International Baccalaureate 

Option B  Engineering Physics


The Core and Additional Higher Syllabus has topics in each of the four options. You take one of the options. If you are lucky enough to be in a centre with four physics groups, you may have the opportunity to choose the option you do. In most schools and colleges, the tutor will choose it for you. 

Note: The syllabus statements about the following have been omitted for space reasons:
You can find these statements in the syllabus.
Guidance shown like this is extra guidance from me, not the syllabus. 

In the exam, you are expected to understand: 

Option A  Relativity 

A.1 The Beginnings of Relativity (Core) 

Understanding 
Applications 
Guidance 
Equations  Link 
Reference frames;
Galilean relativity and Newton’s postulates concerning time and space;

Using the Galilean transformation
equations; Determining whether a force on a charge or current is electric or magnetic in a given frame of reference;

Maxwell’s equations do not need to be described;
Qualitative treatment of electric and magnetic fields as measured
by
Students will be asked to analyse these motions from the point of
view of 

(Basic relativity)
(Electric and magnetic fields)
(Equivalence) 
A.2 The Lorentz Transformation (Core) 

The two postulates of special relativity;
Clock synchronization;
The Lorentz transformations;
Velocity addition;
Invariant quantities (spacetime interval, proper time, proper length and rest mass);
Time dilation;
Length contraction;
The muon decay experiment. 
Using the Lorentz transformations to describe how different measurements of space and time by two observers can be converted into the measurements observed in either frame of reference;
Using the Lorentz transformation equations to show that if two events are simultaneous for one observer but happen at different points in space, then the events are not simultaneous for an observer in a different reference frame;
Solving problems involving velocity addition;
Deriving the time dilation and length contraction equations using the Lorentz equations;
Solving problems involving time dilation and length contraction;
Solving problems involving the muon decay experiment 
Problems will be limited to one dimension;
Derivation of the Lorentz transformation equations will not be examined;
Muon decay experiments can be used as
evidence for both time dilation and 

(Special Relativity)

A.3 Spacetime Diagrams (Core) 

Spacetime diagrams;
Worldlines;
The twin paradox. 
Representing events on a spacetime diagram as points;
Representing the positions of a moving particle on a spacetime diagram by a curve (the worldline);
Representing more than one inertial reference frame on the same spacetime diagram;
Determining the angle between a worldline for specific speed and the time axis on a spacetime diagram;
Solving problems on simultaneity and kinematics using spacetime diagrams;
Representing time dilation and length contraction on spacetime diagrams;
Describing the twin paradox;
Resolving of the twin paradox through spacetime diagrams. 
Examination questions will refer to spacetime diagrams; these are also known as Minkowski diagrams;
Quantitative questions involving
spacetime diagrams will be limited to
Spacetime diagrams can have t or ct on the vertical axis;
Examination questions may use units in which c = 1. 

(Spacetime Diagrams)

A.4 Relativistic Mechanics (Additional Higher) 

Understanding 
Applications 
Guidance 
Equations  Link 
Total energy and rest energy;
Relativistic momentum;

Describing the laws of conservation of
momentum and conservation of Determining the potential difference necessary to accelerate a particle to a given speed or energy;

Applications will involve relativistic
decays such as calculating the
The symbol m_{0} refers to the invariant rest mass of a particle;
Problems will be limited to one dimension 

(Accelerators)
(Relativistic Mechanics) 
A.5 General Relativity (Additional Higher) 

The equivalence principle;
The bending of light;

Using the equivalence principle to deduce and explain light bending near massive objects;
Using the equivalence principle to deduce and explain gravitational time dilation;
Calculating gravitational frequency shifts;
Describing an experiment in which
gravitational redshift is observed
Calculating the Schwarzschild radius of a black hole;
Applying the formula for gravitational time dilation near the event horizon of a black hole. 
Students should recognize the equivalence principle in terms of accelerating reference frames and freely falling frames. 

