Comprehensive IB Physics SL & HL Syllabus

Time is used to distinguish different events. Second (s) is the SI unit of time. 

Mass defines how much matter the object consists of. Kilogram (kg) is the SI unit.

Density is the ratio of mass to the volume occupied by an object. This ratio is the same for objects made of the same material.

Displacement is the distance moved in a particular direction. It defines the movement of an object. 

An angle is formed when two lines intersect. Radian (rad) is the SI unit of angular measurement. 

Significant figures: The first non-zero digit from the left is the most significant digit.

To reduce errors, the mean of all measurements is taken. 

Uncertainties in gradients: To find the uncertainty in gradient, steepest and shallowest lines passing through all the error bars are drawn. Then, the uncertainty is half the range of gradients.

The uncertainty of the form ∆x is absolute uncertainty. Fractional uncertainty is ∆𝑥/x. 

Vectors have magnitude and direction.

Addition of Vectors: Graphical and Analytical Approach

Resolving Vectors: Every vector can be resolved into a number of vectors such that when those vectors are added, the result in the original vector.

Subtracting Vectors: The vector to be subtracted is written as a negative of the vector and added to the other vector.

Velocity is a vector quantity: displacement per unit time

Speed is a scalar quantity: distance traveled per unit time

Acceleration is the rate of change of velocity.

The “suvat” equations of motion:
Here s is distance, u is initial velocity, v is final velocity, t is time taken and a is the acceleration of the body

Projectile motion – When an object moves in a projectile motion as a result of gravitational pull, it travels along a curved route

Fluid resistance and terminal speed – There are opposing forces acting on an object when it moves through a fluid (a gas or a liquid)

Free body diagrams: Free body diagrams are drawn for a single body indicating all the forces acting on the body.

Translational equilibrium: A system is said to be in translational equilibrium if the net force acting on the system is zero.

Gravitational force (weight): The force exerted by the earth on objects 

Friction: There are two types of friction. Static and dynamic. They are denoted by coefficients

Newton’s Laws of Motion

Energy is the quantity which enables a body to do work on another body. 

Law of conservation of energy: Energy can neither be created nor destroyed but can only be transferred from one form to another form.

In a collision, momentum and energy gets exchanged between objects. There are 2 types: Elastic and Inelastic

Power is the work done per unit time.

Impulse is the change in momentum of a body.

Elastic and Inelastic Collision – If there is no kinetic energy lost in the impact, the collision is said to be perfectly elastic. A collision is considered to be inelastic if any of the kinetic energy is converted to another kind of energy during the collision.

Conservation of linear momentum – The momentum never changes in an isolated collection of objects; that is, the total momentum of a system remains constant.

Temperature is the degree of hotness or coldness of a body. It is a scalar.

At absolute zero temperature (0K), the molecular motion stops completely.

Heat transfer can happen in three ways: Conduction, Convection and Radiation

Thermal capacity of a body is the amount of heat required to raise its temperature by 1 ̊C

The specific heat capacity of a material if the amount of heat required to raise the temperature of unit mass of substance by 1 ̊C.

Specific latent heat of vaporisation is the amount of heat required to convert unit mass of substance from liquid to gas at constant temperature.

Specific latent heat of fusion is the amount of heat required to convert unit mass of substance from solid to liquid at constant temperature.

Assumptions made for developing theories for ideal gasses

The total kinetic energy of N molecules of gas at temperature T is 3/2 𝑁𝑘𝑇. Here k is the Boltzmann constant and has a value of 1.38×10-23JK-1.

Pressure: The pressure of a gas is the force exerted per unit area. It is a scalar and is uniform
through the gas

Boyle’s law: The pressure of a fixed amount of gas at constant temperature is inversely proportional to its volume.

Charles law: For a fixed amount of mass at constant pressure, the volume occupied by a gas is directly proportional to absolute temperature.

Gay-Lussac’s law: The pressure of a constant amount of gas contained with constant volume is directly proportional to the absolute temperature of gas.

R is called universal gas constant and has a value of 8.314 J mol-1 K-1

Amplitude (A): maximum displacement from equilibrium position.

Time period (T): the time taken for a complete oscillation.

Frequency (f): the number of oscillations per unit time.

Mechanical waves: Which require a material medium to travel.

Electromagnetic waves: Which can travel through vacuum.

Transverse waves: The direction of vibration of waves is perpendicular to the direction of propagation of waves forming a series of crests and troughs.

Longitudinal waves: The direction of vibration of waves is parallel to the direction of propagation of waves forming a series of compressions and rarefactions.

