Knowledge-21

• Refracting (Galilean):

  • Contain a short focal length eyepiece lens and a long focal length objective lens.
  • suffer from spherical aberration and chromatic
  • have large lenses which are hard to make and unlikely to break under their own weight.
• Reflecting telescopes ( Cassegrain):

  • contain a parabolic concave primary mirror and a convex secondary mirror.
  • suffer from spherical aberration if spherical , not from chromatic aberration
  • can be made much larger than refracting telescopes because the mirrors can be supported from behind.
• Telescopes with two lenses:

  The objective lens collects light from a distant object and forms a real image at focal length f0.

  The eyepiece forms a magnified , virtual image at infinity of the image formed by objective lens.

  The focal plane of the eyepiece fe coincides with the focal plane of the objective.
• Telescopes with two mirrors:

  The primary (parabolic concave) mirror collects light from a distant object.

  The secondary (convex) mirror reflects the light through a hole and into eyepiece lens:

  • the eyepiece forms a magnetic image at the eye
  • the secondary mirror produces a slight dimming but no missing section in the image.
• Eye:

  • Quantum efficiency- 1% at 550nm in low light; colour vision lost , but pupil expands.
  • Resolution- 1mm
  • Ease of use - very convenient but needs time to adjust to light conditions.
• CCD (charge coupled device):

  • Quantum efficiency- 70-80% , number of electrons is equal to the number of photons over intensity.
  • Resolution- dependent on the number of pixels
  • Ease of use - can produce images with long exposure and detect wavelengths of light the eye cant see.
• Non optical telescopes:

  Radio telescopes:

  • Have a similar design to optical reflecting telescopes (parabolic mirrors)
  • Have a receiving aerial instead of secondary mirror

  Satellite based telescopes:

  • all reflecting telescopes
  • placed on balloons in orbit and on mountains in deserts because the atmosphere absorbs radiation.
• Angles in radians :

  If an object of height h is distance d away , then the angle ,theta, subtended by the object:

  radians (theta) = Height (m) / distance (m)
• Calculating magnification:

  Angular magnification M:

  • M = angle subtended by image at eye (rad) / angle subtended by object at eye.

  if the image subtends a larger angle then it appears magnified.
• In spherical aberration , spherical lenses or mirrors do not bring parallel beams to the same focus.
• In chromatic aberration , the edges of lenses behave like prisms , so different colors focus at different points.
• Large diameter in telescopes:

  • light collected is subject to diffraction
  • two sources are just resolved when the maximum of one pattern coincides with the minimum of the other.
  • The Rayleigh criterion says the angle at which this occurs depends on wavelength and the diameter of the mirror or lens. Larger apparatus have better resolving power.
• Convex (converging ) - these make a parallel beam of light converge to a focus.
• principal axis of a lens is an imaginary line that passes through the centre of a lens through the centers of curvature of the faces of the lens.
• Focal point of a lens is the point at which rays parallel to the principal axis of the lens are brought to focus
• focal length is the distance between the centre of the lens and the point at which rays parallel to the principle axis are brought to a focus.
• Diverging (concave) - these make a parallel beam of light spread out so that it appears to come from a focus.
• convex causes lines to bend towards the focal point
• Three rules: Convex

  1. A ray parallel to the axis is refracted through the focus
  2. A ray to the centre of the lens passes through with no reflection.
  3. A ray through the focus is refracted parallel to the axis.
• if image is smaller than the object than the image is diminished.
• If an image is larger than the object than its is magnified.
• if a rays passes through object : real
• If rays only seem to come from an object then they are virtual.
• A magnify glass creates a virtual image as the image in the glass is not the actual object or size.
• Virtual images cannot be projected
• images can be upright or inverted
• At a position of 2F:

  • the image created will be the same size but inverted.
• In between 2f and f:

  • a magnified but inverted image.
• At F :

  • an image will be formed at infinity or no image is made , both explanations can be used.
• Between F and 0 :

  • The rays meet on the left side of the lens.
• For Galilean telescopes :

  • tan(a) = h/f0
  • tan(b) = h /fe
• h is height of real image
• Using a lens with a parabolic shape reduces spherical aberration but are very expensive and can produce some distortion .
• Chromatic aberration can be reduced by constructing a lens made of two different types of glass.
• The area of a telescope mirror is:

  • pie(d)^2/ 4
• collecting power in a reflecting telescopes is proportional to the diameter squared.
• Astronomical Telescope:

  • contains two concave lenses - the objective lens and eye pieces.
  • The focal point at the objective lens must be larger than that at the eye piece.
  • Normal adjustment is where a real image is viewed at the focal point of the eye piece. A magnified virtual image is viewed at infinity.
• The primary mirror in the reflecting telescope is concave whereas the secondary mirror is convex.
• Advantages of a reflecting telescopes:

  • has about 15cm diameter so sufficient light is gathered , difficult to make high-quality lens of diameter 15cm
• Rayleigh's criterion:

  • light collected from a reflecting telescope is subject to diffraction.
  • diffraction affects how well a telescope can resolve fine detail.
  • As two sources get closer the diffraction pattern merges until one diffraction pattern is seen, this makes it hard to tell two stars have been seen.