Physics › Astrophysics › Telescopes across the spectrum
Telescopes across the spectrum
The sky broadcasts at every wavelength, but the atmosphere only opens two windows. 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.
Builds on Diffraction and the single slit and Telescopes and image formation.
IN THIS TOPIC
- Compare radio, infrared, ultraviolet and X-ray telescopes with optical ones in structure, siting and use.
- Use the Rayleigh criterion θ ≈ λ/D, in radians, to compare resolving powers.
- Compare collecting powers through diameter squared, and the CCD with the eye.
WHAT YOU PROBABLY THINK
Observatories sit on mountaintops to be closer to the stars.
Where to stand
Stars, galaxies and everything between them radiate right across the electromagnetic spectrum, and each band tells a different story: cold dust glows in the infrared, violent gas flares in X-rays, cool hydrogen whispers at radio wavelengths. The catch is the atmosphere. Air is transparent to visible light and to radio waves, and opaque to almost everything else, so the sky only opens two windows to the ground.
That single fact dictates where every telescope lives. Radio dishes work at ground level, day and night, straight through cloud: a big steerable dish is a reflecting telescope scaled up, and because the wavelength is so long its surface can even be open mesh. Infrared telescopes climb high, dry mountains, above as much water vapour as possible, and their detectors are cooled so the instrument's own warmth does not glow in the very band it is observing. Ultraviolet and X-ray telescopes must orbit above the atmosphere entirely, and X-rays raise a further problem: they pass straight into an ordinary mirror, so they are focused by skimming off nested metal surfaces at grazing incidence.
And the mountaintop lie? A few kilometres of altitude is nothing against interstellar distances. Observatories climb to get above water vapour and the shimmering turbulence of warm air, which is also why the sharpest visible-light images come from orbit.
| Band | Where it works | Why |
|---|---|---|
| radio | ground level | the atmosphere is transparent to it; cloud and daylight do not matter |
| infrared | high, dry summits, or space | water vapour absorbs it, and warm equipment glows in it |
| visible | ground, better in orbit | a clear window, but turbulence blurs fine detail |
| ultraviolet | orbit | absorbed high in the atmosphere, much of it by ozone |
| X-ray | orbit, grazing-incidence mirrors | the atmosphere absorbs it, and it penetrates ordinary mirrors |
How sharp: the Rayleigh criterion
Every telescope has a sharpness limit it cannot buy its way past, and diffraction sets it. The aperture is a hole that light waves must squeeze through, so a point star never images to a point: it becomes a small bright disc ringed by faint fringes, the aperture's diffraction pattern. Two stars close together in angle mean two overlapping patterns, and if the overlap is too great no instrument behind the telescope can untangle them.
The Rayleigh criterion makes the judgement precise: two sources are just resolved when the centre of one pattern sits on the first minimum of the other, which happens at an angular separation of about
with θ in radians, λ the wavelength observed and D the aperture diameter. Smaller θ means finer detail, so the resolving power improves with a bigger aperture and a shorter wavelength. The equation explains a genuine embarrassment of radio astronomy:
WORKED EXAMPLE
The giant that cannot out-see your eye
The Lovell radio telescope has a 76 m dish and observes the hydrogen line at λ = 0.21 m. Your dark-adapted pupil is about 5.0 mm across, working at λ ≈ 5.0 × 10−7 m. Compare their resolving powers.
Lovell: θ ≈ λ/D = 0.21 / 76 = 2.8 × 10−3 rad.
The eye: θ ≈ 5.0 × 10−7 / 5.0 × 10−3 = 1.0 × 10−4 rad.
The unaided eye resolves detail nearly thirty times finer than a 76-metre national instrument, because its wavelength is a million times shorter. Radio astronomers claw the sharpness back by linking dishes many kilometres apart, which makes D effectively enormous.
YOUR TURN
Two dishes, one wavelength
One radio dish is 64 m across, another 32 m, observing the same 0.21 m line. Compare their resolving powers and say which sees finer detail, before opening the working.
Show the working
θ for the 64 m dish is 0.21/64 = 3.3 × 10−3 rad; for the 32 m dish, 0.21/32 = 6.6 × 10−3 rad.
