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Telescopes across the spectrum questions
The sky broadcasts at every wavelength, but the atmosphere opens only two broad windows at ground level. Where you must stand to observe each band, one small equation that decides how sharp any telescope can ever be, and why astronomers retired their own eyes as detectors.
20 original questions · 57 marks · the telescopes across the spectrum notes · Astrophysics
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Explain why ultraviolet and X-ray telescopes must be placed in orbit, while radio telescopes work at ground level.
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The atmosphere absorbs ultraviolet and X-rays high above the ground, so they never reach a ground-based instrument (1). It is transparent to radio wavelengths, so a dish at sea level receives them day and night, even through cloud (1).State the Rayleigh criterion for two point sources to be just resolved by a telescope of aperture D observing at wavelength λ.
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The sources are just resolved when the central maximum of one diffraction pattern falls on the first minimum of the other (1): their angular separation is then θ ≈ λ/D, with θ in radians (1).Define the quantum efficiency of a detector, and give typical values for a CCD and for the human eye.
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Quantum efficiency is the fraction (or percentage) of the photons arriving at the detector that are actually registered (1). A CCD achieves about 80%; the eye manages about 1% (1).The reflecting surface of a large radio dish can be open wire mesh, yet an optical telescope's mirror must be polished smooth. Explain the difference.
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A surface reflects cleanly provided its irregularities are small compared with the wavelength (1). Radio wavelengths are centimetres to metres, so mesh serves, while visible light at about 5 × 10−7 m demands a far smoother surface (1).State the two regions of the electromagnetic spectrum for which the atmosphere is transparent down to sea level.
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Visible light (1) and radio waves (1).Give two reasons a radio telescope can observe for more hours in a year than an optical telescope at the same site.
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Radio waves pass through cloud (1), and observing can continue in daylight, because the daytime sky is not bright at radio wavelengths (1).Calculate the smallest angle a telescope with a 5.0 m mirror can resolve when observing at 550 nm.
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θ ≈ λ/D = 5.5 × 10−7/5.0 (1)
θ = 1.1 × 10−7 rad (1)A dark-adapted pupil is 5.0 mm across and works at about 500 nm. A radio dish 64 m across observes at 0.21 m. Calculate the resolving power of each and state which can resolve the finer detail.
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Eye: θ ≈ 5.0 × 10−7/(5.0 × 10−3) (1)
θ = 1.0 × 10−4 rad (1)
Dish: θ ≈ 0.21/64 = 3.3 × 10−3 rad (1)
The eye's angle is the smaller, so the eye resolves the finer detail (1)Calculate the ratio of the collecting powers of a 10 m telescope and a 2.0 m telescope.
A space telescope has a 2.4 m mirror and observes at 550 nm. The Moon is 3.8 × 108 m away. Estimate the smallest feature it can resolve on the lunar surface.
An amateur telescope has an objective 130 mm in diameter and observes at 550 nm. The two stars of a binary are separated by an angle of 2.2 × 10−6 rad. Determine whether the telescope can resolve the pair.
A telescope of aperture 0.50 m collects enough light from a faint galaxy in a 1.0 hour exposure. Calculate the exposure a 0.25 m telescope of the same design would need to collect the same amount of light.
A telescope of aperture 0.30 m can observe through a blue filter at 400 nm or a red filter at 700 nm. Calculate the smallest resolvable angle with each filter, and state which filter shows the finer detail.
During one exposure, 6.0 × 104 photons from a faint galaxy arrive at a detector. Calculate the number registered by a CCD of quantum efficiency 80%, and by an eye of quantum efficiency 1%.
Calculate the dish diameter a radio telescope observing at 0.21 m would need to match the resolving power of a 15 cm optical telescope working at 500 nm. Comment on your answer.
An astronomy society is debating whether to image a faint galaxy by eye or with a CCD camera. Give four distinct reasons the CCD will out-perform the eye.
Describe one way the structure or siting of an infrared telescope and of an X-ray telescope must each differ from an ordinary optical telescope, giving the reason in each case.
An astronomy society may borrow one instrument to try to split a double star of angular separation 3.0 × 10−6 rad: an optical telescope of aperture 0.20 m used at 550 nm, or a radio dish of diameter 25 m used at 0.21 m. Deduce which instrument, if either, can resolve the pair, and determine the dish diameter a radio observatory would need to match it.
Two radio dishes 320 km apart are linked so that they act as a single aperture equal to their separation, observing at 0.060 m. Calculate the resolving power of the linked pair and of a single 64 m dish at the same wavelength, and state the improvement factor.
Estimate the greatest distance at which a dark-adapted eye, pupil diameter 4.0 mm working at 500 nm, could resolve a car's two headlamps, which are 1.5 m apart.
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