International Baccalaureate


Home   Core   Additional Higher Level  

Option A - Relativity


Option B - Engineering Physics  


Option C - Imaging


Option D - Astrophysics

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:

  • Nature of Science;

  • International mindedness;

  • Theory of knowledge;

  • Utilisation;

  • Aims.

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)




Equations Link

Reference frames;


Galilean relativity and Newton’s postulates concerning time and space;

Maxwell and the constancy of the speed of light;

Forces on a charge or current.

Using the Galilean transformation equations;

Determining whether a force on a charge or current is electric or magnetic in a given frame of reference;

Determining the nature of the fields observed by different observers.

Maxwell’s equations do not need to be described;


Qualitative treatment of electric and magnetic fields as measured by
observers in relative motion. Examples will include a charge moving in a
magnetic field or two charged particles moving with parallel velocities;

Students will be asked to analyse these motions from the point of view of
observers at rest with respect to the particles and observers at rest with
respect to the magnetic field.

Turning Points 5

(Basic relativity)


Turning Points 6

(Electric and magnetic fields)


Physics 6 Tutorial 1


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 determine the position and time coordinates of various events;


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
length contraction

Turning Points 6

(Special Relativity)


A.3  Space-time Diagrams (Core)

Spacetime diagrams;




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
constant velocity;


Spacetime diagrams can have t or ct on the vertical axis;


Examination questions may use units in which c = 1.

Physics 6 Tutorial 1

(Spacetime Diagrams)


Physics 6 Tutorial 18

A.4  Relativistic Mechanics  (Additional Higher)




Equations Link

Total energy and rest energy;


Relativistic momentum;

Particle acceleration;

Electric charge as an invariant quantity;


MeV c–2 as the unit of mass and MeV c–1 as the unit of momentum.

Describing the laws of conservation of momentum and conservation of
energy within special relativity

Determining the potential difference necessary to accelerate a particle to a given speed or energy;

Solving problems involving relativistic energy and momentum conservation in collisions and particle decays.

Applications will involve relativistic decays such as calculating the
wavelengths of photons in the decay of a moving pion [ π0 -> 2γ ];


The symbol m0 refers to the invariant rest mass of a particle;

The concept of a relativistic mass that varies with speed will not be used;


Problems will be limited to one dimension

Particles 4



Physics 6 Tutorial 19

(Relativistic Mechanics)

A.5  General Relativity (Additional Higher)

The equivalence principle;


The bending of light;

Gravitational redshift and the Pound–Rebka–Snider experiment;

Schwarzschild black holes;

Event horizons;

Time dilation near a black hole

Applications of general relativity to the universe as a whole.

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
and measured;


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.

Physics 6 Tutorial 1



Astrophysics 6

(Schwarzchild Radius)


Physics 6 Tutorial 20 - Pound Rebka Experiment


Physics 6 Tutorial 20

Gravitational Time Dilation


Option B  Engineering Physics

B.1  Rigid Bodies and Rotational Dynamics (Core)




Equations Link


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
when necessary;

Graphs will be limited to angular displacement–time, angular velocity–time and torque–time.

Engineering Physics 1


Engineering Physics 2

B.2  Thermodynamics (Core)

The first law of thermodynamics;

The second law of thermodynamics;


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
pV diagram when pressure is not constant.

Thermal Physics 4

(Laws of Thermodynamics)


Engineering Physics 3

(First Law)


Engineering Physics 4

(PV Diagrams)


Engineering Physics 5



Engineering Physics 6

(Second Law)



B.3 Fluids and Fluid Dynamics (Additional Higher)

Pascal’s principle;

Hydrostatic equilibrium;

The ideal fluid;


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
laminar fluid flow;

Solving problems involving Stokes’ law;

Determining the Reynolds number in simple situations

Ideal fluids will be taken to mean fluids that are incompressible and non-viscous
and have steady flows;

Applications of the Bernoulli equation will involve (but not be limited to) flow
out of a container, determining the speed of a plane (pitot tubes), and venturi tubes;

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 <103 will be taken to represent conditions for laminar flow

Materials 4

(Pressure, viscosity, and Stokes' Law)


Physics 6 Tutorial 10

(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;


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)




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
incident wavefront;

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
spherical diverging mirrors;

Only thin lenses are to be considered in this topic;

The lens-maker’s formula is not required;

Sign convention used in examinations will be based on real being positive (the “real-is-positive” convention)

Medical Physics 2



Astrophysics 1

(Lenses and Telescopes)


Waves 6

Curved mirrors

C.2  Imaging Instrumentation (Core)

Optical compound microscopes;

Simple optical astronomical refracting telescopes;

Simple optical astronomical reflecting telescopes;

Single-dish radio telescopes;

Radio interferometry telescopes;

Satellite-borne 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)


Astrophysics 3

(Radio Telescopes)


Turning Points 3


C.3 Fibre Optics (Core)

Structure of optic fibres;

Step-index fibres and graded-index 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 X-ray 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 X-ray imaging, including attenuation coefficient, half-value thickness, linear/mass absorption coefficients and techniques for improvements
of sharpness and contrast;

 Solving X-ray 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



Medical Physics 6



Medical Physics 7

(X-rays and CT Scanners)


Option D  Astrophysics

D.1  Stellar Quantities (Core)




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
and binary), planetary systems, constellations, stellar clusters (open and
globular), nebulae, galaxies, clusters of galaxies and super clusters of galaxies;

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)


Astrophysics 5




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
properties of stars in these regions;

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,
red giants, super giants and the instability strip (variable stars), as well as lines of constant radius;

HR diagrams will be labelled with luminosity on the vertical axis and
temperature on the horizontal axis;

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)


Astrophysics 6

(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
distances (and hence wavelengths) being stretched out is all that is required;

A qualitative description of the role of type Ia supernovae as providing evidence for an accelerating universe is required.


Astrophysics 7



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
an interstellar cloud may begin if M > Mj;

Students should be aware of the use of type Ia supernovae as standard candles.


Astrophysics 6

(Evolution of stars)


Nuclear Physics 7

(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)


Astrophysics 8


  That is it.