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AS Module 6A 

In this option, fundamental physical principles are applied to the study and interpretation of the Universe. Students will gain deeper insight into the behaviour of objects at great distances from Earth and discover the ways in which information from these objects can be gathered. The underlying physical principles of the optical and other devices used are covered and some indication given of the new information gained by the use of radio astronomy. Details of particular sources and their mechanisms are not required.

15.1 Lenses and optical telescopes

15.1.1 Lenses  Principal focus, focal length of converging lens
power = 1/f
Formation of images by a converging lens
Ray diagrams

1/u  +  1/v  =  1/f

15.1.2 Astronomical telescope consisting of two converging lenses Ray diagram to show the image formation in normal adjustment
Angular magnification in normal adjustment

M =        angle subtended by image at eye
         angle subtended by object at unaided eye

Focal lengths of the lenses

M = f

15.1.3 Reflecting telescopes Focal point of concave mirror
Cassegrain arrangement, ray diagram to show path of rays through
the telescope as far as the eyepiece.
Relative merits of reflectors and refractors including a qualitative
treatment of spherical and chromatic aberration.
15.1.4 Resolving power  Appreciation of diffraction pattern produced by circular aperture, 
Airy disc
Resolving power of telescope, Rayleigh criterion,

q  »  λ

15.1.5 Charge coupled device Structure and operation of the charge coupled device
Quantum efficiency of pixel > 70%

15.2 Radio astronomy

15.2.1 Single dish radio telescopes, general principles and resolving power Similarities with optical telescopes: objective, mirror, detector,
µ diameter 2 , tracking of source

Differences from optical telescopes: resolving power, limit of resolution 
q  »  λ
need for scanning to build up image

Objective diameter, precision of about λ /20 needed in shape of dish. 
Use of wire mesh

15.3 Classification of stars

15.3.1 Classification by luminosity  Relation between brightness and apparent magnitude
15.3.2 Apparent magnitude, Relation between intensity and apparent magnitude
Measurement of
m from photographic plates and distinction between
photographic and visual magnitude not required
15.3.3 Absolute magnitude, Parsec and light year
Definition of M, relation to

m M = 5 log d

15.3.4 Classification by temperature, black body radiation


Stefan’s law and Wien’s displacement law
General shape of black body curves, experimental verification is not
Use of Wien’s displacement law to estimate black-body temperature
of sources

λ max T = constant = 0.0029 mK

Inverse square law, assumptions in its application
Use of Stefan’s law to estimate area needed for sources to have same
power output as the sun

  P =  σ AT4

Assumption that a star is a black body
Problem of detector response as a function of wavelength and
atmospheric effects

15.3.5 Principles of the use of stellar spectral classes


Description of the main classes, O B A F G K M
Temperature required: need for excitation
Helium absorption (O): need for higher temperature
Hydrogen Balmer absorption lines (B, A): need for atoms in n=2
Metals absorption (F, G): occurs at lower temperature
Molecular bands (K, M): occur at lowest temperature
15.3.6 The Hertzsprung-Russell diagram General shape: main sequence, dwarfs and giants
Stellar evolution: path of a star similar to our Sun on the
Hertzsprung- Russell diagram from formation to white dwarf
15.3.7 Supernovae, neutron stars

and black holes


General properties
Calculation of the radius of the event horizon for a black hole

Schwarzchild radius 

R» 2GM

15.4 Cosmology

15.4.1 Doppler effect Df   =     and  Dλ  =  -v
 f         c           
λ        c
for v « c applied to optical and radio frequencies
Calculations on binary stars viewed in the plane of orbit
15.4.2 Hubble’s law 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

15.4.3 Quasars Quasars as the most distant measurable objects
Discovery as bright radio sources
Controversy concerning distance and power – use of inverse square
Quasars show large optical red shifts; estimation of distance



Astrophysics Option index - some old notes from last year that I have not got round to sorting