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3.9 Astrophysics

3.9.1 Telescopes

3.9.1.1 Astronomical telescope consisting of two converging lenses

3.9.1.2 Reflecting telescopes

Ray diagram to show the image formation in normal adjustment.


Angular magnification in normal adjustment.



Focal lengths of the lenses.


Astrophysics 1

Cassegrain arrangement using a parabolic concave primary mirror and convex secondary mirror.


Ray diagram to show path of rays through the telescope up to the eyepiece.


Relative merits of reflectors and refractors including a qualitative treatment of spherical and chromatic aberration.

Astrophysics 2

3.9.1.3 Single dish radio telescopes, I-R, U-V and X-ray telescopes

3.9.1.4 Advantages of large diameter telescopes

Similarities and differences of radio telescopes compared to optical telescopes. Discussion
should include structure, positioning and use, together with comparisons of resolving and
collecting powers.

Astrophysics 3

Minimum angular resolution of telescope.


Rayleigh criterion:

Collecting power is proportional to diameter2.


Students should be familiar with the rad as the unit of angle.


Comparison of the eye and CCD as detectors in terms of quantum efficiency, resolution, and
convenience of use.  No knowledge of the structure of the CCD is required.

Astrophysics 2

3.9.2 Classification of Stars

3.9.2.1 Classification by luminosity

3.9.2.2 Absolute magnitude, M

Apparent magnitude, m.

The Hipparcos scale.


Dimmest visible stars have a magnitude of 6.
 

Relation between brightness and apparent magnitude. Difference of 1 on magnitude scale is
equal to an intensity ratio of 2.56.


Brightness is a subjective scale of measurement.

Astrophysics 4

Parsec and light year.
Definition of
M , relation to m:

 

Astrophysics 4
 

3.9.2.3 Classification by temperature, black-body radiation

3.9.2.4 Principles of the use of stellar spectral classes

Stefan’s law and Wien’s displacement law.


General shape of black-body curves, use of Wien’s displacement law to estimate black-body
temperature of sources.


Experimental verification is not required.



 

Assumption that a star is a black body.
Inverse square law, assumptions in its application.


Use of Stefan’s law to compare the power output, temperature and size of stars:


Astrophysics 5

Description of the main classes:

O, B, A, F, G, K, M.

Temperature related to absorption spectra limited to Hydrogen Balmer absorption lines:
requirement for atoms in an
n = 2 state.

Astrophysics 5

3.9.2.5 The Hertzsprung-Russell (HR) diagram

3.9.2.6 Supernovae, neutron stars and black holes

General shape: main sequence, dwarfs and giants.


Axis scales range from –10 to +15 (absolute magnitude) and 50 000 K to 2 500 K (temperature)
or OBAFGKM (spectral class).


Students should be familiar with the position of the Sun on the HR diagram.


Stellar evolution: path of a star similar to our Sun on the HR diagram from formation to white
dwarf.

Astrophysics 6

Defining properties:

  • rapid increase in absolute magnitude of supernovae;

  • composition and density of neutron stars;

  • escape velocity > c for black holes.
     

Gamma ray bursts due to the collapse of supergiant stars to form neutron stars or black holes.


Comparison of energy output with total energy output of the Sun.


Use of type 1a supernovae as standard candles to determine distances. Controversy concerning
accelerating Universe and dark energy.


Students should be familiar with the light curve of typical type 1a supernovae.


Supermassive black holes at the centre of galaxies.
Calculation of the radius of the event horizon for a black hole, Schwarzschild radius
Rs:

Astrophysics 6

3.9.3 Cosmology

3.9.3.1 Doppler effect

3.9.3.2 Hubble’s law

for v c applied to optical and radio frequencies.
 

Calculations on binary stars viewed in the plane of orbit.
 

Galaxies and quasars.

Astrophysics 7

Red shift v = Hd


Simple interpretation as expansion of universe; estimation of age of universe, assuming
H is
constant.


Qualitative treatment of Big Bang theory including evidence from cosmological microwave background radiation, and relative abundance of hydrogen and helium.

Astrophysics 7

3.9.3.3 Quasars

3.9.3.4 Detection of exoplanets

Quasars as the most distant measurable objects.
Discovery of quasars as bright radio sources.


Quasars show large optical red shifts; estimation involving distance and power output.


Formation of quasars from active supermassive black holes.

Astrophysics 7

Difficulties in the direct detection of exoplanets.


Detection techniques will be limited to variation in Doppler shift (Radial velocity method) and the
transit method.


Typical light curve.

