OCR Physics B

By Oliver Turner (The Night Before the Exam)

Finished at 23:47

Scientific Process

• Ask A Question• Suggest an Answer• Make A Prediction• Carry Out a Test

• Evidence to support or disprove

• Publish Results• Lab Write-Ups• Peer Review• Make New Predictions• Carry Out new Tests

• If all evidence in the world supports – “Scientific Fact”

• Always new evidence...

Evidence• Evidence comes from CONTROLLED LAB

EXPERIMENTS• MEANINGFUL CONCLUSIONS• Must keep everything else constant,

except for one variable• Cause or Correlation?

Evidence

EconomicSocial

Environmental Factors

Decision

Basics of Waves

• Used in Medical Imaging – X-rays / Ultrasound

• Communications• A wave transfers energy from

a source• Reflected- Hits a boundary,

bounces back• Refracted- Changes direction

in different medium as a result of change in speed (ΔS)

PROOF:•Wave Power Generates Electricity• Gamma rays Cause Ionisation

Terms Used with Waves

• Frequency = 1/Time Period

• Hz = S-1

• Velocity = Frequncy x Wavelength

• (Speed) = (1/Time) x (Distance)

• v=fλ

•Transverse (Light, Slinky Up/Down)• Oscillates 90 degrees to

wave movement

•Longitudinal (Sound, Slinky Push/Pull) • Oscillates in the same

direction as wave movement

Polarisation • Oscillates in one direction.• Electromagnetic Waves can be

Polarised• Only happens to transverse waves• PROOVES if a wave is transverse• Reflected LIGHT is polarised (After it

bounces off a material)• Polarising filters polarise light (Only

let through oscillations in certain directions)

• THEREFORE POLAROID sunglasses, don’t let reflected light from snow into your eyes!

• TV Signals are polarised.

• Rotate TV Aerial to the same plane as oscillation of wave

Refraction

• Refraction because of ΔS – Why?• “Pivot Effect” as waves slow

down in a denser medium• Slow down = Decrease

v(velocity)• v=fλ • Decrease in v causes Decrease in

λ• n=c/v• n = refractive index • c = speed of light

Lens Makers Formula• 1/Radius = Curvature (of Wave)• Radius from lens to image = v• Radius from object to lens = u• SO:• Curvature at object = 1/u• Curvature at image = 1/v• What’s the difference? • 1/f – The curvature ADDED by the lens

Radius

• 1/V = 1/U + 1/F• Curvature after = Curvature Before + Curvature

Added

Image Distance, Object Distance and Focal Length

• Object distance = u• Think ubject• Image distance = v• Think vimage • Focal length is distance from lens to focal point (f)

• F = V when image formed at Focal LengthImage formed on Wall

v

f

u

Bits/Bytes

• 1 Bit = A choice of 0 or 1 • 0 and 1’s code computers for ON/OFF

switches• 2n= Number of alternative code• When n is number of bits• Each new bit doubles the number of options

(adds one more choice of ON/OFF)• Number of Bits = Log2(N)• N=Number of alternative codes• 8 Bits = 1 Byte 1000Bytes = 1MB

Images

• Stored in Binary Numbers (Codes of 0’s + 1’s)

• Each pixel is represented by one number

• 256 colours = log2256 = 8• So black = 00000000 White =

11111111 etc• Colour Pictures are much up of 3

numbers• One for RED, GREEN, BLUE

Editing Images

• Add a value to each pixel Increases Brightness (+1)

• Multiplying Increase Contrast (x2)• Map Colours to a certain number to add

False Colour• Replace pixels with median of neighbours

to Reduce Noise• Laplace Rule Finds Edges (multiply pixel by

4, and take away the numbers to N,S,W,E of pixel)

• Everything except edges cancels to give 0 (Black)

9 8 7

6 5 4

3 2 1

9 9 8

7 6 5

4 3 2

9 9 9

9 9 9

8 6 4

Sampling

• Analogue – Continuous• Digital – Discrete

(Limited by number of “levels” = 2n (Slide 10)

• Digital signals are resistant to noise

• Because they only take certain values, they can be RECONSTRUCTED after they pick up noise

Analogue > Digital:Take the values of an analogue signal at regular time intervalsTo the NEAREST digital “level”/valueTurn the value into a binary number

WILL LOSE SOME INFORMATION (But its still pretty close to the real thing)

