A Level Physics OCR

A Level Physics OCR

1. Imaging

   • Lenses
     • Curvature of a circle = 1/r
     • Wave-fronts with a distant source appear to have no curvature
       • Plane wave-fronts
     • Rays travel in the direction of motion of the wave front
       • They are at right angles to the wave front
     • Power = 1/f
       • Dioptres (D)
   • Finding The Image
     • 1/v=1/u+1/f
     • f is the point at which parallel waves are brought to focus
     • The image distance v is greater than f apart from very distant objects
     • Magnification
       • m = image height / object height
       • m = image distance / object distance
         • m = v / u
       • A negative m occurs when the image is inverted
   • Storing and Manipulating the Image
     • Pixels store electric charge when light falls on it
       • The brighter the light, the greater the charge
     • Bits and Bytes
       • 8 bits = 1 byte
       • N = 2^b
       • b = log2(N)
     • Resolution
       • Object width / pixels across object
     • amount of information = number of pixels x bits per pixel
   • Processing
     • Changing brightness
     • Removing noise
     • Edge detection
     • Changing contrast
   • Polarisation
     • Speed = frequency x wavelength
     • Frequency = 1 / T
     • Transverse waves
       • They are polarised if they travel in one plane
       • Unpolarised waves vibrate randomly

2. Signalling

   • Digitisation
     • Sampling occurs are small time intervals
     • Analogue Signals
       • Amplification of analogue signals amplifies the noise as well
       • Filtering noise lowers the level of detail in the signal.
     • The difference between the signal value and the quantisation level is a quantisation error.
     • Resolution
       • Potential difference range of signal / number of quantisation levels
     • Useful levels
       • Max useful number of levels = total noisy signal variation / noise variation
       • b = log2 (V total / V noise)
   • Sampling and Sending
     • minimum sample rate > 2x highest frequency
     • The signal cannot contain frequencies above a maximum
       • If it is higher, aliases will be produced
         • Aliases are lower frequency signals not in the original signal
     • Bit rate = samples per seconds x bits per sample
     • Duration of signal = N of bits in signal / bit rate

3. Sensing

   • Current, P.D, Power
     • Current
       • Flow of charged particles
         • Charge
           • Q
           • Coulombs C
       • Amperes/Amps A
       • I
       • Current = Charge / Time
       • Currents at a junction must add up
     • Potential Difference
       • Voltage V
         • P.D
       • Work done = Change in energy
       • V = E / Q = W / Q
     • Power
       • Watt W
       • P
       • Power = Current x voltage
     • Resistance
       • R = V / I
       • Ohms
         • VA^-1
       • P = I^2R
   • Conductors and Resistors
     • Conductance
       • G = I / V
       • AV^-1
         • Siemen
       • G = 1 / R
       • The amount of amps from 1V
     • Resistance
       • The ratio of P.D to current
       • I is proportional to V
     • Parallel Circuits
       • 1/R1 +1/R2
       • Same P.D
       • Shared current
       • Conductances add
         • G = G1 + G2
     • Series
       • 1/G1 + 1/G2
       • Resistances add
         • R = R1 + R2
       • Same Current
       • Shared P.D
   • Conductivity and Resistivity
     • Conductivity
       • G = OA/L
       • Sm^-1
     • Resistivity
       • Doubling the length doubles the resistance
       • R = PL/A
       • Ohmic metres

4. Materials

   • Testing Materials
     • Classes
       • Hard - difficult to scratch
       • Tough - Difficult to break
       • Brittle - shatters into jagged pieces
       • Stiff - difficult to stretch and bend
       • Malleable - shaped easily
       • Ductile - can be drawn into a wire
     • Stretching Wires
       • Hooke's Law
         • F = kx
         • k is the spring constant
           • k depends on the material, length and CSA
       • An elastically deformed wire can return to its original length
       • Exceeding the elastic limit causes plastic deformation
         • Fracture occurs after plastic deformation
       • E = 1/2 kx^2
     • The Young Modulus
       • Stress
         • Force per unit area
         • PA
         • Yield stress - point at which plastic deformation begins
         • Force / CSA
       • Strain
         • Extension / Length
           • X / L
           • %
         • Fractional increase in length
       • E = FL / xA
       • Often very large
   • Looking Inside Materials
     • Rayner
       • Oil drop
       • h = 4r^3 / 3R^2
     • Number of atoms = total mass / mass of one atom
     • Metal Structure
       • Metals are crystaline
       • Dislocations
         • Mismatches in rows of atoms
         • Atoms move individually rather than as rows
         • Pinned dislocations (addition of an atom) make the slip harder
       • Glass is amorphous
       • Crack Propagation
         • Elastic straining occurs
         • Two atoms are pulled apart
         • It acts like a zip
     • Bonding
       • Metals
         • Metal bonds are strong, making them stiff
         • Ions are free to move - ductile and tough
       • Polymers
         • Bonds rotate, stretching the chain
         • The chain starts off folded

