircosensors to keepit running smoothly.

These small things have to be made by very small tools, such asions.

If you ionise an atom for example, argon it will have a charge andcan be fired at a surface, these ions now have the energy to knockother atoms out of the surface and so can shape something. This ishow diamond styluses are sharpened and more importantly howRichard Hammond wrote his name into his own hair, on that

engineering programme.


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Electricity

But in order to fire ions at a surface you need to have a force moving

them, this force is potential difference, or voltage. It can be created

in a battery, by a chemical reaction that causes the electrons to one

end leaving a positive charge at the other end, this then attracts the

electrons in the circuit including those at the other end of the battery,

causing a current.


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Electrical Formulae

Q= Charge (coulombs) (C)

I = Current (amperes) (A) (C/s)

V = Potential Difference (volts) (V) (J/C)

E = Energy (joules) (J)

P = Power (watts) (W) (J/s)

t = Time (Seconds) (s)

The energy (E) given to a charge (Q) going through a potential difference

(V) = E=QV

If N ions arrive per second then the power : P=NE=NQV so P=IV



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2.2 Miniature Circuits

Transistors are uses as switches to store data in binary data, they

can now be produced incredibly cheaply, cheaper than it costs to

print one letter.

Conductance (G) is the current for a given potential difference

G = I conductance = 1 . Conductance is measured in

V resistance Siemens

Resistance is the potential difference needed for a given current

R = V resistance = 1 . Resistance is measured in

I conductance Ohms

The power equation:

P = IV = V2 = I2R

R


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Resistors (Potential Dividers)

When resistors are added in series the total resistance is the sum of

the value of all the resistors: Rtotal = R1 + R2 Or 1 = 1 + 1

Gtotal

G1

G2

When the resistors are in parallel the total conductance is the sum of

all the value of resistors : Gtotal = G1 + G2

Or 1 = 1 + 1

Rtotal R1 R2

2.2 Miniature Circuits


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2.3 Controlling and Measuring

potential differences Potential dividers are used to control potential difference.

A potential divider tap off a fraction of its input to provide a controlled

output, equal movements of the sliding contact give equal changes

in output.

So as the moving contact moves along the resistor the resistanceincreases, this can be used as a sensor, its called a potentiometer.

There is a linear relationship between sliding displacement out in

p.d.

This is how a fuel gauge measures the amount of in the tank, with a

float on the moving contact. But results can fluctuate so a controlsystem is needed to smooth out errors


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2.4 Sensors and our senses

Types of sensors

Sound sensors Microphones are electronic ears, they produce a

varying electric signal from sound waves.

Temperature sensors Thermocouples and thermistor create

change in p.d. Light Sensors Charge-coupled device (CCD), is a silicon n-p

junction and can detect radiation over varied wavelengths, UV to

infrared.

Strain gauges As a metal gets stretched it gets longer and the

cross-sectional area get smaller, so the resistance increases. Smell SensorsThey cant really smell but smoke detectors can

quantities of certain substances in the air


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Internal Resistance

The electromotive force (e.m.f. or E) is the potential energydifference from a source on the open circuit.

The total internal resistance is the total resistance inside a device(sensor or power source etc.)

If the Rinternal of a sensor is very high then the current will be almost0, so any other device will only show a significant change if thedevice has a very high internal resistance.

I = E .

Rinternal + Rexternal E = Vinternal + Vexternal Vexternal = IRexternal = E IRinternal

2.4 Sensors and our senses


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2.5 Measuring Well

Definitions

Resolution The smallest change a sensor can detect (theresolution can show the uncertainty in the measurement)

Sensitivity Is the ratio of change of output to change of input

Response time The amount of time a sensors takes to reaches itsfinal reading after a sharp change in input

UncertaintyThe extent to which you cant be sure of ameasurement, due to small unsystematic and random variations

Systematic Error An error where something is wrong a needs tobe put right, often human error of zero error (an error when thesensor should be reading zero)


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Summary

Electric current = charge transferred I =Qtime taken t

Potential Difference = potential energy difference V =Echarge transferred Q

Conductance G = I Resistance R = V

V I A conductor obeys Ohms law so has a constant conductance andresistance, so current is directly proportional to potential difference.

Resistors in parallel: 1 = 1 + 1

Rtotal R1 R2 Resistors in series: Rtotal = R1 + R2 The potential difference from a source (E) and internal resistance is

V = E - IR and V = IRload

Power in a circuit: P = IV = V2 = I2R

R


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Chapter 3 - Signalling


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3.1 Digital RevolutionDigital Vs Analogue

Digital signalling has caused a death of distance as a message can be

sent from one side of the world to the other in seconds.

