You are viewing a free preview of this lesson.
Subscribe to unlock all 8 lessons in this course and every other course on LearningBro.
Optical telescopes are the workhorses of observational astronomy. Whether mounted in a back-garden dome or aboard a 6.5 m space platform, they all do the same two things: collect light from a faint source over a much larger aperture than the human eye, and bring that light to a focus where it can be magnified, photographed, or piped into an instrument. This opening lesson of the AQA astrophysics option introduces the two architectural families — refracting telescopes (which use lenses) and reflecting telescopes (which use mirrors) — and the four performance figures that examiners almost always test: angular magnification, resolving power, collecting power, and the Rayleigh criterion. We finish with charge-coupled devices (CCDs), the silicon detectors that have all but replaced the photographic plate.
Spec mapping. This lesson covers AQA 7408 section 3.9.1 on astronomical telescopes (refracting design in normal adjustment, the Cassegrain reflecting design, ray diagrams, angular magnification, resolving power and the Rayleigh criterion, collecting power and CCD detection). The official AQA specification document remains the authoritative source — refer to it for the exact wording.
Synoptic links. This material draws on wave optics (refraction at a lens, image formation, AQA 3.3) and on the diffraction of light at a circular aperture (AQA 3.3.2). Resolution arguments are revisited in the non-optical telescope lesson, and the CCD detector connects back to the photoelectric effect and energy-level transitions in quantum physics (AQA 3.2). Stefan and Wien's laws (later in this course) tell you which wavelength a telescope should be optimised for; this lesson tells you whether the optics can resolve it.
The human pupil opens to about 7 mm in dark-adapted conditions. The amount of light reaching the retina is proportional to the area of the pupil, A = π(D/2)². If you replace the pupil with a telescope objective of diameter D_T, the light-collecting power is improved by a factor
Collecting power ratio = (D_T / D_eye)²
For an amateur 200 mm reflector that ratio is (200/7)² ≈ 816. The telescope shows stars roughly 800 times fainter than the unaided eye, all else being equal. For the 10 m Keck mirrors the ratio reaches over 2 million.
Astronomers therefore care about aperture above almost everything else — the diameter of the objective lens or primary mirror is the most important specification a telescope has. Magnification is comparatively cheap (you can change the eyepiece); aperture is set by the optics.
A refracting telescope uses two converging lenses: a large objective lens of long focal length f_o that forms a real, inverted image of the distant object close to its focal plane, and a short-focal-length eyepiece lens of focal length f_e through which the observer views that intermediate image.
In normal adjustment, the telescope is set up so that the intermediate image lies at the common focal point of the two lenses. Light from the distant object enters as parallel rays, converges to the common focal plane, and emerges from the eyepiece as parallel rays again — the final image is at infinity, so the observer's eye is fully relaxed. The separation of the two lenses is therefore
L = f_o + f_e
The diagram shows three sets of parallel rays from a distant object (in red) entering the objective. The objective brings them to a focus in the common focal plane, where they cross. The diverging rays then strike the eyepiece, which re-collimates them. They leave the eyepiece (in green) as a parallel bundle, but inclined at a larger angle to the axis than they entered.
The angular magnification M is the ratio of the angle subtended at the eye by the image to the angle subtended by the object at the unaided eye. For a refractor in normal adjustment
M = angle of image at eye / angle of object at unaided eye = f_o / f_e
So a telescope with f_o = 1200 mm and f_e = 25 mm has M = 48×. Increase magnification by either lengthening the objective focal length (changing the telescope) or shortening the eyepiece focal length (changing one small component).
Why magnification is not the whole story. As M grows, the image becomes dimmer (light spreads over more area on the retina) and the field of view shrinks. Beyond about M ≈ 2D (with D in mm), the image deteriorates because diffraction and atmospheric seeing dominate. A 100 mm aperture at 400× is doing nothing useful — you are magnifying mush.
A refractor has objective focal length 900 mm. The observer wants an image angular magnification of 60×. Calculate the eyepiece focal length and the overall length of the tube in normal adjustment.
Solution. From M = f_o / f_e: f_e = 900 / 60 = 15 mm. The tube length in normal adjustment is L = f_o + f_e = 900 + 15 = 915 mm.