5. Wave Behaviour

   • Superposition
     • If two waves are at the same point, they are in phase
     • Two waves doing the opposite are in anti-phase
     • Otherwise they are 'not in phase'
     • When two or more waves overlap
     • The sum of phasors gives the resultant amplitude
     • On a string
       • Waves move along a string
       • They reflect and superpose
       • Antinodes are where waves meet at a maximum amplitude in phase
       • Zero amplitude in antiphase creates nodes
   • Velocity = wavelength x frequency
   • Refraction
     • Refractive index = c in medium 1 / c in medium 2
     • RI of material = c vacuum / c material
     • Snell's Law
       • The ray bends towards the normal
       • sin 1 / sin r
       • c first / c second
   • Diffraction
     • Young's Double Slit
       • Light passing through two small pinholes create bright and dark spots
       • Light going through a slit spreads out
       • When in phase, a bright fringe is created
       • Sin(angle) = wavelength / slit separation
     • Order of Maxima
       • The 0th order is where the path difference is 0
       • Wavelength = xd/L
       • Line separation = 1 / lines per m

6. Quantum Behaviour

   • Packets of light are called quanta
   • Quanta
     • EM radiation is emitted and absorbed in quanta
     • Energy = Planck constant x frequency
       • The Planck constant is 6.6 x 10^-34 Js
       • E = hc / wavelength
   • The Photoelectric Effect
     • Intensity is the amount of energy transferred per metre squared per second
     • KE is not affected by intensity
     • If f is lower than the threshold frequency no elections are released regardless of how bright it is
     • Maximum energy depends on light frequency
     • EK(max) = hf - work function
       • The work function is the energy needed to release the electron from the surface
   • Probability
     • Square the amplitude to find the chance
     • Add phasors tip to tail
   • Reflection
     • Photons obey the law of refraction
     • Phasors from end paths curl up
   • Electron Diffraction
     • Wavelength = h/mv

7. Motion

   • Graphs
     • Displacement - distance travelled from the starting point
     • Velocity - the speed including direction
     • Avg v = s / t
     • A = v / t
   • Modelling Motion
     • Iterative models
       • Step by step
       • It assumes a constant DV
       • Accuracy can be improved with smaller time intervals
         • Vectors can be used
     • SUVAT
       • v = u + at
       • s = (u + v) / t
       • s = ut + 1/2at^2
       • v^2 = u^2 + 2as
       • s = (u + v) / 2
   • Momentum, Force, Energy
     • Momentum
       • p = mv
       • Total p = m1v1 + m2v2
       • Momentum is conserved
         • Momentum before equals the momentum after
     • Newton's laws
       • Momentum will not change unless a force acts upon it
       • F = p / t
         • F = mv /t
       • If a exerts a force on b, b exerts a force of equal magnitude and opposite direction on a
     • F = ma
     • Energy
       • Work = force x displacement
       • Kinetic Energy = 1/2mv^2
       • Gravitational potential = mgh
     • Work and Power
       • Work = Fs
         • Fs x cos(angle)
       • Power = work done / time

8. Modelling

   • Decay
     • Decay and Half-Life
       • Types
         • Alpha - Helium nuclei
         • Beta - fast moving electrons
         • Gamma - high energy photons
       • Activity and Half-Life
         • Activity A
           • 1 Bq
             • 1 decays^1
           • Number of nuclei decaying per second
         • Half- Life
           • T1/2
           • N is reduced by 2^L
             • L half lives
         • Time required for the sample to half
         • A = prob of decay in 1s x N
       • A=A0e-^-λt
         • T1/2 = LN2/ λ
           • - λ is the gradient
     • Capacitors
       • Electrical conductors separated by a layer of insulator
       • Capacitance
         • C=Q/V
         • Charge separated per volt
         • Farad F
           • CV^-1
         • E=1/2QV
       • Q=Q0e^-t/RC
       • t=RC
         • RC is the time constant of discharge
   • Oscillations
     • Simple Harmonic Motion
       • Time period is the time for once complete swing
       • The displacement is about an equilibrium position
       • x = Acosωt
         • ω = 2πfrad/s
       • Acceleration
         • Proportional to the displacement
         • Is always directed towards the equilibrium position
         • a = -kx
           • a = -ω^2x
     • Time and Frequency
       • T = 2π√ m/k
       • Pendulum
         • F = -T x/L
         • a = -g x/L
         • T = 2π√L/g
     • Resonance
       • Free Oscillations
         • It will have a constant amplitude
         • It swings at a constant, natural frequency
           • When the driving and natural frequency match, it goes into resonance
       • Forced Oscillations
         • A periodic driving force causes the driving/forced oscillation
         • e.g Marching soldiers on a bridge
       • E = 1/2 kA^2
         • E = Ek + Ep
     • Damping
       • The action of forces such as friction
       • Removal of energy from a system
   • Gravitational Field
   • The Universe

9. Matter

10. Fields

11. Particles