Astrophysics 7

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3.10 Medical physics

3.10.1 Physics of the eye

3.10.1.1 Physics of vision

3.10.1.2 Defects of vision and their correction using lenses

The eye as an optical refracting system, including ray diagrams of image formation.


Sensitivity of the eye; spectral response as a photodetector.


Spatial resolution of the eye; explanation in terms of the behaviour of rods and cones.

Med Phys 1

Properties of converging and diverging lenses; principal focus, focal length and power:



 

Myopia, hypermetropia, astigmatism.


Ray diagrams and calculations of powers (in dioptres) of correcting lenses for myopia and hypermetropia.
 

The format of prescriptions for astigmatism.

Med Phys 2

3.10.2 Physics of the ear

3.10.2.1 Ear as a sound detection system

3.10.2.2 Sensitivity and frequency response

Simple structure of the ear, transmission processes.

Med Phys 3

Production and interpretation of equal loudness curves.
Human perception of relative intensity levels and the need for a logarithmic scale to reflect this.
 

Definition of intensity.



where the threshold of hearing I0= 1.0 × 10−12 W m−2
 

Measurement of sound intensity levels and the use of dB and dBA scales; relative intensity levels of sounds.

Med Phys 3

3.10.2.3 Defects of hearing

 

 

 

The effect on equal loudness curves and the changes experienced in terms of hearing loss due to injury resulting from exposure to excessive noise or deterioration with age (excluding physiological changes).

Med Phys 3

3.10.3 Biological measurement

3.10.3.1 Simple ECG machines and the normal ECG waveform

 

 

Principles of operation for obtaining the ECG waveform; explanation of the characteristic shape of a normal ECG waveform.

Med Phys 4

3.10.4 Non-ionising imaging

3.10.4.1 Ultrasound imaging

3.10.4.2 Fibre optics and endoscopy

Reflection and transmission characteristics of sound waves at tissue boundaries, acoustic
impedance,
Z , and attenuation.
 

Advantages and disadvantages of ultrasound imaging in comparison with alternatives including safety issues and resolution.


Piezoelectric devices.


Principles of generation and detection of ultrasound pulses.


A-scans and B-scans.


Examples of applications.


Use of the equations:

Med Phys 5

Properties of fibre optics and applications in medical physics; including total internal reflection at the core–cladding interface.


Physical principles of the optical system of a flexible endoscope; the use of coherent and non- coherent
fibre bundles; examples of use for internal imaging and related advantages.

Med Phys 6

3.10.4.3 Magnetic Resonance (MR) Scanner

 

 

Basic principles of MR scanner:
• cross-section of patient scanned using magnetic fields
• protons initially aligned with spins parallel
• spinning hydrogen nuclei (protons) precess about the magnetic field lines of a superconductingmagnet
• 'gradient' field coils used to scan cross-section, causing excitation and change of spin state in
successive small regions
• protons excited during the scan emit radio frequency (RF) signals as they de-excite
• RF signals detected and the resulting signals are processed by a computer to produce a visual
image.


Students will not be asked about the production of magnetic fields used in an MR scanner, or about de-excitation relaxation times.

Med Phys 6

3.10.5 X-ray imaging

3.10.5.1 The physics of diagnostic X-rays

3.10.5.2 Image detection and enhancement

Physical principles of the production of X-rays; maximum photon energy, energy spectrum;
continuous spectrum and characteristic spectrum.


Rotating-anode X-ray tube; methods of controlling the beam intensity, the photon energy, the image sharpness and contrast, and the patient dose.

Med Phys 7

Flat panel (FTP) detector including X-ray scintillator, photodiode pixels, electronic scanning.


Advantages of FTP detector compared with photographic detection.


Contrast enhancement; use of X-ray opaque material as illustrated by the barium meal technique.


Photographic detection with intensifying screen and fluoroscopic image intensification; reasons for using these.

Med Phys 7

3.10.5.3 Absorption of X-rays

3.10.5.4 CT scanner

Linear coefficient m , mass attenuation coefficient mm , half-value thickness:



Differential tissue absorption of X-rays excluding details of the absorption processes.

Med Phys 7

Basic principles of CT scanner:
• movement of X-ray tube
• narrow, monochromatic X-ray beam
• array of detectors
• computer used to process the signals and produce a visual image.
 

Comparisons will be limited to advantages and disadvantages of image resolution, cost and safety issues. Students will not be asked about the construction or operation of the detectors.

Med Phys 7

3.10.6 Radionuclide imaging and therapy

3.10.6.1 Imaging techniques

3.10.6.2 Half-life

Use of a gamma-emitting radioisotope as a tracer; technetium-99m, iodine-131 and indium-111 and their relevant properties.