(Equivalence)
(Schwarzchild Radius)
Physics 6 Tutorial 20  Pound Rebka Experiment
Gravitational Time Dilation 
Option B Engineering Physics 

B.1 Rigid Bodies and Rotational Dynamics (Core) 

Understanding 
Applications 
Guidance 
Equations  Link 
Torque; Moment of inertia; Rotational and translational equilibrium; Angular acceleration; Equations of rotational motion for uniform angular acceleration; Newton’s second law applied to angular motion; Conservation of angular momentum. 
Calculating torque for single forces and couples; Solving problems involving moment of inertia, torque and angular acceleration; Solving problems in which objects are in both rotational and translational equilibrium. Solving problems using rotational quantities analogous to linear quantities; Sketching and interpreting graphs of rotational motion; Solving problems involving rolling without slipping. 
Analysis will be limited to basic geometric shapes;
The equation for the moment of inertia
of a specific shape will be provided Graphs will be limited to angular displacement–time, angular velocity–time and torque–time. 

Engineering Physics 1

B.2 Thermodynamics (Core) 

The first law of thermodynamics; The second law of thermodynamics; Entropy; Cyclic processes and pV diagrams Isovolumetric, isobaric, isothermal and adiabatic processes; Carnot cycle; Thermal efficiency 
Describing the first law of thermodynamics as a statement of conservation of energy; Explaining sign convention used when stating the first law of thermodynamics ΔQ = U + W; Solving problems involving the first law of thermodynamics; Describing the second law of thermodynamics in Clausius form, Kelvin form and as a consequence of entropy; Describing examples of processes in terms of entropy change; Solving problems involving entropy changes; Sketching and interpreting cyclic processes; Solving problems for adiabatic processes for monatomic gases using (pV)^5/3 = constant; Solving problems involving thermal efficiency. 
If cycles other than the Carnot cycle
are used quantitatively, full details will be
Only graphical analysis will be
required for determination of work done on a 

(Laws of Thermodynamics)
(First Law)
(PV Diagrams)
(Engines)
(Second Law)

B.3 Fluids and Fluid Dynamics (Additional Higher) 

Pascal’s principle; Hydrostatic equilibrium; The ideal fluid; Streamlines; The continuity equation; The Bernoulli equation and the Bernoulli effect; Stokes’ law and viscosity; Laminar and turbulent flow and the Reynolds number 
Determining buoyancy forces using Archimedes’ principle; Solving problems involving pressure, density and Pascal’s principle; Solving problems using the Bernoulli equation and the continuity equation; Explaining situations involving the Bernoulli effect;
Describing the frictional drag force
exerted on small spherical objects in Solving problems involving Stokes’ law; Determining the Reynolds number in simple situations 
Ideal fluids will be taken to mean
fluids that are incompressible and nonviscous
Applications of the Bernoulli equation
will involve (but not be limited to) flow Proof of the Bernoulli equation will not be required for examination purposes; Laminar and turbulent flow will only be considered in simple situations; Values of R <10^{3} will be taken to represent conditions for laminar flow 

Materials 4 (Pressure, viscosity, and Stokes' Law)
(Continuity equation, Bernoulli Effect, and Reynolds Number)

B.4 Forced Vibrations and Resonance (Additional Higher) 

Natural frequency of vibration; Q factor and damping; Periodic stimulus and the driving frequency; Resonance. 
Qualitatively and quantitatively
describing examples of under, over and critically damped Graphically describing the variation of the amplitude of vibration with driving frequency of an object close to its natural frequency of vibration; Describing the phase relationship between driving frequency and forced oscillations; Solving problems involving Q factor; Describing the useful and destructive effects of resonance 
Only amplitude resonance is required 

Further Mechanics 3 
Option C Imaging 

C.1 Introduction to Imaging (Core) 

