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Telescopes and Resolving Power

Every telescope faces the same fundamental limit: no matter how good the optics, there is an absolute cap on how much fine detail it can ever resolve, set by nothing more than its aperture size and the wavelength of light it collects. This single idea explains why the biggest astronomical telescopes on Earth (and in space) are always built as large as engineering allows.

40 min Video by Williams Physics Education Module 5.5 Astrophysics and cosmology

Astrophysics: Telescopes — Reflecting Telescopes and Resolving PowerWatch the full walkthrough before the notes below.

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What you'll be able to do

Describe the structure and operation of a refracting telescope
Describe the structure and advantages of a reflecting telescope
Calculate the angular magnification of a refracting telescope in normal adjustment
Use the Rayleigh criterion to calculate resolving power

The refracting telescope

A $refracting telescope$ uses two converging lenses: a long-focal-length $objective lens$ , which collects light from a distant object and forms a real image at its focal plane, and a short-focal-length $eyepiece lens$ , which magnifies that image for viewing. In $normal adjustment$ , the final image is formed at infinity, so the objective’s image lies exactly at the eyepiece’s focal point, and the two focal lengths add to give the telescope’s overall length.

M = \frac{f _{o}}{f _{e}}

Angular magnification in normal adjustment (fo = objective focal length, fe = eyepiece focal length).

1Convert units:

f_{e} = 25 \times 1 0^{- 3}

2Magnification:

M = \frac{f _{o}}{f _{e}} = \frac{1.2}{0.025}

3Length in normal adjustment:

L = f_{o} + f_{e} = 1.2 + 0.025

AnswerM = 48; length ≈ 1.225 m.

Tip — A larger objective focal length (relative to the eyepiece) gives greater magnification, but also a physically longer telescope — a real engineering trade-off.

The reflecting telescope

A $reflecting telescope$ replaces the objective lens with a large concave (parabolic) mirror. This avoids $chromatic aberration$ entirely — a lens refracts different wavelengths by slightly different amounts, blurring the image with coloured fringes, but a mirror reflects all wavelengths identically. Mirrors can also be manufactured, supported and scaled to much larger diameters than lenses, which — as you’ll see below — is exactly what improves a telescope’s ability to resolve fine detail.

Tip — Chromatic aberration is a problem specific to LENSES (refraction depends on wavelength); mirrors (reflection) are unaffected by it, which is why every major modern research telescope is a reflector.

Resolving power

The $resolving power$ of a telescope is its ability to distinguish two closely-spaced objects as separate, rather than a single blur. Diffraction of light at the telescope’s circular aperture sets an absolute limit, given by the Rayleigh criterion: two objects are just resolvable when the angle between them equals the minimum resolvable angle, $θ$ .

θ \approx \frac{λ}{D}

Rayleigh criterion (θ in radians); λ = wavelength, D = aperture diameter.

1Use

θ \approx \frac{λ}{D}

θ \approx \frac{550 \times 1 0 ^{- 9}}{0.20}

Answer

θ \approx 2.75 \times 1 0^{- 6}

rad

Tip — Resolving power improves with a LARGER aperture and a SHORTER wavelength — this is exactly why astronomers build enormous telescope mirrors, and why X-ray/UV telescopes can in principle resolve finer detail than visible-light ones of the same size.

Equation recap

M = \frac{f _{o}}{f _{e}}

Angular magnification (refracting telescope, normal adjustment).

θ \approx \frac{λ}{D}

Rayleigh criterion for resolving power.

Common mistakes to avoid

Believing a bigger eyepiece focal length gives more magnification.

Magnification M = fo/fe — a LARGER eyepiece focal length actually REDUCES magnification; it is the objective’s focal length that should be large.

Thinking chromatic aberration affects reflecting telescopes.

Chromatic aberration is specific to refraction (lenses); mirrors reflect all wavelengths identically, so reflecting telescopes avoid it entirely.

Assuming a telescope’s resolving power depends only on its magnification.

Resolving power is set by aperture diameter and wavelength (θ≈λ/D) — a telescope can magnify a blur without resolving any extra genuine detail.

Key takeaways

A refracting telescope uses two lenses; magnification (normal adjustment) M = fo/fe.
A reflecting telescope uses a mirror as its objective, avoiding chromatic aberration and allowing much larger apertures.
Resolving power (Rayleigh criterion): θ ≈ λ/D — larger aperture and shorter wavelength both improve resolving power.

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Telescopes and Resolving Power

40 min Video by Williams Physics Education Module 5.5 Astrophysics and cosmology