Telescopes & Their Limitations — Quick Summary
Mr Toogood's Physics · Astrophysics
AQA 3.9.1.1 / 3.9.1.2 / 3.9.1.4
M = fₒ/f_e
Angular magnification
θ ≈ λ/D
Rayleigh criterion
Power ∝ D²
Collecting power
θ = s/r
Angular size/sep.
Refracting telescopes — normal adjustment
Learn this diagram — commonly examined.
The objective lens focuses light to a real intermediate image at its focal length, f_o. The eyepiece sits exactly 1F beyond that image, producing parallel emergent rays — the eye stays relaxed (unaccommodated), and the final image is at infinity.
M = β/α = fₒ/f_e
β = angle subtended by the image at the eye; α = angle subtended by the object at the unaided eye. Long f_o + short f_e gives high magnification — but also a long telescope.
Reflecting telescopes
Cassegrain arrangement — also commonly examined.
- Newtonian: eyepiece near the top/side of the tube.
- Cassegrain: eyepiece behind the primary mirror, rays pass through a central aperture — better for cameras and large scale-ups.
- Both use a large parabolic primary mirror reflecting onto a smaller secondary mirror.
Collecting power ∝ D². A 15 cm mirror gathers ~350× more light than an 8 mm dilated pupil — crucial for seeing faint objects, since magnifying a star doesn't make it bigger (still a point source).
Aberrations
- Spherical aberration: rays further from the axis focus closer to the lens/mirror (shorter f) — image blurs. Mnemonic: cLoser to axis = Longer focal length. Fixed with a parabolic mirror/lens.
- Chromatic aberration: different wavelengths refract by different amounts (blue focuses closer than red) — only affects lenses, never mirrors.
Reflectors vs. refractors
| Reflectors | Refractors |
|---|---|
| Larger diameters possible; no chromatic aberration; no spherical aberration (parabolic); can observe non-visible λ; lighter/shorter for a given M. | Less sensitive to temperature changes; less maintenance (mirrors need periodic re-aluminising). |
Resolving power
Just resolved: central max of one pattern falls on the first minimum of the other.
θ ≈ λ/D (or 1.22λ/D)
Rayleigh's criterion: two sources are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other. Bigger D or smaller λ → smaller θ → more detail resolvable.
Exam essentials
Key equations
- M=fₒ/f_e
- θ≈λ/D (Rayleigh)
- Collecting power ∝ D²
Units of angle
- 1° = 60 arcmin = 3600 arcsec.
- Equations use radians; results often reported in degrees/arcmin/arcsec.
Common slips
- Multi-wavelength questions: use the smallest λ for the best (smallest) resolvable angle.
- A telescope doesn't "magnify" a star into a disc — it stays a point; a bigger aperture reveals more detail/brightness, not star size.
- Check whether a question wants reflector- or refractor-specific advantages before answering.