The properties should include the radiation emitted, the half-life, the energy of the gamma radiation, the ability for it to be labelled with a compound with an affinity for a particular organ.


The Molybdenum-Technetium generator, its basic use and importance.

PET scans.

Med Phys 8

Physical, biological and effective half-lives;

 

 

Definitions of each term.

Med Phys 8

3.10.6.3 Gamma camera

3.10.6.4 Use of high-energy X-rays

Basic structure and workings of a photomultiplier tube and gamma camera.

Med Phys 8

External treatment using high-energy X-rays. Methods used to limit exposure to healthy cells.

Med Phys 8

3.10.6.5 Use of radioactive implants

3.10.6.6 Imaging comparisons

Internal treatment using beta emitting implants.

Med Phys 8

Students will be required to make comparisons between imaging techniques. Questions will be
limited to consideration of image resolution, convenience and safety issues.

Med Phys 8

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3.11 Engineering physics

3.11.1 Rotational dynamics

3.11.1.1 Concept of moment of inertia

3.11.1.2 Rotational kinetic energy

for a point mass.

 

 

for an extended object.
 

Qualitative knowledge of the factors that affect the moment of inertia of a rotating object.
 

Expressions for moment of inertia will be given where necessary.

Eng Phys 1

 

Factors affecting the energy storage capacity of a flywheel.


Use of flywheels in machines.


Use of flywheels for smoothing torque and speed, and for storing energy in vehicles, and in machines used for production processes.

Eng Phys 1

3.11.1.3 Rotational motion

3.11.1.4 Torque and angular acceleration

Angular displacement, angular speed, angular velocity, angular acceleration:

 


Representation by graphical methods of uniform and non-uniform angular acceleration.


Equations for uniform angular acceleration:

 


 

Students should be aware of the analogy between rotational and translational dynamics.

Eng Phys 1

Eng Phys 1

3.11.1.5 Angular momentum

3.11.1.6 Work and power


Conservation of angular momentum.


Angular impulse = change in angular momentum;

 

 

where T is constant.
 

Applications may include examples from sport.
 

Eng Phys 2

 

Awareness that frictional torque has to be taken into account in rotating machinery.

Eng Phys 2

3.11.2 Thermodynamics and engines

3.11.2.1 First law of thermodynamics

3.11.2.2 Non-flow processes

 

where Q is energy transferred to the system by heating, Δ U is increase in internal energy and W is work done by the system.


Applications of first law of thermodynamics.

Eng Phys 3

Isothermal, adiabatic, constant pressure and constant volume changes.

 


 


 

Application of first law of thermodynamics to the above processes.

Eng Phys 3

3.11.2.3 The p–V diagram

3.11.2.4 Engine cycles

Representation of processes on p–V diagram.


Estimation of work done in terms of area below the graph.


Extension to cyclic processes: work done per cycle = area of loop


Expressions for work done are not required except for the constant pressure case,

 

Eng Phys 4

Understanding of a four-stroke petrol engine cycle and a diesel engine cycle, and of the corresponding indicator diagrams.


Comparison with the theoretical diagrams for these cycles; use of indicator diagrams for predicting and measuring power and efficiency.


input power = calorific value × fuel flow rate


Indicated power = area of p−V loop × no. of cycles per second × no. of cylinders


Output or brake power:


friction power = indicated power – brake power
 

Engine efficiency; overall, thermal and mechanical efficiencies.

 


 

A knowledge of engine constructional details is not required.


Questions may be set on other cycles, but they will be interpretative and all essential information will be given.

Eng Phys 5

3.11.2.5 Second Law and engines

3.11.2.6 Reversed heat engines

Impossibility of an engine working only by the First Law.


Second Law of Thermodynamics expressed as the need for a heat engine to operate between a source and a sink.


 


 

Reasons for the lower efficiencies of practical engines.


Maximising use of
W and QH for example in combined heat and power schemes.

Eng Phys 6

Basic principles and uses of heat pumps and refrigerators.

 


A knowledge of practical heat pumps or refrigerator cycles and devices is not required.


Coefficients of performance:

 

Eng Phys 6

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3.12 Turning points in physics

3.12.1 The discovery of the electron

3.12.1.1 Cathode rays

3.12.1.2 Thermionic emission of electrons

Production of cathode rays in a discharge tube.

Turning Points 1

The principle of thermionic emission.


