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Telescopes (CCDs (CCDs have very high quantum efficiency of > 80% (The…
Telescopes
CCDs
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Quantum Efficiency
The percentage of incident photons that produce a measurable signal in a light detector
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CCDs can be designed to detect radiation that is outside the visible range, so false colour images can be produced
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Have very high spacial resolution, meaning that two objects very close to each other can be resolved by a CCD
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Lenses
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Diverging lenses
Diverge parallel rays away from one another. Rays will appear to meet at a point on the negative focal plane
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Ray Diagrams
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For a converging lens
Draw ray from top of object parallel to principal axis to lens, and then through principal focus
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Draw rays through negative principal focus, then parallel to principal axis after lens
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"Real" means that the image is formed by real rays meeting at a point, and so can be projected into a screen
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Refracting Telescopes
Normal Adjustment
When the principal foci of the objective and eyepiece lenses are aligned in the same position
Structure
A large, thin objective lens with large focal length and a small fat eyepiece lens with a short focal length
Rays from a particular point emerge parallel through the eyepiece lens, and so virtual image is formed at infinity
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The angle of emerging rays from principal axis is greater than rays entering telescope and so an object appears magnified by telescope, as it's angular extent in FOV is greater.
Angular Magnification
\[M=\frac{Angle\;subtended\;by\;image at\;eyepiece}{angle\;subtended by\;object\;by\;unaided\;eye}=\frac{f_{o}}{f_{e}}\]
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Rays from very distant objects are treated as being parallel by eye, and so the lens in the eye does not need to change shape to focus them
Issues
Spherical Aberration
Rays that travel through the top of the lens are focused to a slightly nearer focal point than rays that travel through the centre of the lens
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Can use aspherical lenses to counter this, but they can be difficult to manufacture, and so can be quite expensive
Chromatic Abberation
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Parallel rays are focused to different points and so the image becomes blurred, with different colours separating out
Eye piece lens is very fat and so needs to be carefully smoothed to correct shape, and be very pure to prevent scattering of light. This can be expensive
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To give large objective focal length objective lens must be very thin and can only be supported at the edges.
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Resolving Power
When light enters a telescope it diffracts through the aperture to produce a single slit ring pattern
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The two objects will only be resolvable if the centre of the airy disk one of the patterns is no closer to the centre of the other pattern than the first minimum of the diffraction pattern of the second object.
This corresponds to a minimum angular resolution of:
\[\theta_{min}=\frac{\lambda}{D}\]
where \(\lambda\) is the wavelength of light being observed and \(D\) is the diameter of the aperture.
Reflecting Telescopes
Structure
A large parabolic, concave primary mirror with a smaller, convex hyperbolic mirror placed with one of it's foci aligned with the focus of the primary mirror.
There is a gap in the back of the primary mirror to allow light through to the eyepiece lens
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Issues
Spherical Aberration
If primary mirror is not perfectly parabolic then rays from the top and bottom of the mirror will be focused to a closer focal point than those incident near the centre
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The secondary mirror will block some incident light, decreasing the collecting power of the telescope
Light will diffract around the edges of the secondary mirror, making parallel rays non-parallel. This causes them to be focused to different points and blurring the image
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Non-Optical Telescopes
Infrared
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Infrared has longer wavelength than visible and so infrared telescopes have an inherently worse angular resolution than visible telescopes
The mirrors in an infrared reflector can be less finely made than in visible, as long wavelength means that infrared radiation will not be as sensitive to impurities in the mirror.
Short wavelength IR can make it to Earth but water molecules in the atmosphere will absorb IR radiation. Therefore, IR telescopes are best used at high altitudes, in dry climates
IR telescopes produce IR radiation themselves, and so they need to be supercooled to avoid interference
UV
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mirrors must be more carefully made as UV light is more sensitive to scratches and shape of mirror than visible light
Must be placed at very high altitude (in plane) or in orbit as most UV radiation cannot make it through the ozone layer
X-Ray
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A modified GM tube, a highly sensitive CCD or a finely woven wire mesh can be used to detect the x-rays
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Radio
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By \(\theta=\frac{\lambda}{D}\) radio telescopes must have very large dishes to have a reasonable angular magnification
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Can connect telescopes from across the globe to achieve angular resolutions thousands of times better than ordinary visible telescopes.
Can connect many radio telescopes into an array to create an effective diameter equal to the maximum separation of the telescopes in the array
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Axial Rays are focused to the antenna where a pre amplifier amplifies the signal without adding too much noise to the signal
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