The velocity of wave is given by c=fλ

Electromagnetic waves travel with varying electric and magnetic fields. They travel with a velocity of 3 × 108ms-1 in vacuum and exhibit all properties of transverse waves

The principle of superposition says that, when two waves meet, the total displacement is the vector sum of their individual displacements.

Polarization is a process in which the direction of oscillation is restricted to a plane perpendicular to the direction of propagation.

Snell’s law: For light going from medium 1 to medium 2, 𝑠𝑖𝑛𝜃1 / 𝑠𝑖𝑛𝜃2 = 1𝑛2 

Refractive index = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔h𝑡 𝑖𝑛 𝑣𝑎𝑐𝑢𝑢𝑚 / 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔h𝑡 𝑖𝑛 medium = 𝑐/v

The angle of incidence for which the angle of refraction of a light ray traveling from an optically denser medium to rarer medium reaches the right angle is called critical angle.

When the angle of incidence is greater than the critical angle, the light gets completely reflected without being refracted. This phenomenon is called total internal reflection.

Traveling waves are formed when the positions of maximum and minimum amplitude move through the medium

Nodes are the points at which the displacement is always zero.

Anti-nodes are the points at which the displacement varies from a maximum in one direction to a maximum in another direction

When the string is excited from zero frequency, a standing wave with a single loop is formed at a particular frequency with half the wavelength. This is called the first harmonic.

Electric forces: This force is attractive if the objects are of opposite charge and repulsive if the objects are of same charge.

𝜖0 is the permittivity of free space. It has a value of 8.854 × 10−12𝐶2𝑁−1𝑚−2

The electric field strength of a charge is the force exerted by the charge on a unit charge

The electric field is a vector and the resultant field due to two charges is the vectorial sum of two fields due to charges at that point

Metals: In metals, the free electrons are charge carriers. The electric current is due to the movement of electrons.

Drift speed: The charge carriers move at extremely slow speed when a current flows through a conductor.

A device which generates electrical energy produces Electromotive force. Emf is analogous to potential difference. 

In few liquids and gasses, the presence of free ions allows for the conduction of electricity.

Electric power: The power transmitted when a current I flows across a pd V is P = VI

Electronvolt (eV) is a unit of energy obtained by the product of charge of an electron and a volt. This value is equal to 1.6 × 10−19𝐽

Kirchhoff’s Laws: First law: It is a consequence of conservation of charge. It states that at any junction, the sum of incoming currents is equal to sum of outgoing currents.

Kirchhoff’s Laws: Second law: It is a consequence of law of conservation of energy. It states that the sum of all variations of potential in a closed loop is zero.

Electrical resistance of a component is defined as 𝑅 = 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑐𝑟𝑜𝑠𝑠 𝑡h𝑒 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 / 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑖𝑛 𝑡h𝑒 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡. The SI unit of resistance is ohm (Ω).

Ohm’s Law: The potential difference across a component changes linearly with current when the physical conditions of the component do not change.

Digital meters: Shows the value of pd across its terminals digitally.

Ammeter: It measures the current in the circuit. It is connected in series with the circuit and ideally there is no drop in pd across it.

Voltmeter: It measures the pd across a component. It is connected in parallel to the component where the pd has to be measured and ideally, no current passes through it.

Resistivity is the resistance of a material of unit length of unit area of cross section.

Semiconducting diodes are made such that it allows current flow in only one direction.

Thermistors exhibit high sensitivity to temperature. Its resistance falls with increase in temperature and can be used to measure temperature.

A capacitor is effectively two parallel conducting plates separated by a distance.

Primary cells are consumed completely after a single use and cannot be used multiple times.

Secondary cells can be charged using electrical energy when consumed multiple times. 

The capacity of a cell is the ability of the cell to store charge. 

A secondary cell can be charged by connecting an external current source of pd higher than that of highest pd that the cell can exhibit.

Fleming’s left-hand rule: This is used to find the direction of force on a wire placed in a magnetic field.

The magnetic field strength of a field is given by 𝐵=𝐹 / 𝐼𝐿

Magnetic force is when electrically charged particles that are in motion, exhibit either attraction or repulsion.

Angular velocity (ω): The angle swept per unit time. Unit is radian s-1

Time period (T): The time required by the body to complete a revolution

Frequency (f): Number of revolutions per unit time

If the speed of an object remains constant during the travel in a circle, then it is called uniform circular motion. Although the speed remains constant, the velocity changes due to change in direction. So, there must be acceleration. This acceleration is called centripetal acceleration and is directed towards the centre. 

The force that causes centripetal acceleration is centripetal force.