Work done on an electron accelerated through a pd V

 

Turning Points 1

3.12.1.3 Specific charge of the electron

3.12.1.4 Principle of Millikan’s determination of the electronic charge, e

Determination of the specific charge of an electron

by any one method.

 

Significance of Thomson’s determination of

 


Comparison with the specific charge of the hydrogen ion.

Turning Points 1

Condition for holding a charged oil droplet, of charge Q, stationary between oppositely charged parallel plates.
 


Motion of a falling oil droplet with and without an electric field; terminal speed to determine the mass and the charge of the droplet.


Stokes’ Law for the viscous force on an oil droplet used to calculate the droplet radius.



 

Significance of Millikan’s results.
 

Quantisation of electric charge.

Turning Points 2

3.12.2 Wave-Particle duality

3.12.2.1 Newton’s corpuscular theory of light

3.12.2.2 Significance of Young’s double slits experiment

Comparison with Huygens’ wave theory in general terms.


The reasons why Newton’s theory was preferred.

Turning Points 3

Explanation for fringes in general terms, no calculations are expected.


Delayed acceptance of Huygens’ wave theory of light.

Turning Points 3

3.12.2.3 Electromagnetic waves

3.12.2.4 The discovery of photoelectricity

Nature of electromagnetic waves.


Maxwell’s formula for the speed of electromagnetic waves in a vacuum


where
eo is the permeability of free space and m0 is the permittivity of free space.


Students should appreciate that
e0 relates to the electric field strength due to a charged object in free space and mo relates to the magnetic flux density due to a current-carrying wire in free space.


Hertz’s discovery of radio waves including measurements of the speed of radio waves.


Fizeau’s determination of the speed of light and its implications.

Turning Points 3

(Electromagnetic Waves)

 

Turning Points 5

(Fizeau's experiment)

The ultraviolet catastrophe and black-body radiation.


Plank’s interpretation in terms of quanta.


The failure of classical wave theory to explain observations on photoelectricity.


Einstein’s explanation of photoelectricity and its significance in terms of the nature of electromagnetic radiation.

Turning Points 4

3.12.2.5 Wave–particle duality

3.12.2.6 Electron microscopes

de Broglie’s hypothesis:



 

Low-energy electron diffraction experiments; qualitative

explanation of the effect of a change of electron speed on the diffraction pattern.

Turning Points 4

Estimate of anode voltage needed to produce wavelengths of the order of the size of the atom.


Principle of operation of the transmission electron microscope (TEM).


Principle of operation of the scanning tunnelling microscope (STM).

Turning Points 4

3.12.3 Special relativity

3.12.3.1 The Michelson-Morley experiment

3.12.3.2 Einstein’s theory of special relativity

Principle of the Michelson-Morley interferometer.


Outline of the experiment as a means of detecting absolute motion.


Significance of the failure to detect absolute motion.


The invariance of the speed of light.

Turning Points 5

The concept of an inertial frame of reference.


The two postulates of Einstein’s theory of special relativity:
1. physical laws have the same form in all inertial frames
2. the speed of light in free space is invariant.

Turning Points 6

3.12.3.3 Time dilation

3.12.3.4 Length contraction

Proper time and time dilation as a consequence of special relativity.


Time dilation:


Evidence for time dilation from muon decay.

Turning Points 6

Length of an object having a speed v

 

Turning Points 6

3.12.3.5 Mass and energy

 

Equivalence of mass and energy:

 


Graphs of variation of mass and kinetic energy with speed.


Bertozzi’s experiment as direct evidence for the variation of kinetic energy with speed.

Turning Points 6

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3.13 Electronics

3.13.1 Discrete semiconductor devices

3.13.1.1 MOSFET

(metal-oxide semiconducting field-effect transistor)

3.13.1.2 Zener diode

Simplified structure, behaviour and characteristics.


Drain, source and gate.


VDS , VGS , IDSS , and Vth


Use as a switch, use as a device with a very high input resistance.


Use in N-channel, enhancement mode only is required.

Electronics 1

Characteristic curve showing zener breakdown voltage and typical minimum operating current.


Anode and cathode.


Use with a resistor as a constant voltage source.
Use to provide a reference voltage.


Use as a stabiliser is not required.

Electronics 2

3.13.1.3 Photodiode

3.13.1.4 Hall effect sensor

Characteristic curves and spectral response curves.


Use in photo-conductive mode as a detector in optical systems.


Use with scintillator to detect atomic particles.

Electronics 3

Use as magnetic field sensor to monitor attitude.


Use in tachometer.


Principles of operation are not required.