Analogue signals are a series of continuous data that can be at any value,

like a wave.

Digital signals are either 1 or 0 (binary), they are discrete data.

As signals are sent they pick up noise from other signals that interfere with

them, this can cause inaccuracies in analogue signals

But digital signals are unaffected by noise as it is always easy to see

whether it was a 0 or 1

Also because digital signals work in binary it is easy to send data stored as

binary

Because analogue signals are affected by noise it means they cant be

transmitted very long distances, as they become unreadable, whereas digitalsignals can.


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Digitising Analogue

In order to convert a analogue to digital to things need to be done:

sampling, binary coding and further encoding

Sampling: - To digitalise you need to break up the continuous data

tiny discrete figure, to avoid losing accuracy this needs to be done

more than twice the highest frequency. So if the highest frequency is

20kHz then is must be sampled 40,000 times a second. If this is not

done than the original signal is not recovered correctly or aliases

form where low frequency waves appear to form in the places of

higher frequency.

Binary coding The numbers from the sampling have to be converted

into binary, so they can be sent by digital signal. This size of

bandwidth needed to transmit the digital sampled signal depends on:

- The resolution of each sample (number of bits specifying the value)

- The rate of sampling

Further encoding This is used to ensure your picture or email arrives

error free.

3.1 Digital Revolution


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3.2 Signalling with E.M. Waves

E.M. Waves and Polarisation

There are many different types of the E.M waves, each with differentproperties, such as range and bandwidths.

E.M waves are formed by flowing charges flow back and forth in anaerial causing the electric field to form a wave. The magnetic plane

is then formed from this. Polarisation is when the waves all oscillate on the same plane, most

e.m wave generated for signalling are polarised, this why the aerialrod are always parallel to waves so they can receive the greatestsignal.

The light from the sky is polarised, because the electrons on atomsin the atmosphere absorb the energy and the emit it on a certainplanes, this is also why the sky is blue, as the wavelength theelectrons emit is that of blue light.


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Multiplexing Multiplexing means sending more than signal at once. There is two types, time-

division and frequency-division.

Frequency-division means sending each signal at a different frequency so theydont interfere. This means they can be sent at exactly the same time, but it uses alot of bandwidth so not very many can be sent at once.

Time-division means sending the signals on the same frequency but one after the

other, for example in a telephone line it sends 8 bits every 100 microseconds, thisis undetectable to the receive but it means many signals can be sent on the samefrequency. There is still a limit depending on how fast it can send the 8 bits but thisis a lot higher than of frequency-division.

Bandwidth

The bandwidth needed to send a signal is: B = b bits per second

2

This is because a pair of bits is like one cycle of a wave. So the larger thebandwidth the faster the signal can be sent.

To make a analogue signal digital you need to sample it:

Rate of sampling per second = 2W (W is the width of the spectrum)

Rate of transmission (bits per second) = 2Wb (b is the number of bits persample)

And the bandwidth is half the rate of transmission B=Wb



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Noise

Although noise doesnt affect digital signals as much analogue if the

amplitude isnt high enough it can cause errors in reading.

Ifb is the bits per sample then:

2b total noisy signal variation = Vtotalnoise variation Vnoise

The largest number of bits per sample its worth using is:

b = log2(Vtotal)

Vnoise Communication engineer measure the ratio of signal power S to

noise power N, using these measure the formula can be rewritten:b = log2(1+S )

N



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Chapter 4 Testing Materials


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4.1 Making the best choice

Different materials have different properties, so this means if youneed a material for a job you have to make the right choice.

Ceramic materials are hard and brittle, made up of crystals, whereaspolymers strong and sometimes flexible, made up of long chains.

Compression is when forces squash the material. Compressivestrength is a materials strength to withstand these forces

Tension is when forces stretch a material along its length. Tensilestrength is a materials ability to withstand these forces.

When a material is bent there is compression on the inside of it andtension on the outside.

The toughness of a material is measure by the energy needed tocreate a new fracture. Brittle materials, such as glass have a lowfracture energies, whereas tough materials such as rubber havehigh fracture energies.

Composite materials are materials made up of two or more verydifferent substance to take the best properties from each.


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4.2 Better Buildings

Stress is force per unit area usually measured in Nm-2 commonlycalled Pascal's (Pa).

The elastic limit of a material is point where the stress on thematerial causes it to become permanently deformed. Before theelastic limit the material deforms elastically so it will return to itsoriginal shape, but after the elastic limit it deforms plastically so it

wont return to its original shape. The breaking stress is the stress at which the material breaks.

