11. Astrophysics

• Rayleigh Criterion:

  • the minimum subtended angle between two objects whose (images) can be resolved.
  • (Minimum angle is when) the central maximum of (the diffraction pattern of light from) one object coincides with the first minimum of (the diffraction pattern) of the second object.
• Real image: when light rays from an object are made to pass through another point in space. The light rays are actually there, and the image can be captured on a screen
• Virtual image: formed when light rays from an object appear to have come from another point in space. The light rays aren't really where the image appears to be so the image can't be captured on a screen.
• Lens Equation:

  • u = distance between the object and the lens axis
  • v = distance between image and lens axis (positive if image is real)
  • f = focal length

  
• Refracting telescopes:

  • Objective lens converges the rays from the object to form a real image
  • Eye lens acts as a magnifying glass on the real image to form a magnified virtual image
  • Assume the object is at infinity: the rays from the object are parallel and the real image is formed on the focal plane
  • A telescope is set up so that the principal focus of the objective lens is in the same position as the principal focus of the eye lens, so the final magnified image appears to be at infinity
  • Magnification can be calculated in terms of angles or the focal length
• Converging Lens:

  • makes parallel rays converge to a focus
  • the point where rays parallel to the principal axis are focused = principal focus

  A) Principal Focus

  
• Advantages of Reflecting Telescopes:

  • Bigger since it can be supported from behind
  • fainter objects can be seen greater the resolving power
  • No chromatic aberration.
  • Spherical aberration will easily be solved
• Disadvantages of Reflecting Telescopes:

  • Some refraction at the eyepiece
  • Aperture diffraction as diffraction for secondary mirror and struts
  • Objective mirror is exposed
• Advantages of Refracting Telescopes:

  • Only aperture diffraction occurs
  • Objective lens is protected
• Disadvantages of Reflecting Telescopes:

  • Smaller since it can only be held at the edges and will break under its own weight
  • Chromatic aberration due to the diffusion of colours
  • Also experiences spherical aberration
• Resolving Power: the ability of a telescope to distinguish two close together objects as being separate (the minimum angular separation achievable by a telescope)
• Diffraction: the spreading out of light waves as they pass an obstacle
• Objective lens: converging lens at the front of the telescope
• Eyepiece lens: lens you look down
• Magnification: how big the image appears to be when compared to the object
• Intensity: the power per square metre
• Principal Focus: the point where the light rays converge
• Focal Length: the distance between the principal focus and the lens axis
• Reflecting Telescope: image is magnified using a concave mirror
• Cassegrain Telescope: image is viewed through an eyepiece at the back of the instrument
• Newtonian Telescope: image is viewed through an eyepiece at the side of the instrument
• 1 degree = 60 arc minutes = 3600 arc seconds
• Resolution:

  • When light from an object enters a telescope, it is diffracted, resulting in the loss of detail in the image
  • The aperture of the telescope is assumed to have the same diameter as the objective lens
  • How much detail the telescope can show is called its resolution
• Resolving Power - Problems in Exams:

  • Better the resolution, the smaller the angle and therefore the greater the detail that can be seen
  • This angle should be referred to as the minimum angular resolution/separation of the telescope
  • Angle --> unit is in radians
  • Angle is a theoretical minimum
  • Effects include refraction of light as it passes through the atmosphere, Cassegrain --> diffraction problems
• Summary:

  • Diffraction means that light from objects next to each other can overlap and they look like one object
  • How far apart the objects are should be given by the Rayleigh Criterion
  • Numerically, this is called the 'minimum angular separation'
• Charge-Coupled Devices (CCDs):

  • Electronic light receptor --> central to digital cameras
  • Is an array of light sensitive pixels
  • Become charged when they are exposed to light via the photoelectric effect
• Collecting Power:

  • A measure of the ability of a lens or mirror to collect incident EM radiation
  • Collecting power increases with the size of the objective lens/mirror
  • Directly proportional to the area of the objective lens
  • The greater the collecting power, the brighter the images produced by the telescope area
• Features of a CCD:

  • Quantum efficiency - the percentage of incident photons which cause an electron to be released
  • Spectral range - the detectable range of wavelengths of light
  • Pixel resolution - the total number of pixels used to form the image on a screen. A lot of small pixels will resolve an image more clearly than a small amount of large pixels
  • Spatial resolution - the minimum distance two objects must be apart in order to be distinguishable. This is used to observe small details
  • Convenience - how easy images are to form and use
• CCDs Vs Human Eye:

  CCDs are more useful for detecting finer details and producing images which can be shared and stored.

