Astrophysics

• Definition of Principal focus (Focal Point)


  The point through which all light parallel to the axis of the lens passes through
• Definition of Focal length


  The distance between the centre of the lens and the focal point.
• Formation of images by converging lenses

  Object beyond 2F

  image upside down

  small

  
  

  object between F and the lens

  virtual image

  right way up

  small

  
• Ray diagram of a refracting telescope in normal adjustment

  
• Angular magnification in normal adjustment

  Angular magnification = B/a = fo/fe

  
  

  B- angle to image

  a- angle to object
• Ray diagram of a Cassegrain telescope

  
• Definition spherical aberration - lens


  Where parallel rays at different distances from principal axis are brought to focus at different points (on principal axis).
• How to solve spherical aberration

  Use a parabolic mirror.
• Diagram of spherical aberration of a mirror

  rays further from principal axis are focused to a point closer to mirror

  
• Effect on image of spherical aberration


  Image is blurred
• Definition chromatic aberration


  Where different wavelengths are refracted by different amounts resulting in different focal lengths for different wavelengths (colours).
• Effect on image of chromatic aberration


  Images have multicoloured, blurred edges
• Diagram of chromatic aberration from a lens

  blue light (shorter wavelengths) are focused closer to lens that red light (longer wavelengths)

  
• Minimum angular resolution

  (Resolving power)


  the smallest angular separation that two point objects can still be discerned as separate
• Definition Rayleigh criteria


  two point objects can be just be resolved when the central maximum of the diffraction pattern of one object lies over the first minimum of the diffraction pattern of the other.
• Definition of Airy Disc

  The bright central maximum (spot) of the diffraction pattern produced when light from a point source passes through a circular aperture.
• Sketch of diffraction pattern from a circular aperture

  note that width of airy disc (central bright spot) is twice the width of bright fringes

  
• Sketch illustrating Rayleigh criteria

  
• Structure and operation of a CCD

  • A CCD is silicon chip divided into picture elements (pixels).

  • Incident photons cause electrons to be released.

  • The number of electrons liberated is proportional to the intensity of the light.

  • These electrons are trapped in 'potential wells' in the CCD.

  • An electron pattern is built up which is identical to the image formed on the CCD.

  • When exposure is complete, the charge is processed to give an image.
• Definition of quantum efficiency

  QE = number of photons detected/number of photons incident x 100
• Quantum efficiency of a CCD

  Quantum efficiency of CCD >80%

  a measure of the proportion of the incident photons that release electrons
• Quantum efficiency of an eye

  Quantum efficiency of eye = 1%
• Why are telescopes put into space?

  • Electromagnetic waves are absorbed by the atmosphere

  • Light pollution and other interference at ground level

  • The effect the atmosphere has on the path of the light as it passes through
• What does collection power of a telescope depend upon?

  Collection power of a telescope (rate at which energy is collected) is proportional to the cross-sectional area of the objective (lens or mirror).

  
  

  As cross-sectional area= pir^2 = pi(d/2)^2 = pid^2/4

  
  

  Where d is the diameter of the objective, therefore

  
  

  Collecting power of a telescope is proportional to d^2
• What absorbs X-rays, UV and infra-red in Earth's atmosphere?

  • X-rays are absorbed by Ozone (and Oxygen)

  • UV are absorbed by Ozone (and Oxygen)

  • Infra-red are absorbed by water vapour (and carbon-dioxide)
• Similarities and differences between radio and optical telescopes

  Similarities

  • Radio telescopes have a similar structure in that a concave reflecting surface reflects electromagnetic radiation to a detector at the focal point (of the reflecting surface).

  
  

  Differences

  • Radio telescopes are much larger - radio wavelengths are much longer than optical wavelengths

  • Radio telescopes have a lower resolving power - the wavelengths of radio waves are very much larger than optical wavelengths (even though the diameters of radio telescopes are larger).

  • Radio telescopes have a greater collecting power - collecting power depends on the area of the objective which is much larger for radio telescopes (depends on the square of the diameter).

  • Radio telescopes are not as affected by atmosphere so their positioning is less critical

  • Radio telescopes have only 1 reflecting surface not 2
• Advantages of mirrors in telescopes rather than convex lens

  • No chromatic aberration - mirrors do not refract light

  • no spherical aberration - use of parabolic mirror

  • no distortion - mirrors can be supported across its whole surface (lenses can only be supported around their edge)

  • better resolving power and/or greater brightness - mirrors can be made larger

  • more light gets through (image is brighter) - lens absorbs more light
• Disadvantages of mirrors in telescopes rather than convex lens

  • they have a frame holding the central mirror (secondary), that:

  o reduces the light intensity (as it blocks some light from hitting the primary mirror)

  o creates diffraction effects around the edges causing blurring of the image
• Advantage of larger objective diameter (mirror or lens)

  • It collects more light - so can observe fainter objects

  • It has a higher resolution - possible to distinguish (resolve) two objects close together.
• Definition parsec


  the distance to an object subtending 1 second of arc to the radius of the Earth's orbit.

  (1 second of arc (arcsecond) = 1/3600 of a degree).

  
• Units parsec


  pc
• Definition light year


  Distance light travels in a vacuum in 1 year.

  (number of seconds in 1 year = 365 x 24 x 60 x 60 = 3.15x107s
• Units light year


  ly
• Definition astronomical unit


  The mean distance between the Earth and the Sun
• Units astronomical unit


  AU
• Definition of absolute magnitude


  The brightness an object would appear if it was 10 parsecs from the Earth.
• Definition of apparent magnitude

  The brightness of an object as seen from Earth
• What is black body radiation?

  The electromagnetic radiation emitted by an object because of its temperature
• General shape of black body curves

  Temperature is DECREASING going from P to R.

  Area under curve is total power output per m2 (as given by Stefan's Law)

  You need to able to sketch these curves

  
• Definition λmax


  The wavelength at which maximum emission occurs.