A simple single-lens objective suffers from two principal aberrations, which limit image quality.
Chromatic aberration — different wavelengths refract by different amounts (the refractive index of glass varies with λ), so blue light comes to a focus closer to the lens than red light. The result is coloured fringes around bright objects. The cure is an achromatic doublet: a crown-glass converging element cemented to a flint-glass diverging element. The two glasses have different dispersions, and the combination brings two chosen wavelengths to a common focus.
Spherical aberration — rays striking the edge of a spherical lens come to a focus closer than rays near the axis. A perfect image therefore cannot be formed. The cure is to use aspheric surfaces (or, for mirrors, a parabolic profile).
Refractors also become impractical at large apertures because:
For these reasons no major research refractor has been built since the 40-inch Yerkes refractor of 1897. All modern professional telescopes are reflectors.
A reflecting telescope replaces the objective lens with a concave primary mirror. Light reflects off the silvered surface rather than refracting through glass, so reflectors have no chromatic aberration whatsoever — all wavelengths reflect at the same angle. The mirror only needs to be optically perfect on its front surface, so the glass behind can be cheap (and even foamed for lightness). It can also be supported across its entire back surface, removing the sag problem.
The Cassegrain reflector is the dominant design for professional telescopes. The arrangement is:
Whatever the design, every telescope is limited by diffraction at its circular aperture. Light from a point source does not form a true point image but an Airy disc surrounded by faint rings. Two stars are said to be just resolved when the central maximum of one Airy disc falls on the first minimum of the other — this is the Rayleigh criterion.
For a circular aperture of diameter D the angular separation at the resolution limit is
θ ≈ 1.22 λ / D
with θ in radians, λ the wavelength of the light, and D the aperture diameter. The smaller the angle, the better the resolution. Resolution improves with larger aperture and shorter wavelength. That is one of the reasons astronomers chase ever-bigger mirrors.
The Hubble Space Telescope has a 2.4 m primary mirror. Estimate its theoretical angular resolution at λ = 550 nm (yellow-green light).
Solution. θ ≈ 1.22 × (550 × 10⁻⁹) / 2.4 = 2.80 × 10⁻⁷ rad. Converted to arcseconds (1 rad = 206 265 arcsec): θ ≈ 0.058 arcsec. Hubble can therefore in principle separate two stars only 0.06 arcsec apart — about the angle subtended by a 1-pence coin viewed from 60 km.
Two stars are 5.0 × 10¹⁰ m apart and lie at a distance of 4.0 light-years (3.78 × 10¹⁶ m) from Earth. What minimum aperture telescope is needed to resolve them at λ = 550 nm?
Solution. Angular separation: θ = 5.0 × 10¹⁰ / 3.78 × 10¹⁶ = 1.32 × 10⁻⁶ rad. Setting θ = 1.22 λ / D and solving for D: D = 1.22 × 550 × 10⁻⁹ / 1.32 × 10⁻⁶ = 0.51 m. A modest 0.5 m telescope is sufficient in theory. In practice atmospheric seeing (typically 1–2 arcsec from a good ground site) would prevent ground-based resolution unless adaptive optics were employed.
Earth's turbulent atmosphere imposes a practical limit of about 1 arcsec (≈ 5 × 10⁻⁶ rad) on ground-based optical resolution unless adaptive optics corrects the wavefront in real time. This is one of the principal motivations for placing telescopes in space — Hubble achieves its diffraction limit precisely because there is no atmosphere above it.
The collecting power of a telescope is the rate at which it gathers energy from a source. Because the flux at the aperture is uniform, collecting power is proportional to the area of the aperture, which is proportional to the square of its diameter:
Collecting power ∝ D²
Two telescopes of aperture D₁ and D₂ collect light in the ratio (D₁/D₂)². The Keck 10 m telescope therefore collects (10 / 2.4)² ≈ 17 times more light than Hubble at any given moment, and shows fainter objects accordingly. (Hubble wins on resolution; Keck wins on light grasp.)
The limiting magnitude a telescope reaches scales approximately as
m_lim ≈ m_eye + 5 log₁₀(D_T / D_eye)
For a 200 mm telescope and a dark-adapted eye limit of m_eye ≈ 6: m_lim ≈ 6 + 5 log₁₀(200/7) ≈ 13.3. Such a telescope can pick up galaxies of magnitude 13, almost a million times fainter than the dimmest naked-eye star.