  A) Infrared, UV, Visible

  B) Only Visible

  C) 10

  D) 100

  
• Similarities - Radio and Optical Telescopes:

  • Both telescopes function in the same way - they intercept and focus incoming radiation to detect its intensity
  • Both radio and optical telescopes can be moved to focus on different sources of radiation/to track a moving source
  • The parabolic dish of a radio telescope is extremely similar to the objective mirror of a reflecting optical telescope
  • Both optical and radio telescopes can be built on the ground since both radio waves and optical light can pass through the atmosphere
• Differences - Radio and Optical Telescopes:

  • Radio telescopes have to be much larger in diameter than optical telescopes in order to achieve the same quality image/resolving power. Radio waves also have a larger collecting power
  • Radio telescopes are cheaper and simpler because a wire mesh is used instead of a mirror - as long as its less than λ/20, radio waves will be reflected and not refracted
• Differences - Radio and Optical Telescopes:

  • A radio telescope must move across an area to build up an image
  • Radio telescopes experience a large amount of man-made interference from radio transmissions, phones, microwave ovens, etc.
  • Optical telescopes experience interference from weather conditions, light pollution, stray radiation, etc.
• Infra-red telescopes:

  • Use infrared radiation to create images of astronomical objects
  • Consist of large, concave mirrors which focus radiation onto a detector
  • Infrared telescopes must be cooled using cryogenic fluids to almost absolute zero
  • Must be well shielded to avoid thermal contamination from nearby objects and its own infrared emissions
  • Used to observe cooler regions in space
  • Has to be launched in space and be accessed remotely
• Ultraviolet telescopes:

  • Use UV radiation to create images of astronomical objects
  • Needs to be positioned in space
  • Utilise the Cassegrain configuration to bring ultraviolet rays to a focus
  • Rays are detected by solid state devices which use the photoelectric effect to convert UV photons into electrons, which then pass around a circuit
  • UV telescopes can be used to observe the interstellar medium and star formation regions
• X-Ray Telescopes:

  • Need to be positioned in space to collect data
  • Rays have such a high energy that using mirrors wouldn't work as they would pass straight through
  • Are a combination of extremely smooth parabolic and hyperbolic mirrors
  • The rays enter the telescope, skim off the mirrors and are brought into focus on CCDs, which convert light into electrical pulses
  • Since X-Rays are high-energy, they can be used to observe high-energy events and areas of space such as active galaxies, black holes and neutron stars
• Gamma Telescopes:

  • Use gamma radiation to create images of astronomical objects
  • These telescopes do not use mirrors at all as gamma rays have so much energy they would just pass straight through
  • Instead, they use a detector made of layers of pixels.
  • As gamma photons pass through, they cause a signal in each pixel they come into contact with
  • Telescopes are used to observe things such as gamma ray bursts, quasars, black holes and solar flares.
• Types of Gamma Ray Bursts (GRB):

  • Short-lived: these last anywhere between 0.01 and 1 second are are thought to be associated with merging neutron stars (forming a black hole) or a neutron star falling into a black hole
  • Long-lived: these can last between 10 and 1000 seconds and they are associated with a Type II supernova (death of a massive star)
• Luminosity: rate of light energy released/power output of a star
• Intensity:

  • power received from a star (its luminosity) per unit area
  • has the unit Wm^-2
  • follows the inverse square law, meaning that its inversely proportional to the square of the distance from the star
  • Intensity is the effective brightness of an object - brightness is a subjective scale of measurement
• Apparent Magnitude (m):

  • How bright an object appears in the sky
  • Depends on a star's luminosity and distance from the Earth