Telescopes: Optics, Magnification and Resolution
Why We Need Telescopes
The human eye has two fundamental limitations as an astronomical instrument: its pupil diameter is only about 7 mm at maximum dilation, restricting the amount of light collected, and it cannot accumulate light over time — it samples the scene afresh every fraction of a second. Telescopes overcome both limitations. A larger aperture collects more light, revealing fainter objects. A camera or CCD sensor attached to a telescope can expose for minutes or hours, allowing very faint detail to build up. Telescopes also magnify, enabling small angular separations on the sky to be resolved.
Refracting and Reflecting Telescopes
There are two fundamental designs based on how they gather and focus light. A refracting telescope (refractor) uses a large convex objective lens to converge parallel rays from a distant object to a focus. The original Galilean telescope (1609) was a refractor. The eyepiece then magnifies the image formed at the focal point. Refractors produce sharp, high-contrast images for planets and the Moon, but suffer from several practical limitations at larger apertures.
A reflecting telescope (reflector) uses a large concave mirror to focus incoming light. The most common design for amateur astronomers is the Newtonian reflector, in which a small flat secondary mirror redirects the focused beam to an eyepiece at the side of the tube. The Cassegrain reflector uses a convex secondary mirror to send the beam back through a hole in the primary mirror to an eyepiece at the rear. Virtually all large professional observatories use reflecting designs, as mirrors can be made much larger than lenses and support from behind, eliminating sag.
Refractors use a convex objective lens; reflectors use a concave mirror. Both focus incoming parallel light rays to a point, after which the eyepiece magnifies the image. Reflectors are preferred for large apertures because mirrors are cheaper, easier to manufacture to high precision, and free from chromatic aberration.
Magnification
The magnification of a telescope is defined as the ratio of the focal length of the objective to the focal length of the eyepiece:
$$M = \frac{f_o}{f_e}$$where \(M\) is the magnification, \(f_o\) is the focal length of the objective (lens or mirror) and \(f_e\) is the focal length of the eyepiece. A longer objective focal length or shorter eyepiece focal length increases magnification. For example, a telescope with a 1,200 mm objective focal length used with a 6 mm eyepiece produces a magnification of \(M = 1200 / 6 = 200\times\). Swapping to a 20 mm eyepiece reduces magnification to \(M = 1200 / 20 = 60\times\) but gives a wider, brighter field of view.
There is a practical maximum useful magnification for any telescope, roughly 50 times the aperture in inches or 2 times the aperture in millimetres. Beyond this limit, the image becomes too dim and blurred by atmospheric turbulence (seeing) to show extra detail. Higher magnification always means a dimmer image (the same light is spread over a larger area) and a narrower field of view.
Light Grasp and Aperture
The amount of light a telescope collects depends on the area of its objective. Since area scales with the square of diameter:
$$A = \pi \left(\frac{D}{2}\right)^2$$where \(D\) is the aperture diameter. A telescope with an aperture of 200 mm collects \((200/7)^2 \approx 816\) times more light than the human eye (aperture ~7 mm). Doubling the aperture quadruples the light-gathering area, allowing stars roughly 1.5 magnitudes fainter to be detected. This is why astronomers relentlessly pursue larger apertures: the Extremely Large Telescope (ELT) under construction in Chile will have a 39-metre primary mirror, collecting around 30 million times more light than the human eye.
Resolution
Resolution is a measure of the finest detail a telescope can distinguish. The minimum angular separation between two objects that can just be resolved depends on the wavelength of light \(\lambda\) and the aperture \(D\):
$$\theta \approx \frac{\lambda}{D}$$(where \(\theta\) is in radians). A larger aperture resolves finer detail. Longer wavelengths (e.g. radio waves) are harder to resolve than shorter wavelengths (visible light), which is why radio telescopes must be enormously large — or linked into arrays — to match the resolution of an optical telescope of modest size. In practice, Earth's atmosphere limits the resolution of ground-based telescopes to about 1 arcsecond (due to atmospheric turbulence), regardless of aperture size — this is the “seeing” limit.
Chromatic aberration is a defect of lenses only. Glass refracts different wavelengths of light by different amounts — the refractive index varies with wavelength (dispersion). This means different colours in starlight are brought to focus at slightly different points along the optical axis, producing coloured fringes around bright stars and planets. The defect is fundamental to refraction and cannot be eliminated, only reduced using achromatic doublet lenses (two lenses of different glass cemented together). Crucially, mirrors reflect all wavelengths equally — so reflecting telescopes are completely free of chromatic aberration. This is one of the principal reasons professional observatories use reflectors.
Spherical aberration affects mirrors (and lenses). A spherical mirror does not bring all incoming parallel rays to the same focal point — rays near the mirror's edge are focused slightly differently from rays near the centre. The result is a blurred image even in monochromatic light. The Hubble Space Telescope suffered severe spherical aberration when launched in 1990 because its primary mirror was ground to the wrong shape; it was corrected by installing the COSTAR corrective optics in 1993. Spherical aberration is solved by making mirrors parabolic in shape rather than spherical. To summarise the critical distinction: chromatic aberration = lenses, wavelength-dependent refraction; spherical aberration = mirrors or lenses, incorrect shape of the optical surface.
Galileo's Discoveries
Galileo Galilei began systematic telescopic astronomy from 1609 using a Galilean refractor of modest aperture. His discoveries fundamentally changed the understanding of the Solar System: he observed the phases of Venus (proving Venus orbited the Sun inside Earth's orbit), four moons of Jupiter (Io, Europa, Ganymede and Callisto — now called the Galilean moons), mountains and craters on the Moon (showing it was not a perfect sphere), and sunspots (showing the Sun was not perfect and unchanging). These observations provided powerful evidence against the Earth-centred model of the Universe.
Refractors: advantages include a sealed tube (less dust and air turbulence inside), no secondary mirror obstruction reducing light, and high contrast for planetary observing. Disadvantages: chromatic aberration, expensive to manufacture large lenses, glass sags under its own weight for large apertures, and very long tubes are physically impractical above about 100–150 mm aperture.
Reflectors: advantages include no chromatic aberration, mirrors can be made much larger (ground and polished from the rear, supported across their full back surface), shorter tube lengths (mirrors fold the optical path), and lower cost per unit aperture. Disadvantages: mirrors must be periodically re-coated with fresh aluminium, secondary mirrors block some incoming light, and open tubes allow air currents that degrade images (thermal equilibration time).
A telescope’s ability to resolve close-together objects is set by aperture diameter (the diffraction limit θ ≈ λ/D), not by magnification. Two stars 1 arcsecond apart can never be split by a 50mm scope no matter how high the eyepiece magnification — only a bigger aperture fixes it.