The photographic plate has been almost entirely replaced by the CCD — a silicon chip divided into a grid of light-sensitive pixels. Each pixel exploits the photoelectric effect: an incoming photon of energy hf > Eg liberates an electron-hole pair in the silicon, and the resulting charge is trapped in a potential well at the pixel site. After the exposure, charge is shifted row-by-row to an output amplifier and digitised.
| Property | Photographic plate | CCD |
|---|---|---|
| Quantum efficiency | 1–4 % | 70–95 % |
| Linearity | Highly non-linear (reciprocity failure) | Excellent (output ∝ photons) |
| Dynamic range | ~50:1 typical | 10 000:1 or better |
| Output | Chemical, requires development | Digital, immediate |
| Reusability | Single use | Used indefinitely |
| Calibration | Difficult | Bias, dark, flat-field straightforward |
A CCD's quantum efficiency (the fraction of incident photons it detects) approaches 90 % in the red and near-IR, against a photographic plate's 2–3 %. That single fact alone makes a 1 m telescope with a CCD roughly equivalent to a 5 m telescope with a plate — a dramatic improvement.
The CCD pixel pitch must match the optics. To sample the Airy disc properly (the Nyquist criterion), the pixel size should be no larger than half the diffraction-limited image size at the focal plane. Too-large pixels under-sample; too-small pixels are wasteful and noisy.
Specimen question modelled on the AQA paper format.
A Cassegrain reflecting telescope has a primary mirror of diameter 0.40 m and effective focal length 5.0 m. It is fitted with an eyepiece of focal length 25 mm and used in normal adjustment for visual observation in the V band (λ = 550 nm).
(a) State and explain two advantages of a reflecting telescope over a refracting telescope of the same aperture. (4 marks)
(b) Calculate the angular magnification of the telescope in normal adjustment. (2 marks)
(c) The telescope is used to observe a binary star system in which the two components have an angular separation of 0.50 arcsec. Determine, with calculation, whether the binary will be resolved. (4 marks)
(d) Compare and contrast the use of a CCD detector with a photographic plate at the Cassegrain focus, referring to two specific physical advantages of the CCD. (4 marks)
AQA Physics is assessed against AO1 (knowledge and understanding), AO2 (application) and AO3 (analysis, evaluation and interpretation). For a 14-mark question of this type:
Refer to the official AQA assessment guidance for the precise weighting of any given question.
Grade C response. Reflectors have no chromatic aberration because mirrors reflect all wavelengths the same way, whereas lenses refract different wavelengths by different amounts (M1). Reflectors are easier to build at large apertures because mirrors can be supported across the back, but lenses can only be supported at the edge and sag under their own weight (M2).
Examiner commentary: Two correct comparisons stated, each scored cleanly. M1 for chromatic aberration, M2 for mechanical support. This answer earns 2 of the 4 marks because it states the differences but offers no developed explanation of why — to reach full marks the candidate must connect the physics to the consequence.
Grade A response.* A reflector uses a mirror as its objective. Because reflection obeys θ_i = θ_r independently of wavelength, a mirror has no chromatic aberration at all, whereas a refractor's objective brings short-wavelength light to a focus closer than long-wavelength light, producing coloured fringes around bright objects unless an expensive achromatic doublet is used (M1, M2). Secondly, a large mirror can be supported continuously across its rear surface, whereas a lens can only be supported at its edge and therefore sags under its own weight when the diameter exceeds about 1 m. This restricts refractors to small apertures and limits both their light-gathering power (∝ D²) and resolution (∝ 1/D), neither of which compromises a large reflector (M3, M4).
Examiner commentary: The response gives two valid points (M1, M3), each developed with the underlying physics (M2 = wavelength-dependence of refraction; M4 = mechanical scaling consequences for D² collecting power and 1/D resolution). The synoptic link to the Rayleigh criterion lifts this to the A* band — the candidate is not just listing but reasoning about the consequence of each design choice.
Grade C response. Using θ = 1.22 λ / D with λ = 550 nm and D = 0.40 m: θ = 1.22 × 550 × 10⁻⁹ / 0.40 = 1.68 × 10⁻⁶ rad (M1). Converting to arcseconds: θ ≈ 0.35 arcsec (M2). This is less than 0.50 arcsec so the binary is resolved (M3).