Strain is a measure of extension in relation to length, it has no unitsas it is a ratio.

Stress = Load Strain = Extension .

Area Original length

Youngs modulus of elasticity is a measure of elasticity, it is higherfor stiffer materials.

Youngs modulus = Stress

Strain


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4.3 Conducting well, conducting

badly

Conductance (G) is the inverse of resistance (R), and

conductivity () is the inverse of resistivity ().

G = 1 G = A

R L

R = 1 R = LG A

= 1 = GL

A

= 1 = RA L


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4.4 Problem of measuring

mechanical and electrical properties. Problems of measuring breaking stress A break will

usually start at a weaker point or a fault, and each pieceof a material will have different amounts and kinds offaults so you get a wide spread of results.

Problems with measuring youngs modulus Most

materials yield only a few percentage under a largestress, so you need to have a large load and a smallcross-sectional area, this can causes errors inmeasuring.

Problems with measuring resistivity Resistivity can

vary over 20 orders of magnitude so measuring valuesaccurately for it can be hard. Also for insulators getting acurrent at all can be hard, for good conductors seeingany resistance at all is also hard.


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Chapter 5 Looking Inside

Materials


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5.1 Materials under the microscope

To see very tiny thing we used two special types of microscopes; ascanning electron microscope (SEM) and an atomic forcemicroscope (AFM).

A SEM works by firing electrons at a tiny spot on the specimen, andcollecting them where they scatter off to. The specimen has to bekept in a vacuum with a metal film coating so it cant be alive, also

you only get a black and white image. But the SEM has a gooddepth of focus.

Magnification = scan line spacing on monitor

scan line spacing on specimen

An AFM works by using a tip on the end of an arm, the forcebetween the tip and specimen is kept the same, so the arm bends to

do this. A laser beam is bounced off the tip on to a detector so it canread when the arm bends, this is then used to create an image. The

AFM specimen does not have to be in a vacuum and doesnt need ametal coating so it can be alive.


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5.2 Stiff stuff, Tough stuff As I said earlier the fracture energy is a measure of how tough something

is. Cracks can propagate through a material and cause it to break, because as

the material is bent there is tension on the area of the crack, this putsextreme stress at the point of the crack, so the bond at the tip of the crackbreaks and then the next bond until the crack has spread throughout thewhole material.

Metals can resist cracks propagating because they are ductile and so thecrack is made wider, so less stress is put on the bond below the crack.

Fracture energy = total energy used to fracture

specimen cross-sectional area

Tensile strength = breaking force .

specimen cross-sectional area

Large fracture energy = tough, large tensile strength = strong.

Composite materials can combine the properties of two materials to make itbetter. Fibre composites are strong because of the fibres and toughbecause the soft matrix spreads the stress over many fibres, so that cracksdont propagate.


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5.3 Making more of materials Many materials are made up of a crystal lattice, but the crystals are not

perfect they have dislocations, where atoms dont fit to together. Thismeans the atoms can move making the metal more ductile and malleable.

Alloys can contain more than one element, these are less ductile than purecrystals, because the smaller atoms can fill the dislocations.

There are three different types of bonding structures:

Covalent structures such as silica, atoms share electrons with neighbouring

atom, there bonds are directional and hold the atoms in place making ahard and brittle structure.

Ionic structures like sodium chloride, give electron to each to form ionswhich attract each making a bond. These bonds are strong and hold theatoms in place.

Metallic structure such has gold, atoms are ionised and the free electronsform a negative glue holding the nuclei in place. But the ions can slip

making it strong but ductile. When stretching metal it is the bond the lengthens but only by 0.1% this is

why metals have a high youngs modulus. In polymers the bonds rotatemaking the chains fold so when stretched can extend up to 1%.

In rubber sulphur cross-links hold the chains together in certain points butthey can fold up in between and when stretched the chains straighten out,allowing for a lot more elastic stretching.


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5.4 Controlling Conductivity

For metals as temperature increase so does resistance, this isbecause the atoms get excited and this blocking the electrons tryingto carry the current.

But for semi-conductors the opposite occurs, this happens becausesemi-conductors are covalently bonded, so have no or very few freeelectrons, but as it is heated these bonds break causing electrons to

be freed so they can conduct electricity. We can also control how well the semi-conductors conduct by

doping, there are two kinds positive and negative doping:

Negative doping (N-type) involves adding phosphorus to the silicon,phosphorus has 5 electrons in its outer shell so can complete the 4bonds with the silicon with an electron free to conduct electricity.

Positive doping (P-type) involves adding boron to the silicon, borononly has 3 electrons in its outer shell so when completing the 4bonds with silicon it leaves a hole which other electrons can moveinto moving the hole in the opposite direction to the electrons, so itacts as a positive particle.