Electronics 4

3.13.2 Analogue and digital signals

3.13.2.1 Difference between analogue and digital signals

 

Bits, bytes.


Analogue-to-digital conversion:
• sampling audio signals for transmission in digital form
• conversion of analogue signals into digital data using two voltage levels
• quantisation
• sampling rate
• effect of sampling rate and number of bits per sample on quality of conversion
• advantages and disadvantages of digital sampling
• process of recovery of original data from noisy signal
• effect of noise in communication systems.
 

Pulse code modulation.


Students should appreciate the use of a variety of sensors to collect analogue data.


The ability to carry out binary arithmetic is not required.

 Knowledge of binary numbers 1 to 10 is adequate.

Electronics 5

3.13.3 Analogue signal processing

3.13.3.1 LC resonance filters

3.13.3.2 The ideal operational amplifier

Resonant frequency


Only parallel resonance arrangements are required.


Analogy between LC circuit and mass–spring system.

  • Inductance as mass analogy.

  • Capacitance as spring analogy.


Derivation of the equation is not required.
 

Energy (voltage) response curve.


The response curve for current is not required.


Q factor:

 
fB is the bandwidth of the filter at the 50% energy points.

Electronics 6

Operation and characteristics of an ideal operational amplifier:
• power supply and signal connections
• infinite open-loop gain
• infinite input resistance.


Open-loop transfer function for a real operational amplifier:

 

 

Use as a comparator.
 

The operational amplifier should be treated as an important system building block.

Electronics 7

3.13.4 Operational amplifier in:

3.13.4.1 inverting amplifier configuration

3.13.4.2 non-inverting amplifier configuration

Derivation of:

 

calculations.


Meaning of virtual earth, virtual-earth analysis.

Electronics 8A

 

Derivation is not required.

Electronics 8B

3.13.4.3 summing amplifier configuration

3.13.4.4 Real operational amplifiers

Summing Amplifier:

 

 

Difference Amplifier:

 

 

Derivations not required

Electronics 8 C

(Summing Amp)

 

Electronics 8 D

(Difference Amp)

Limitations of real operational amplifiers.


Frequency response curve.


gain × bandwidth = constant for a given device.

Electronics 7

3.13.5 Digital signal processing

3.13.5.1 Combinational logic

3.13.5.2 Sequential logic

Use of Boolean algebra related to truth tables and logic gates.
 


Identification and use of AND, NAND, OR, NOR, NOT and EOR gates in combination in logic circuits.


Construction and deduction of a logic circuit from a truth table.


The gates should be treated as building blocks. The internal structure or circuit of the gates is not
required.

Electronics 9

Counting circuits:
• Binary counter
• BCD counter
• Johnson counter.


Inputs to the circuits, clock, reset, up/down.


Outputs from the circuits.


Modulo-
n counter from basic counter with the logic driving a reset pin.


The gates should be treated as building blocks. The internal structure or circuit of the gates is not
required.

Electronics 10

3.13.5.3 Astables

 

The astable as an oscillator to provide a clock pulse.


Clock (pulse) rate (frequency), pulse width, period, duty cycle, mark-to-space ratio.


Variation of running frequency using an external
RC network.


Knowledge of a particular circuit or a specific device (e.g. 555 chip) will not be required.

Electronics 11

3.13.6 Data communication systems

3.13.6.1 Principles of communication systems

3.13.6.2 Transmission media

Communication systems, block diagram of 'real time' communication system.


Only the purpose of each stage is required.
 

Electronics 12

Transmission-path media: metal wire, optic fibre, electromagnetic (radio, microwave).


Ground wave, refraction and reflection of sky waves, diffraction of long-wavelength radiation around the Earth’s surface.


Satellite systems and typical transmission frequencies.


Students should recognise that up- and down-links require different frequencies so that the receivers are not de-sensed.


Advantages and disadvantages of various transmission media. Students should consider data transmission rate, cost, and security issues.

Electronics 12

3.13.6.3 Time-division multiplexing

3.13.6.4 Amplitude (AM) and Frequency Modulation (FM) techniques

Basic principles of time-division multiplexing.

Electronics 13

Principles of modulation; bandwidth.


Carrier wave and information signal.


Details of modulation circuits for modulating a carrier signal with the information signal will not be required.


Graphical representation of both AM and FM modulated signals.


A detailed mathematical treatment is not required.


Students will be expected to identify the carrier frequency and the information frequency from a graph of the variation of signal voltage with time.


Bandwidth requirements of simple AM and FM:
 


 

Data capacity of a channel.
 

Comparison of bandwidth availability for various media.

Electronics 14

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