G is called the universal gravitational constant and has a value 6.6742 × 10−11𝑚3𝑘𝑔−1𝑠−2

The force per unit mass that a small point mass experiences at a particular location determines the strength of the gravitational field there.

Atomic spectrum is the series of wavelengths of light released when a gas at low pressure is subjected to high voltages

Discrete energy levels: Energy is received or emitted as a photon as an electron moves from one energy level to another.

A nucleus loses energy through the haphazard process of radioactive decay by producing radiation.

Half life is the time taken for the number of nuclei to fall to half the initial number

Background Radiation: It is the radioactive noise emitted by objects in a place which interferes with the results of an experiment

Absorption spectrum is similar to emission spectrum except the energy is absorbed in place of emission by the gas

Bohr’s model of atoms revolves around the assumption that an electron does not emit any radiation when it revolves in orbits of certain radius

De Broglie’s hypothesis explains the dual nature of matter-matter exhibits wave-like nature

Heisenberg’s uncertainty principle puts a limit to the theoretical resolution for the measurement of position and momentum simultaneously.

The mass of an atom is approximately the sum of the mass of neutrons and protons in the nucleus. 

The mass of a neutron is approximately the same as that of a proton.

Binding energy is the energy released when the nucleus is put together from its constituent protons and neutrons.

The binding energy released per nucleon determines the stability of the neutron.

Mass defect: The difference between the mass of an atom and the sum of mass of its constituent parts

Nuclear fusion: It is the fusion of two nuclei to form a bigger one

Nuclear fission: A nucleus splits into two stable nuclei

Protons and neutrons being nucleons, take part in nuclear interactions.

Quarks are fundamental constituents of matter and are defined as elementary particles. 

Hadrons are heavy particles that take part in nuclear interactions. Protons and neutrons fall in this category.

Leptons are light particles. Electrons and neutrinos fall in this category. 

Feynman diagrams represent the exchange particle theory in a diagrammatic manner

Particles are assigned baryon and lepton numbers which are also conserved along with charge in nuclear reactions.

Spin is similar to electron spin in an atom which can be either ½  or 1 ½  for baryons and 0 or 1 for mesons.

Strangeness is another quantum number which is not conserved in weak interactions

Quark confinement: Quarks are confined by very strong attractive forces

Gluons are the exchange particles of color force. Gluons have a combination of color and anti-color. 

Higgs Boson is a fundamental particle created by the quantum excitation of the Higgs field in the Standard Model of particle physics.

Secondary source is obtained by transforming a primary fuel.

Renewable sources like biomass replenish themselves in short periods of time or have unlimited supply such as solar, wind or water

Non-renewable resources are consumed much faster compared to the rate at which they are formed

Sankey diagram is a diagrammatic representation of flow of energy in a device or a process

Convection occurs due to the difference in densities of a liquid at different temperatures

Radiation is the transfer of energy in the form of electromagnetic waves

Black-bodies are ideal bodies that absorb all the radiation incident on them

Wein’s displacement law: The wavelength at which the intensity is maximum (𝜆𝑚𝑎𝑥) emitted by a black body at temperature (T) is given by 𝜆𝑚𝑎𝑥 = 𝑏𝑇

Stefan-Boltzmann law: The total power emitted by a black body at a temperature T is given by 𝑃 = 𝜎𝐴𝑇^4

The albedo of a surface is the ratio of energy reflected by it to the energy incident on it

The greenhouse effect is the absorption and emission of infrared and ultraviolet radiation by gasses in atmosphere and leading to a higher temperature

Global warming is the increase in average temperature of earth over years primarily due to human actions. 

The total energy of the object always remains constant in absence of dissipative forces.

Dispersion: The angle of refraction is different for different wavelengths of light. So, white light disperse into its constituent wavelengths when passed through a prism.

Single slit diffraction: When light is diffracted by a single slit that is almost the same size as the light’s wavelength, unique diffraction patterns are produced.

Young’s double-slit experiment

Water waves follow all laws and exhibit all properties exhibited by light like reflection, refraction, interference and diffraction.

Electric potential is the work done on a unit charge to move it from a point of zero reference (infinity) to the point of concern

The gravitational field of an object is the region in which another object experiences gravitational force.

Gravitational field strength of a mass is the force acting on a unit mass due to the mass. 

Field lines are lines drawn in the direction that a mass would accelerate if placed in the field.

The gravitational potential at a point is the work done per unit mass in taking a point mass from zero potential (reference) to the point of concern.

The lines along which potential energy does not change are called equipotential lines. They are perpendicular to field lines.

Potential difference between two points is the work done to move a unit charge between two points.

The escape speed of a planet is the minimum speed with which a body projected would escape the gravitational field of the planet.