Understanding 
Applications 
Guidance 
Equations  Link 
Thin lenses; Converging and diverging lenses; Converging and diverging mirrors; Ray diagrams; Real and virtual images; Linear and angular magnification; Spherical and chromatic aberrations. 
Describing how a curved transparent
interface modifies the shape of an Identifying the principal axis, focal point and focal length of a simple converging or diverging lens on a scaled diagram; Solving problems involving not more than two lenses by constructing scaled ray diagrams. Solving problems involving not more than two curved mirrors by constructing scaled ray diagrams; Solving problems involving the thin lens equation, linear magnification and angular magnification; Explaining spherical and chromatic aberrations and describing ways to reduce their effects on images. 
Students should treat the passage of light through lenses from the standpoint of both rays and wavefronts;
Curved mirrors are limited to spherical
and parabolic converging mirrors and Only thin lenses are to be considered in this topic; The lensmaker’s formula is not required; Sign convention used in examinations will be based on real being positive (the “realispositive” convention) 

Medical Physics 2 (Lenses)
(Lenses and Telescopes)
Curved mirrors 
C.2 Imaging Instrumentation (Core) 

Optical compound microscopes; Simple optical astronomical refracting telescopes; Simple optical astronomical reflecting telescopes; Singledish radio telescopes; Radio interferometry telescopes; Satelliteborne telescopes 
Constructing and interpreting ray diagrams of optical compound microscopes at normal adjustment; Solving problems involving the angular magnification and resolution of optical compound microscopes; Investigating the optical compound microscope experimentally; Constructing or completing ray diagrams of simple optical astronomical refracting telescopes at normal adjustment 
Simple optical astronomical reflecting telescope design is limited to Newtonian and Cassegrain mounting; Radio interferometer telescopes should be approximated as a dish of diameter equal to the maximum separation of the antennae; Radio interferometry telescopes refer to array telescopes 

Astrophysics 2 (Reflecting Telescopes)
(Radio Telescopes)
(Wavefronts) 
C.3 Fibre Optics (Core) 

Structure of optic fibres; Stepindex fibres and gradedindex fibres; Total internal reflection and critical angle; Waveguide and material dispersion in optic fibres; Attenuation and the decibel (dB) scale. 
Solving problems involving total internal reflection and critical angle in the context of fibre optics; Describing how waveguide and material dispersion can lead to attenuation and how this can be accounted for; Solving problems involving attenuation; Describing the advantages of fibre optics over twisted pair and coaxial cables. 
Quantitative descriptions of attenuation are required and include attenuation per unit length; The term waveguide dispersion will be used in examinations. Waveguide dispersion is sometimes known as modal dispersion.
In the notes modal dispersion is used. 

Waves 6 (Optical Fibres)

C.4 Medical Imaging (Additional Higher) 

Detection and recording of Xray images in medical contexts; Generation and detection of ultrasound in medical contexts; Medical imaging techniques (magnetic resonance imaging) involving nuclear magnetic resonance (NMR). 
Explaining features of Xray imaging,
including attenuation coefficient, halfvalue thickness, linear/mass
absorption coefficients and techniques for improvements Solving Xray attenuation problems; Solving problems involving ultrasound acoustic impedance, speed of ultrasound through tissue and air and relative intensity levels; Explaining features of medical ultrasound techniques, including choice of frequency, use of gel and the difference between A and B scans; Explaining the use of gradient fields in NMR; Explaining the origin of the relaxation of proton spin and consequent emission of signal in NMR; Discussing the advantages and disadvantages of ultrasound and NMR scanning methods, including a simple assessment of risk in these medical procedures. 
Students will be expected to compute final beam intensity after passage through multiple layers of tissue. Only parallel plane interfaces will be treated. 

Medical Physics 5 (Ultrasound)
(NMR)
(Xrays and CT Scanners) 
Option D Astrophysics 

D.1 Stellar Quantities (Core) 

Understanding 
Applications 
Guidance 
Equations  Link 
Objects in the universe; The nature of stars; Astronomical distances; Stellar parallax and its limitations; Luminosity and apparent brightness. 
Identifying objects in the universe; Qualitatively describing the equilibrium between pressure and gravitation in stars; Using the astronomical unit (AU), light year (ly) and parsec (pc); Describing the method to determine distance to stars through stellar parallax; Solving problems involving luminosity, apparent brightness and distance. 
For this course, objects in the
universe include planets, comets, stars (single Students are expected to have an awareness of the vast changes in distance scale from planetary systems through to super clusters of galaxies and the universe as a whole. In the notes the physics code F is used instead of b for flux. 

