Optical and Radio Telescopes

A refracting telescope in normal adjustment has angular magnification $M=\frac{f_o}{f_e}$ and length $f_o+f_e$ . Reflectors use curved mirrors and avoid chromatic aberration. A telescope's resolving power is limited by diffraction, $\theta\approx\frac\lambda D$ ; its collecting power is proportional to $D^2$ . CCDs record images far more efficiently than the eye or film.

AQA 7408 Paper 3B≈ 40 minRevision 1 · updated 2026-10-27

Section 1 of 14

Learning objectives

Use $M=\frac{f_o}{f_e}$ for a refractor in normal adjustment.
Compare refractors and reflectors, including aberrations.
Use the Rayleigh criterion and collecting power.
Compare telescopes for different wavelengths and the CCD.

Pause and think

Why are radio telescopes so much bigger than optical ones?

Section 2 of 14

Core idea

Start hereSeeing further

Galileo's first telescope magnified about 20 times and showed moons around Jupiter. Today's telescopes are judged less by magnification than by two other numbers: how much light they gather and how fine a detail they can separate.

The big idea

Magnification $M=\frac{f_o}{f_e}$ . Resolution is limited by diffraction, $\theta\approx\frac\lambda D$ . Collecting power grows as $D^2$ . Big apertures win on both counts.

1. The refracting telescope

Angular magnification in normal adjustment

$\alpha\approx\frac h{f_o}$
The object subtends $\alpha$ ; the objective forms an image of height $h$ at its focal point.
$\beta\approx\frac h{f_e}$
That image is at the eyepiece's focal point; rays leave parallel at angle $\beta$ .
$M=\frac\beta\alpha=\frac{f_o}{f_e}$
$h$ cancels.

Length of the telescope

=f_o+f_e

Worked exampleA small refractor

$f_o=1.20$ m, $f_e=40$ mm.

Goal: $M$ and length.
Strategy: Use the result above, same units.

$M=\frac{1.20}{0.040}=30$
Ratio of focal lengths.
$L=1.20+0.040=1.24\text{ m}$
Lenses share a focal point.

Answer

M=30

, length

1.24

✓ CheckLong objective, short eyepiece: high magnification ✓.

2. Resolution and light gathering

Worked exampleRadio vs optical

Compare a $76$ m radio dish at $0.21$ m with a $0.10$ m optical telescope at $550$ nm.

Goal: Resolution of each.
Strategy: $\theta\approx\frac\lambda D$ .

$\frac{0.21}{76}=2.8\times10^{-3}\text{ rad}$
Radio dish.
$\frac{550\times10^{-9}}{0.10}=5.5\times10^{-6}\text{ rad}$
Small optical telescope.

AnswerThe small optical telescope resolves about 500 times finer detail.

✓ CheckThis is why radio telescopes are linked across continents (interferometry) ✓.

Telescopes across the spectrum

Drawing diagram…

Pick the instrument for the wavelength.

Key takeawayAberrations Chromatic: lenses focus colours differently (mirrors don't). Spherical: edges of a spherical surface focus closer (parabolic mirrors fix it).

Common misconceptionRadians

\theta\approx\frac\lambda D

gives radians; convert to degrees only if asked.

Pause and think

Why put an optical telescope in space if ground ones are bigger?

Summary

$M=\frac{f_o}{f_e}$ .
$\theta\approx\frac\lambda D$ .
Collecting power $\propto D^2$ .
CCD QE ≈ 80%.

Normal adjustment: Final image at infinity.
Rayleigh criterion: Limit of resolution, θ ≈ λ/D.
Quantum efficiency: Fraction of photons detected.

HistoryGalileo’s spyglass. In 1609 Galileo turned a spyglass with magnification about 20 to the sky and saw Jupiter's moons, overturning the idea that everything orbits Earth.

Fun factA dish across a valley. China's FAST radio telescope fills a natural valley: its dish is 500 m across.

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