Quality and Noise

• Quality depends on:1. Number of levels2. Time from one sample to the next• Higher the resolution (more values) the more

closely it matches the original 2n (Slide 10)• IF TOO MANY LEVELS, noise is reproduced

• Maximum bits = log2(Total Variation/Noise Variation)

• b = log2(VT/VN) • Variation can be measured in volts

Minimum sampling rate = 2x Highest

frequency, or else you get “aliases”

Digital Signals > Analogue Signals

1. Sent, Received, Reproduced easily– They take a limited number of values

2. Resistant to the effects of Noise– Analogue signals are negatively effected by noise

3. Store different kinds of information in the same way– Can be stored as a string of bits

4. Easy to Process using computers– Computers are digital devises too

Signal Spectra / Bandwidth

• Signals made up of lots of frequencies

• Bandwidth is the range of frequencies e.g

• Maximum f – Minimum f = Bandwidth

• Carrier wave is mixed with signal when signal is sent

• Carrier wave is separated from the signal, and then signal is played

• Carrier frequencies have to be different to avoid interference

• Bandwidth determines how different they have to be

• Gaps are left between say 105.8, and 106.2

• Larger Bandwidth > Larger the gap has to be to stop overlapping

• Number of stations = Range of frequencies / Gap Size

• E.g from 30MHz to 300MHz

Rate of Transmission

• Rate of transmission (bits per second) =

• Samples per second x Bits per sample

• Samples per second must be twice the highest frequency (to ensure all the frequencies are transmitted accurately, none are lost)

• Bits per sample must be high enough so close match original but not too high so it is affected by noise (Slide 14)

Proof:

R=S/t x B/S samples second x bits sampleRS=SB/t multiply both sides by SR=B/t divide by S again

Charge and Current

• Sensors sense things we cant / don’t want to detect• A change in input will change the current. • This gives a reading

• ΔQ=I Δt • I = ΔQ/t• Coulomb is the UNIT of charge• Amount of charge that passes in 1 second with

current of 1 Amp

Potential Difference and Power

• V=W/Q• W = work done in Joules• 1V = 1JC-1

• P = Wt• I=Q/t• P = IV > (V=P/I)

• V=Wt/Q/t• V=W/Q

• W=Pt• P=IV• W=IVt

Resistance / Conductance

• R=V/I• P=IV• V=IR• P=I2R• I/V graph shows

resistance as gradient• Shallow curve = R is

high.• High voltage needed for

a small current

• G=1/R• R=1/G• V=IR• V=I/G• P=I2/G

I

V

Filament Lamps and Thermistors• Filament Lamp I/V graph is curved (V=-I3) style• Starts steep gets shallow• Resistance increases! • This is because Temp increases as current flows• Resistivity/Temp graph of a Thermistor is like a (1/x) graph.

(I/V graph is like I=V3)• Therefore resistance decreases with temperature.• This is because increase Temp allows more electrons to escape

atoms• More charge carriers - Higher Current - Lower Resistance R=V/I• Sensitivity = Change in Dependant(y)/ Change in

Independent(x)

E.m.f and Internal/External R • ε= electromotive force e.m.f• Its not a force its a voltage • Its the voltage when there is no internal resistance. (Which is the

resistance of the battery)• ε=V+v ε=I(R+r) • V= ε-v V= ε-Ir• Normally want LOW internal resistance so less energy is lost as heat.• High Voltage power supplies want HIGH internal resistance because

I=V/R so small current flows, less danger of if short circuited. • Graph of V/I gradient = -r • V intercept = ε• V= -rI+ ε is the equation of the line

Resistance and Potential Dividers

• Series R=R1+R2+R3....

• Parallel G= G1+G2+G3....• G=1/R R=1/G• Vout=(R1/R=R1+R2+R3....)Vs

• Voltage is split up across resistors in the ratio of their resistances.

• Transistors are like switches that are turned on when voltage is high.