Astrophysics 4 (Stellar Distances and Magnitudes)
(Luminosity)

D.2 Stellar Characteristics and Stellar Evolution (Core) 

Stellar spectra; Hertzsprung–Russell (HR) diagram; Mass–luminosity relation for main sequence stars; Cepheid variables; Stellar evolution on HR diagrams; Red giants, white dwarfs, neutron stars and black holes; Chandrasekhar and Oppenheimer–Volkoff limits. 
Explaining how surface temperature may be obtained from a star’s spectrum; Explaining how the chemical composition of a star may be determined from the star’s spectrum; Sketching and interpreting HR diagrams;
Identifying the main regions of the HR
diagram and describing the main Applying the mass–luminosity relation; Describing the reason for the variation of Cepheid variables; Determining distance using data on Cepheid variables; Sketching and interpreting evolutionary paths of stars on an HR diagram; Describing the evolution of stars off the main sequence; Describing the role of mass in stellar evolution. 
Regions of the HR diagram are
restricted to the main sequence, white dwarfs,
HR diagrams will be labelled with
luminosity on the vertical axis and Only one specific exponent (3.5) will be used in the mass–luminosity relation; References to electron and neutron degeneracy pressures need to be made. 

Astrophysics 5 (Luminosity and Spectra)
(Evolution of stars)

D.3 Cosmology (Core) 

The Big Bang model; Cosmic microwave background (CMB) radiation; Hubble’s law; The accelerating universe and redshift (z); The cosmic scale factor (R) 
Describing both space and time as originating with the Big Bang; Describing the characteristics of the CMB radiation; Explaining how the CMB radiation is evidence for a Hot Big Bang; Solving problems involving z, R and Hubble’s law; Estimating the age of the universe by assuming a constant expansion rate 
CMB radiation will be considered to be isotropic with T ≈ 2.76K;
For CMB radiation a simple explanation
in terms of the universe cooling down or A qualitative description of the role of type Ia supernovae as providing evidence for an accelerating universe is required. 


D.4 Stellar Processes (Additional Higher) 

The Jeans criterion; Nuclear fusion; Nucleosynthesis off the main sequence; Type Ia and II supernovae 
Applying the Jeans criterion to star formation; Describing the different types of nuclear fusion reactions taking place off the main sequence; Applying the mass–luminosity relation to compare lifetimes on the main sequence relative to that of our Sun; Describing the formation of elements in stars that are heavier than iron including the required increases in temperature; Qualitatively describe the s and r processes for neutron capture; Distinguishing between type Ia and II supernovae 
Only an elementary application of the
Jeans criterion is required, ie collapse of Students should be aware of the use of type Ia supernovae as standard candles. 

(Evolution of stars)
(Fusion in Stars)

D.5 Further Cosmology (Additional Higher) 

The cosmological principle; Rotation curves and the mass of galaxies; Dark matter; Fluctuations in the CMB; The cosmological origin of redshift; Critical density; Dark energy. 
Describing the cosmological principle and its role in models of the universe; Describing rotation curves as evidence for dark matter; Deriving rotational velocity from Newtonian gravitation; Describing and interpreting the observed anisotropies in the CMB; Deriving critical density from Newtonian gravitation; Sketching and interpreting graphs showing the variation of the cosmic scale factor with time; Describing qualitatively the cosmic scale factor in models with and without dark energy. 
Students are expected to be able to refer to rotation curves as evidence for dark matter and must be aware of types of candidates for dark matter; Students must be familiar with the main results of COBE, WMAP and the Planck space observatory;
Students are expected to demonstrate that the temperature of the universe varies with the cosmic scale factor as: . 

Astrophysics 7 (Cosmological Principle, Critical Density)

That is it. 