Doubling D halves θ, so the 64 m dish resolves detail twice as fine. Smaller θ is better: the number is the angle at which two sources stop being separable.
How deep: collecting power, and what detects the light
Most objects astronomers care about are desperately faint, so the second currency of telescope design is collecting power: the rate at which the aperture gathers light. That is proportional to the aperture's area, and hence to the square of its diameter:
An 8.2 m mirror against your 5.0 mm pupil is a diameter ratio of 1640, so it gathers 16402 ≈ 2.7 × 106 times the light: two and a half million times deeper into the dark, before any camera tricks. Both figures of merit, resolving and collecting, reward the same thing, and the lie of the previous lesson stays dead: diameter, not magnification, is what a telescope is for.
The detector matters as much as the mirror. For a century that meant the eye, then photographic plates; now it means the charge-coupled device, the CCD at the heart of every astronomical camera. The headline comparison is quantum efficiency: the fraction of photons arriving at the detector that are actually registered. A CCD detects roughly 80% of them; the eye manages about 1%.
| CCD | the eye | |
|---|---|---|
| quantum efficiency | about 80% | about 1% |
| exposure | can accumulate light for hours | refreshes many times a second |
| record | permanent, shareable, measurable | none |
| wavelengths | visible and into the infrared and ultraviolet | visible only |
| convenience | needs power, cooling and a computer | always with you |
The eye keeps exactly one advantage, convenience, and astronomy happily traded it away: a detector that stores light for hours, records it permanently and measures it in numbers is a different kind of instrument, and it is why a modest amateur telescope with a CCD now reaches objects the great Victorian refractors never saw.
TRY IT UNSEEN
Could Hubble read a number plate on Mars?
The Hubble telescope's mirror is 2.4 m across, observing at 5.0 × 10−7 m. Mars at its closest is about 5.6 × 1010 m away. Estimate the smallest detail Hubble can resolve on the Martian surface.
Show the working
θ ≈ λ/D = 5.0 × 10−7 / 2.4 = 2.1 × 10−7 rad.
At distance d the smallest separable detail is s ≈ θd = 2.1 × 10−7 × 5.6 × 1010 ≈ 1.2 × 104 m.
About twelve kilometres: whole craters, not rovers. Small angle times huge distance is the working pattern for every question of this shape.
THE EXAM BIT
- θ ≈ λ/D answers live in radians. If a question supplies degrees or arcseconds, convert before comparing.
- To compare resolving powers, compute θ for both instruments and say explicitly that the smaller angle resolves the finer detail. The comparison sentence is where the mark sits.
- Collecting power comparisons square the diameter ratio. Show the ratio first, then square it: examiners look for D2, not D.
- Siting questions want the atmosphere named and blamed: which band the air absorbs, or the turbulence that blurs. Altitude for its own sake earns nothing.
- Quantum efficiency has a one-sentence definition, the percentage of incident photons the detector registers, and the CCD-versus-eye comparison starts with it. No CCD internal structure is needed.
CHECK YOURSELF
What diameter would a radio telescope observing at 0.21 m need to match the resolving power of a 10 cm optical telescope working at 5.0 × 10−7 m? Comment on the answer.
Show a hint
Find the optical telescope's θ first; then ask what D gives the radio dish the same θ.
Show the answer
Optical: θ ≈ λ/D = 5.0 × 10−7 / 0.10 = 5.0 × 10−6 rad.
Radio: D = λ/θ = 0.21 / 5.0 × 10−6 = 4.2 × 104 m.
A single dish 42 km across is not buildable, which is the point of the comment: matching a small optical telescope at radio wavelengths takes networks of dishes spread across the countryside, acting together as one giant aperture.
Resolution: θ ≈ λ over D, in radians, and smaller is sharper.
Collection: the light gathered grows as the diameter squared.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
CHECK YOUR PROGRESS
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- Compare radio, infrared, ultraviolet and X-ray telescopes with optical ones in structure, siting and use.
- Use the Rayleigh criterion θ ≈ λ/D, in radians, to compare resolving powers.
- Compare collecting powers through diameter squared, and the CCD with the eye.
Open the full revision checklist to track your progress across the whole unit.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.