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Chapter 6 Wave Behaviour


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6.1 Beautiful colours, wonderful

sounds Superposition This is when waves interfere with each other, either

constructively or destructively

If two waves are in phase they will interfere constructively, thewaves will added together to produce a larger amplitude.

If the two waves are out of phase they are exact opposites and theywill interfere destructively. If they were perfectively out of phase the

wave will have been destroyed If the two waves are in between these two marks their phasors will

add up to produce a resultant phasor with a amplitude bigger thanone but double and an average of the angles. This can worked outfrom Pythagorass theorem.

This is why you get a light spectrum shining off the oil some of the

light is reflected off the top surface but some goes through and isreflected off the surface of the water, if this difference is x and a halfwavelength of one colour of light (say red) then this colour will be inphase and be amplified more than the others and it will appear red.


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Waves travelling opposite directions can form standing waves(waves that look like they are staying still), these are in phase andso amplify to give a greater colour or sound. They are antinodeswhere the waves add up to from a large oscillation and nodes wherethe waves cancel out so have no oscillation.

Standing make music because waves go back and forth in the

instrument so that the right frequency constructively interfere andamplify to make the note you hear. This is why long distances insidethe instrument (e.g. the organ) form lower notes, a longerwavelength forms the standing wave and so a lower frequency,hence lower note. You hear the note that has a wavelength of twicethe length of the string, pipe etc, this is called the fundamentalfrequency

Only in waves with a stable interference can you see the effects of it,this is called coherent interference.

6.1 Beautiful colours, wonderful

sounds


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6.2 What is Light

Angle of incidence = Angle of reflection

Another theory of light is that it is made up

of tiny wavelets and these wavelets can

interfere with each other.


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6.3 Wave behaviour in detail Youngs double slit interference pattern shows that has light passes

through two slits and diffracts the waves interfere with each other.

Depending on the angle the waves are either in phase or out ofphase because you are at different distances from each slit. Thiscauses a series of maxima and minima to occur on the screen.

This formula is the same when you are using a diffraction grating,though the order of the maximum is relevant to where you aremeasuring it from

The formula for working the angle of

each of the maxima is:

n = dsin

Where n is the order of the maximum


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6.4 Looking Forward

Waves also diffract when they goesthrough a single slit, you can see this inwater waves as they you through a smallgap, and because of this the tiny waveletscan interfere with each other.

This can be seen in the single slit

experiment: At the right angle the wavelets that go

through the bottom of the gap are out ofphase with those in the middle and the verytop. This is repeated as you go up the gap.So the resultant phasor is zero.

To find the angle of this minimum you usethe equation :

= dsin


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Chapter 7 Quantum

Behaviour


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7.1 Quantum Behaviour

Quantum behaviour explains the behaviour of light as photons. Photon can and do explore every possible path of getting from the

source to where it is detected.

Light arrives in is lump or quanta, called photons, if less than theright amount of photons arrives then the image appear grainy.Because the photons arrive in some place but not in others. There is

also light where there shouldnt be because another photon wouldbe out of phase with it and cancel it out.

When it is bright there is a higher probability of all the photonsarriving, but when it is dim the probability is low.

LEDs work using photons because they drop each electron by acertain p.d. when glowing so it releases a photon of that colour of

light.


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The relationship between frequency and energy isconstant for all electromagnetic radiation,

E/f= 6.634x10-34 J s, this is called Planck's constant (h).

So electromagnetic radiation of frequency f is emitted

and absorbed in quanta of energy E where E = hf. If the different photons explore different paths, some

may take longer than others, this means that the phasorwill be out of phase. So in order to get the resultantphasor you need to add the phasor tip to tail and the

distance between the start and finish is the resultantphasor.


A

B

C

A

B

C

Resultant

Phasor


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Photons also produce the same superposition patterns as waves:

Diffraction - In the double slit experiment, the photons explore both

paths through the slits, this causes one to be out of phase with the

other, when detected at a certain angle, hence causing interference

and a minimum.



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7.2 Many paths at work

Reflection - When light reflects off a mirror all of the light reflected inthe same angle, no quantum behaviour there. But there is, thephotons explore all the paths, you only see the light at the angle.The photons that reflect off the mirror in the centre have a muchshorter trip time than those near the edge, this means the ones nearthe middle are in phase and all those at the edge are randomly out

of phase, so cancel each other out. This means that the resultantphasor is made up from the photons following the centre path andthis is what you see.