• You can use transistors to make sensor circuits (page 24 CGP)

• Potentiometers:• Move a slider

down a resistor, to split it in 2

• Vary the voltage output continuously

• Useful in CD player volume controls

Hooke’s Law & Plastic/elastic

• F=ke• e is the extension of a wire• F is the force on the wire• k is the stiffness constant of

the material

• Elastic• Return to original shape• Atoms pulled apart• Move small distances • Return to equilibrium distance• In metals this happens as long as

Hooke’s law is obeyed

• Plastic• Permanent Stretch• Atoms move position

relative to one another• Dont’ return to

positions• Metals this happens

when stretch beyond elastic limit

Young Modulus

• Stress = F/A• Strain = e/l = Δl/l l is length e is extension = Δl (change in length)

• E=(Tensile)Stress/(Tensile)Strain• E = F/A/Δl/l = F/A/e/l• E = Fl/Ae

• Units are Nm-2

• Young Modulus works up to “limit of proportionality”• Used by engineers to see if materials can withstand

certain forces

Stress Strain Graph Labelled

A. Limit of Proportionality - no longer obeys Hooke’s Law, but will stretch elastically

B. Elastic Limit – No more elastic stretching after this point. All plastic deformation.

C. Yield Point - stretches without extra load, large amount of plastic deformation

D. UTS (Ultimate Tensile Stress)

E. Fracture Stress

Structures• Crystalline • Regular Repeating

Crystalline Structure• Usually form a

crystalline lattice• Electrons don’t need

much energy to escape atoms, form a sea of free electrons

• Good conductors• Tough• Ions can move within

the lattice making it ductile

• Ceramics• Giant Rigid Structure• Crystalline or

Polycrystalline (grains of crystalline structure) atoms in each grain line up in a different direction

• Can be Amorphous, quicker it cools, more like to be amorphous

• Ionic or Covalent• Strong bonds make them

Stiff rigid structure makes them Brittle

• Polymers• Molecular Chain

made of repeating monomers

• Man Made• Covalently bonded

so Strong• Rotate about bonds

making them flexible

• Bonds Between Chains make polymers Rigid, if they have them

Composites – Combine two materials to get a material with the properties you want

Electron Microscopes

• Scanning electron microscopes:• Don’t let you see the surface• See an atom by atom image• Estimate the size of atoms in a material• Only shows surface of a material• To see arrangement you need X-Ray

Crystallography

Properties

• Brittle – Break without deforming plastically

• Ductile– Can be drawn into wires (changed shape), retains strength

• Malleable– Change shape but might lose strength

• Hard– Resistant to abrasion, and indentation

• Stiff– High resistance to bending and stretching (high YM)

• Tough– Difficult to break, take a lot of energy to break

Electrical Properties

• Resistance depends on• L – longer is more difficult to make a current flow• A – wider easier it is for electrons to pass along it• ρ – depends on material, structure may be hard or

easy for charge to flow, ρ depends on environmental factors too

• R= ρl/A• ρ=RA/l

Materials and Charge Carriers

• Metals, charge carriers are electrons.

• Charge carrier density is high

• The temp is raised, lattice structure vibrates and electron scattering occurs so the electrons are slightly less free to move

• As temp increase• Resistance increases

• Semiconductors’, charge carriers are electrons.

• Charge carrier density is low

• The temp is raised, more electrons are freed to conduct

• Lattice vibrates but the effect is overcome

• As temp increases• Resistance decreases

RAPIDLYInsulators – A perfect insulator will not have any charge carriers so will not conduct at all

Superposition

• Constructive – Phasors Add• Destructive – Phasors Subract• In phase, interfere constructivly• Coherant means same λ and f and fixed phase

difference• Any point equal distance from both, Constructive

• Constructive = nλ• Destructive = (n+1/2) λ

Standing Waves

• No energy transmitted • Reflected back and forth• Original and reflected waves reinforce each other• At “resonant frequencies” you get a standing wave• Resonant frequencies an exact number of half

wavelengths fits onto the string• Fundamental Frequency:• OPEN/OPEN = ½ λ• CLOSED/CLOSE D= ½ λ• OPEN/CLOSED = ¼ λ

Measure speed of sound

• Closed/Open Tube filled with water

• Tap tuning fork with known frequency

• Until you find shortest distance where a sound resonates

• ¼ λ• V=f λ• Do it.

Diffraction

• Spread out through a narrow gap• Maximum spread when λ = gap• If gap < λ most waves reflected• Phasors add when there is a constant phase

difference• At all other points, phasors point in slightly

different directions, and form a smaller resultant• Dark fringes occur where resultant phasor = 0

becauses phasors add to make a circle.

Two Source Interference

• Fringes form depending on constructive or destructive interference

• Fringe spacing X = Dλ/d• D is distance slits to screen• d is spacing between slit• Work out wavelength of light with this• f=c/λ work out the frequency• Evidence for wave nature of light

If anyone’s interested its now 10:29pm

Diffraction Gratings

• Interference patters get sharper when you diffract through more slits.