Orbital motion, orbital speed and orbital energy

Kepler’s third law: The orbital period T of a planet revolving around a sun in a circular path of radius r is related to orbital radius as 𝑇2 ∝ 𝑟3

Forces and inverse-square law behavior: Both fields obey an inverse-square law, where the force between the objects is inversely proportional to the distance between them squared.

Faraday’s law: The magnetic flux of a field across a cross-section is ∫ 𝐵 𝑐𝑜𝑠𝜃 𝑑𝐴. 𝜃 is the angle made by the area element with the magnetic field

Lenz’s law: The direction of induced emf is such that it opposes the change in flux

Diode bridges: A diode bridge is a bridge rectifier circuit of four diodes that is used in the process of converting alternating current (AC) from the input terminals to direct current (DC, i.e. fixed polarity) on the output terminals.

Alternating current generators

A transformer consists of two coils wound around a single core. A transformer is used to increase or decrease the pd at which the power is transmitted.

Rectification is the process of converting AC to DC. This is done by using diodes which are semiconductors doped on one side as P-type and the other as N-type.

Half wave rectification can be achieved with a single diode 

Full wave rectification involves a bridge of rectifiers 

Dielectric materials: A dielectric material is a non-metallic substance having a high specific resistance, a negative temperature coefficient of resistance and a high insulating resistance. 

Capacitors in series and parallel

Resistor-capacitor (RC) series circuits

Photoelectric effect describes the phenomenon of electrons ejected out of the metal when a light of certain minimum frequency is incident on the metal

Matter waves

Pair production: The conversion of a photon into an electron-positron pair on its interaction with the strong electric field surrounding a nucleus

Pair annihilation: Annihilation of matter is the opposite of pair creation, where an electron and a positron join to form two photons

Tunneling is a passage of minute particles through seemingly impassable force barriers

Nuclear energy levels

Neutrino takes part in weak interactions.

The law of radioactive decay and the decay constant

Types of radioactive decay: Alpha, Beta and Gamma

Translation: Step from one reference frame to another – Position is relative.

Rotation: The set of axes can be rotated to form another set – Direction is relative.

Boost: One frame can move with a constant velocity relative to another – Velocity is relative.

Maxwell developed four equations that describe all aspects of electromagnetism.

Galilean transformation equations

The Lorentz transformation and factor

Rest mass:The rest mass is the mass of a particle in frame which is at rest with respect to the particle. 

Proper time: The time interval between two events in a stationary frame (Δ𝑡0) is called proper time.

Proper length: Proper length (𝐿0) is the length of an object measured from a frame which is at rest with respect to object.

Using spacetime diagrams, it can be shown that simultaneous events occurring in one frame are not simultaneous in all frames.

The twin paradox

Particle acceleration

Relativistic momentum: The momentum of an object moving at relativistic velocity

Bending of light near masses: Light changes its path due to curvature of spacetime influenced by masses. 

For a mass M, the Schwarzschild radius is given by 𝑅 = 2𝐺𝑀 / c^2 . If the whole mass falls within a sphere of this radius, then it forms a black hole

Pound-Rebka-Snider experiment 

Time dilation

Moment of inertia is the inertial equivalent of mass in rotational dynamics.

Torque causes rotation. The maximum torque (Fr) acts on a body when the force applied is perpendicular to the radius.

A couple is said to act on a body when two forces of equal magnitude act on the body in opposite directions. 

Rotational equilibrium: A body is said to be in rotational equilibrium if the net torque acting on it is zero. 

Angular momentum of a body of moment of inertia I rotating at an angular velocity 𝜔 is 𝐼𝜔.

When no external torque acts on a system, the total angular momentum of the system remains constant. This is called the law of conservation of angular momentum.

The first law of thermodynamics states that energy can neither be created nor destroyed but can only be transformed from one form to another form.

Types of processes: Isobaric, Isochoric, Isothermal and Adiabatic

A cyclic process is one in which the initial state is the same as the final state. On a P-V diagram, it forms a closed loop.

A carnot cycle is the most efficient cycle which converts heat to work working between two fixed temperature reservoirs which provide and take heat during the cycle.

Kelvin-Planck Statement and the Clausius Statement of the second law of thermodynamics.

Pascal’s principle: The pressure applied at one point in an enclosed point under equilibrium conditions is equally transmitted to all points in the fluid.

Archimedes’ principle: The buoyancy acting on an object immersed in a fluid is equal to the weight of fluid displaced by the object.

In a streamlined flow, the motion of one particle passing through a point is similar to the motion of all points passing through that point. This is also called laminar flow.