Refraction The photons that make up the resultant phasor arethose that travel fastest, those that travel close to the shortest butslightly further than in the faster medium than the slow one, thismeans the main photons will bend towards the normal as they entera slower medium.

Propagation The photons which will be in phase are those that dothe journey fastest and so go in the straightest line.


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Lenses -

7.2 Many paths at work


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7.3 Electrons do it too

Quantum mechanics is important because it is commonin all fundamental particles, including electrons. It is notexactly the same because electron have a mass so theycant travel at the speed of light.

This can be seen when Youngs double slit experimentwas repeated for electrons, and they showed diffraction.

For electrons: = h .

mv

Or: = h .

momentum


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Chapter 8 Distance, Speed

and Time


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8.1 Journeys

Time can be used to describe distance, for example a 30 min carjourney or 100 light years.

Speed = Distance

time

Average speed = Total distanceTotal time

Instantaneous speed is the speed at one instant in time and is very

hard to work out, normally we just use a very small period of time.

A journey can represent on two different graphs, distance-time and

speed-time graphs. On a distance-time graph the speed is the gradient of the line.

On a speed-time graph the distance is the area under the line.


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8.2 Maps and vectors

Vectors have a quantity (magnitude) and a direction (for examplevelocity).

Scalar has a magnitude but no direction (for example speed).

Vectors can be added to give a resultant. For example if you travelalong A and then B your resultant is C so A+B=C.

If you know any of the angles in the vector map you can use the sineand cosine rules to work out the distances.

Sine Rule: a = b = c .

sin A sin B sin C

Or: Sin A = Sin B = Sin C

a b c

Cosine rule: a2 = b2 + c2 2abCos A Or: Cos A = b2 + c2 - a2

2ab

AB

C


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8.3 Velocity

Velocity is speed in a certain direction.

Velocity = displacement (s)

time (t)

You can add velocities but you have to take into accountthe direction of each velocity, you add them the much

like you add vectors.

There is instantaneous and average velocities the same

as there is for speed.

Vplane

VairVresultant


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Chapter 9 Computing the

Next Move


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9.1 Whats the next move?

We constantly make calculations about what will happennext, e.g. catching a tennis ball you work the velocity tofind out where its going so you can catch it.

Displacements = vt

Relative velocities are two velocities in comparison to

each other, so if two planes are travelling at 1000kmtowards each other they have relative velocities of2000km.

Relative velocities can be calculated by reversing yourvelocity and adding it to the other velocity.

For example car A is travelling at 30m/s and car B istravelling at 25m/s in the same direction, the relativevelocity of B from A is -30m/s +25m/s = -5m/s


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9.2 Speeding up, slowing down

Acceleration is an increase in velocity, deceleration is adecrease in velocity.

For uniform acceleration:v = u +v

Andv = at so, v = u + at

Acceleration (a) = change of velocity a = v - utime taken t These two are the same formula reversed. All formulae: v = u + at

s = u+v x t2

v2 = u2 + 2ass = ut + at2

On a speed-time graph the gradient is the acceleration.

V = final velocity

U = initial velocity


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Force (N) = mass (kg) x acceleration (ms-2) (F=ma)

Gravitational force = mass x gravitational field

Acceleration in free fall = gravitational force

mass

Gravitational field = gravitational forcemass

So acceleration in free fall = gravitational field

The gravitational field strength can be measured by the acceleration

in free fall.

Forces are require to change velocity, either slow it down, speed it

up or change its direction.

9.3 Force, mass and gravitation


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9.4 Transport Engineering

Force x time = mass x acceleration x time

Acceleration x time = velocity

Force x time = mass x velocity (mv)

mv is also called momentum so

Force x time = momentum

Displacement = average velocity x time

Average velocity = v/2

Force x displacement = average velocity x force x time

Force x displacement = mv x v/2

Force x displacement = mv2

This is also called kinetic energy


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The distance taken for an object to stop can be worked out from theformula:

u2 = -2as

This taken from the formula v2 = u2 + 2as but the final velocity iszero as its stopped.

Weight = mass x gravitational field (mg)

Displacement vertically = h

Work done = force x displacement = mgh

When going uphill the energy used is mgh this is also the gain ingravitation potential energy.

The gravitation potential energy is mgh = mv2

The kinetic energy from falling is v = gt (g is the acceleration) So t = v/g and distance = average velocity x time

So distance (h) = v/2 x (v/g)2

gh = v2 and this is the same as mgh = mv2 so the increase iskinetic energy is the same as the decrease in gravitational potentialenergy



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When something is giving energy to something changein kinetic energy = energy in energy out.

Work done = drag force x displacement

Work done per second = drag force x velocity

Power = drag force x velocity


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