• So many beams all reinforcing the pattern• More accurate measurements can be made• nλ=dsinѳ• White light through a diffraction grating

produces spectra

Photoelectric Effect

• Shine light of high f on metal, emits electrons• Free electrons absorb energy• Vibrate > Bonds Break > Electron Released• Photoelectric effect - Photoelectrons are released• Conclusion 1: Below threshold f, no photoelectrons are emitted• Conclusion 2: Photoelectrons are emitted with EK ranging from 0

to a maximum, max is not affected by intensity but by f• Conclusion 3: Number of photoelectrons emitted per second is

proportional to the intensity• WAVE THEORY CANT EXPLAIN 1+2

According to wave theory

• E proportional to intensity• Energy would be spread evenly over wave

front• Each free electron would get a bit more

energy from each wave• Eventually get enough energy to leave the

material.

Quantum?

• A single packet of EM radiation is called a Quanta• Called packets of energy photon• E=hf of a photon• E=hc/λ using f=c/ λ

• Higher f more energy wave packet carries• Photon acts like a particle and transfers all or none of its energy• Metal bombarded by photons• If photon collides with electron electron gains E=hf• Before an electron can leave the surface it must overcome the

work function φ (energy to break bond)• E- φ= ½ mv2

Electrons

• Electrons exist in discrete energy levels• Move down energy levels by emitting a photon• Line spectra are produced as only discrete

values of E are given out, different f• Cool gases produce emission spectra (opposite,

discrete holes in continuous spectra)• Line spectra and emission spectra are

individual to each element

Sum Over Paths

• Phasors try every path• Rotate, Phasors add• Consider only shortest routes, as the rest cancel• Young’s slits: Phasors that travel through a

grating, take a longer trip time, therefore phasors rotate a bit more.

• Phasors rotate at same rate, same f• Resultant Phasor 2= Probability = Brightness

Using Sum Over Paths

• Angle of incidence = Angle of reflection• Because paths near the quickest route almost line up.

Therefore largest QA + Prob• Long path phasors “curl up” and cancel so QA is

reduced• Refraction• Light takes all paths, path that takes shortest time

adds up to the largest QA• Shortest time is when refraction occurs, as one

median is different speed to another.

Using Sum Over Paths

• Focus• To make a lens that focuses well, all trip times must

add up to the same. • Concave – no matter what part of the mirror a

photon hits, it will have the same trip time (travelled same distance, rotated same amount) when it reaches the focal point

• Convex – Outer paths are longer, so make quicker paths take the same time by increasing the thickness of the slower to travel through glass sections.

Electrons• λ=h/mv• Probability wave

• Diffraction patterns observed when accelerated electrons in a vacuum interact with spaces in a graphite crystal.

• As an electron hits a fluorescent screen, photons are released, so you can see the diffraction pattern.

• Higher prob, brighter area on screen• Electrons show quantum behaviour• Only happens when gap is the same size as De Broglie wavelength• f = EK/h

Vectors and SUVAT

• Add tail to tail• v=u+at• s=(u+v)/2 x t• s=ut+ ½at2

• v2=u2+2as

• g=-9.81m/s = a when falling

ICT and Graphs

• Ultrasound Position Detector• Graph Drawing Software• The main advantages:• More Accurate Data• Higher Sampling Rate• Real Time Visualisation

Newton

• F=ma• No resultant force, velocity will not change (no

acceleration• Circular motion, velocity is constantly

changing as its a vector, even though speed is constant. (If you plot it against angle, form a sine or cosine wave)

The time is now.... 23:10

Work and Power and Energy

• Work = Force x Distance• W = Fd• P=Fv• P=W/t• W=Fs• P=Fs/t s is

displacement

• Conservation of energy:

• Cannot be Created or Destroyed

• Can be transferred• Total energy In

=Total energy Out• Efficiency = Useful

Output/ Energy Input

Errors

• Every measurement has uncertainty• Random Errors– Cant get rid of them– Cant keep everything exactly the same each time– Repeat measurements and average– Higher Precision

• Systematic Errors– Measuring a known value– If there's a difference, use this to correct the inaccuracy

of they appuratus

Error Analysis

• Estimate values by averaging • To get uncertainty look at the distance from

maximum and minimum to the mean• Error Bars show uncertainty on a graph• Draw Maximum and Minimum gradient curve

DONE YEAHHHHHHHHHHHHHHHHHHHHHHHHHH