Bernoulli’s Equation and effect: as the speed of a moving fluid increases (liquid or gas), the pressure within the fluid decreases

Viscosity impedes the relative motion between layers of fluids. It is measured in terms of coefficient of viscosity (𝜂).

Stokes law: When a sphere of radius r falls through a fluid of coefficient of viscosity 𝜂 at a velocity v, the viscous force acting on it is 6𝜋𝜂𝑟𝑣.

Turbulent Flow and Reynolds Number

Forced vibration: When an oscillating system is subjected to a sinusoidal force, then the system oscillates with the frequency of force rather than its natural frequency.

Resonance: When the driving frequency of the force matches with the natural frequency of the system, then the amplitude of vibration reaches a maximum.

Electrical resonance: A resistor, conductor and an inductor connected in series forms a damped oscillating system.

Pole (P): The geometric centre of the reflecting or refracting surface is called pole.

Centre of curvature: The centre of the sphere that forms a part of the reflecting or refracting surface.

Principal axis: The line passing through the pole and centre of curvature is the principal axis

Concave mirrors are converging mirrors and convex mirrors are diverging mirrors. Double convex lenses are converging lenses and double concaves are diverging.

Chromatic Aberrations and viewing the image at the point of convergence of green light. This point is called the circle of least confusion.

Astronomical reflecting telescopes: Large parabolic mirrors are used to focus light from distant objects.

Types of telescopes

Types of optical fibres used

The pulse passing through the fibre suffers attenuation – loss of power and dispersion – spreading out of pulse.

The main causes of attenuation are absorption and scattering 

Dispersion is due to material dispersion and waveguide dispersion.

I is the intensity of the attenuated beam and I0 is the intensity of the incident beam. 𝜇1 is the linear absorption coefficient.

The intensity of attenuated beam can also be expressed in terms of mass absorption coefficient (𝜇𝑚) and density (𝜌)

Computed Tomography (CT) and Ultrasound in Medicine

Acoustic impedance is a measure of how easy it is to transmit the signal through various materials.

Nuclear magnetic resonance in medicine (MRI): Magnetic resonance imaging involves the use of nuclear magnetic resonance for diagnosis of the brain and central nervous system.

A planet is a celestial object that is in orbit around the sun.

Stellar distances – distances between celestial objects 

Light year: The distance traveled by light in vacuum in one year.

Astronomical unit: Average distance between earth and sun.

Parsec(pc): If the angle subtended between two points separated by a distance 1A.U and a distant star is one arcsec, the distance to the star is 1 parsec.

Apparent brightness (b) is the brightness of the star as perceived on earth.

Luminosity (L) of a star is the total energy emitted by the star per unit time.

Absorption spectra: The dark lines in the spectra of a star can be used to determine the gasses present in the outer layer of a star. 

Mass-Luminosity Relationship

Stellar parallax: Parallax is the change in angle when an object is viewed from two different places.

Birth of the star: 

• • Stars start as giant molecular clouds. These clouds consist of swirling dust and gases, especially hydrogen. 
  • The shockwave from a nearby exploding star or collision between two clouds overcomes the pressure of gasses and the cloud begins to collapse. Jeans criterion
  • The core of such a star (protostar) becomes so dense and hot that hydrogen undergoes nuclear fusion to become helium.
• Main sequence

• Hydrogen fusion occurs and the star then transforms into a red giant.

Chandrasekhar and Oppenheimer-Volkhoff limit

Hubble’s law: The recessional velocity of a galaxy is directly proportional to its distance. Hubble constant.

Early development of the universe

Cosmic Microwave Background (CMB) and its characteristics

Nucleosynthesis off the main sequence

Hydrogen fusion occurs and the star then transforms into a red giant.

• Sun sized stars: The core continues to get smaller until electron degeneracy prevents it. It becomes a white dwarf. May cause a type 1a supernova when the white dwarf collapses (happens only when it exceeds the Chandrasekar limit)
• Large stars: The fusion happens until iron is produced. When the core runs out of nuclear fuel, it collapses. The explosion blows away outer layers and what remains is the core now called a neutron star. This is called a type II supernova. 

Rotation curves and the mass of galaxies

Dark matter – Matter that cannot be observed

Fluctuations in the CMB – Anistropy

The frequencies of light from distant galaxies were measured and were found to be red shifted. This is called Cosmological red shift

The density parameter (Ω) is used instead of density. This is the ratio of density to the critical density.

Dark energy – It is the increase in potential energy that causes kinetic energy to decrease and causes the rate to decrease. If there is some sort of negative energy, then it would cause the opposite effect. This energy is termed dark energy. It has density and can be represented with a density parameter (R^).