Examiner commentary: The candidate applies the Rayleigh formula correctly, performs the unit conversion, and reaches a defensible conclusion. The omission of any explicit statement of the Rayleigh criterion (the condition for resolution) means the response sits in the Grade C band — 3 of 4 marks. Adding a one-line statement of the criterion would secure the final mark.
Grade A response.* The Rayleigh criterion states that two point sources are just resolved when the centre of the Airy disc of one coincides with the first diffraction minimum of the other. For a circular aperture this corresponds to a minimum angular separation θ_min = 1.22 λ / D. Substituting λ = 5.50 × 10⁻⁷ m and D = 0.40 m gives θ_min = 1.22 × 5.50 × 10⁻⁷ / 0.40 = 1.68 × 10⁻⁶ rad, which is 0.35 arcsec in conventional units (1 rad = 206 265 arcsec) (M1, M2). The binary's actual angular separation is 0.50 arcsec, which is larger than θ_min, so the two components are resolved by the telescope's diffraction limit (M3, M4). In practice ground-based seeing of order 1 arcsec would prevent resolution from a typical site unless adaptive optics is used — a caveat worth noting but not required to score full marks here.
Examiner commentary: Full marks. The Rayleigh criterion is explicitly stated (M1), the calculation is correctly executed in SI (M2), the conclusion is reached and justified (M3), and the comparison with the actual separation is explicit (M4). The seeing caveat is editorial and would not lose marks if omitted, but signals A*-band evaluative awareness.
Many candidates lose marks here by quoting θ = λ / D rather than θ = 1.22 λ / D — the 1.22 factor is required for circular apertures and is examined regularly. Others forget the unit conversion: a value in radians cannot be compared with an arcsecond separation without 1 rad = 206 265 arcsec.
On the magnification equation, a frequent slip is to compute f_e / f_o rather than f_o / f_e. Sketching the ray diagram and asking "what angle is bigger?" usually fixes it — the image angle (subtended at the eye) is much larger than the original object angle, so the magnification must be > 1, which forces the ratio to be f_o / f_e.
Aberration questions catch candidates who claim that reflectors suffer from chromatic aberration. They do not. Spherical aberration affects both reflectors and refractors (and is corrected by a parabolic primary mirror or aspheric lens), but chromatic aberration is exclusive to systems with refracting elements.
When comparing CCDs and plates, weak responses say "CCDs are better because they are digital". Strong responses quantify: ~90 % quantum efficiency vs ~2 %, linear response vs reciprocity failure, dynamic range ~10⁴ vs ~50. The exam rewards specific physics, not adjectives.
At undergraduate level you meet the full diffraction theory of optical instruments — the modulation transfer function (MTF), point-spread function (PSF), and the use of interferometry to combine signals from physically separated telescopes (the VLT interferometer; the Event Horizon Telescope, which gave the first image of a supermassive black hole in 2019). Adaptive-optics theory builds on Fried's coherence length and Strehl ratios. Books to look for: Kitchin's Astrophysical Techniques; Hecht's Optics (chapters on diffraction and aperture imaging); admissions interviewers often ask: "Why are bigger telescopes built on top of mountains?" — atmospheric pressure, water vapour, and turbulence all answer that question.
A common A vs A* distinction is over the role of the primary mirror profile. Many candidates state that mirrors avoid spherical aberration. They do not — a spherical mirror still suffers from spherical aberration. The Cassegrain primary is parabolic, not spherical, and that is what removes the spherical aberration. A Schmidt-Cassegrain uses a spherical primary plus a correcting plate at the aperture.
Another subtle error is conflating resolution with magnification. Magnification can be increased arbitrarily by changing the eyepiece; resolution is fixed by the aperture diameter via the Rayleigh criterion. Beyond the diffraction limit, additional magnification produces an "empty" image — bigger, but no more detail.
Finally, candidates sometimes claim CCDs detect more photons than reach them. They do not — they detect a higher fraction of incident photons (higher quantum efficiency), which is mathematically constrained to be ≤ 1.
This content is aligned with the AQA A-Level Physics (7408) specification.