Telescopes

Explore refracting and reflecting telescopes, angular magnification, resolving power, and the role of radio telescopes in modern astronomy.

AQA A-Level Physics · Astrophysics Option

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Describe the construction of refracting and reflecting telescopes

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Use M = f_o / f_e for angular magnification in normal adjustment

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Apply the Rayleigh criterion for resolving power

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Describe the construction and use of radio telescopes

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Compare advantages and disadvantages of each telescope type

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State advantages of space-based telescopes

The Refracting Telescope

A refracting telescope uses two converging lenses: an objective lens (long focal length f_o, large diameter) and an eyepiece lens (short focal length f_e).

Normal adjustment: The instrument is set so that the final image is at infinity (parallel rays exit the eyepiece). This means:

The objective forms a real, diminished image at its focal point F_o
F_o coincides with the focal point of the eyepiece
The eyepiece acts as a magnifying glass for the intermediate image
Total length of telescope in normal adjustment = f_o + f_e

Angular magnification M = f_o / f_e

Angular magnification is the ratio of the angle subtended at the eye by the image through the telescope to the angle subtended by the object viewed with the naked eye.

The Reflecting Telescope

A reflecting telescope uses a large concave primary mirror (instead of a lens) plus an eyepiece. Common designs:

Newtonian reflector: A small flat secondary mirror deflects the converging beam to a focuser at the side of the tube
Cassegrain reflector: A convex secondary mirror sends light back through a hole in the primary mirror — gives a long effective focal length in a compact tube

M = f_o / f_e (same formula — f_o is the focal length of the primary mirror)

Advantages of reflectors over refractors: no chromatic aberration (mirrors reflect all wavelengths equally), mirrors can be made much larger than lenses (no need to be perfectly transparent throughout), lighter support structures, easier to grind a mirror than a large lens.

Resolving Power

Resolving power is the ability of a telescope to distinguish two closely spaced objects as separate (rather than blurring into one). It is limited by diffraction at the aperture.

The Rayleigh criterion gives the minimum resolvable angle θ_min (in radians):

θ_min = 1.22 λ / D

Where:

λ = wavelength of light (m)
D = diameter of the objective lens or mirror (m)

A smaller θ_min means better resolution. To improve resolution: use a larger diameter objective (D↑) or observe shorter wavelengths (λ↓).

Atmospheric turbulence limits optical telescope resolution to much worse than the diffraction limit for ground-based instruments. This is why space telescopes like the Hubble Space Telescope achieve near-diffraction-limited performance.

Radio Telescopes

Radio telescopes detect radio waves (wavelengths from mm to metres) from astronomical objects. Key features:

A large parabolic dish focuses radio waves onto a receiver at the focal point
Dishes must be much larger than optical mirrors to achieve comparable resolution (because λ_radio >> λ_visible)
Examples: Jodrell Bank (76 m), Arecibo (305 m — now decommissioned), FAST (500 m, China)

Interferometry / aperture synthesis: Multiple radio dishes separated by large baselines act as a single telescope with diameter equal to the baseline separation. The Event Horizon Telescope used Earth-spanning baselines to image a black hole shadow.

Radio telescopes can operate in daytime and through cloud cover (radio waves pass through the atmosphere). They reveal cool gas, pulsars, quasars, and the CMB — objects invisible to optical telescopes.

Comparing Telescope Types

Feature	Refractor	Reflector	Radio
Chromatic aberration	Yes (achromatic needed)	None	N/A
Max practical aperture	~1 m (Yerkes, 40")	10+ m (VLT, ELT)	500 m (FAST)
Atmospheric limits	Seeing, absorption	Seeing, absorption	Little effect
Wavelength range	Visible/near-UV/IR	UV to IR	Radio (~1 mm–30 m)
Cost per aperture	High	Lower	Lower

Space-based telescopes (e.g. Hubble, James Webb) operate above the atmosphere — no seeing effects, access to UV and infrared wavelengths absorbed by the atmosphere, and near-diffraction-limited resolution.

Example 1: Angular magnification calculation

A refracting telescope has an objective lens of focal length 1200 mm and an eyepiece of focal length 25 mm. Calculate (a) the angular magnification in normal adjustment, and (b) the length of the telescope tube.

1 (a) M = f_o / f_e = 1200 / 25

2 (b) Length = f_o + f_e = 1200 + 25 = 1225 mm

(a) M = 48× (b) Length = 1225 mm = 1.225 m

Example 2: Resolving power — minimum angle

The Hubble Space Telescope has a mirror diameter of 2.4 m. Calculate the minimum resolvable angle for green light (λ = 550 nm).

1 θ_min = 1.22λ / D = 1.22 × 550 × 10⁻⁹ / 2.4

2 θ_min = 671 × 10⁻⁹ / 2.4 = 2.80 × 10⁻⁷ rad

θ_min = 2.8 × 10⁻⁷ rad ≈ 0.058 arcseconds — far better than ground-based telescopes (~0.5–2 arcseconds)

Example 3: Radio telescope resolution

A radio telescope dish has diameter 25 m and observes at wavelength 21 cm (neutral hydrogen line). Calculate the minimum resolvable angle in degrees.

1 θ_min = 1.22 × 0.21 / 25 = 0.256 / 25 = 0.01024 rad

2 Convert to degrees: 0.01024 × (180/π) = 0.587°

θ_min ≈ 0.59° — much worse than the Hubble Telescope. This illustrates why radio telescopes need vast diameters or interferometry to achieve fine resolution.

Example 4: Finding eyepiece focal length

A reflecting telescope has an angular magnification of 120× in normal adjustment. The primary mirror has focal length 3.0 m. What focal length eyepiece is used?

1 M = f_o / f_e → f_e = f_o / M = 3.0 / 120

f_e = 0.025 m = 25 mm

Q1. A refracting telescope is in normal adjustment when:

Q2. A telescope has f_o = 800 mm and f_e = 20 mm. What is its angular magnification?

Q3. How can the resolving power of a ground-based optical telescope be improved?

Q4. Why do radio telescopes need to be much larger than optical telescopes for comparable resolution?

Q5. Which of the following is an advantage of a space-based telescope over a ground-based one?

Challenge 1. A pair of stars is separated by an angle of 5.0 × 10⁻⁷ rad. What minimum objective diameter is needed to resolve them in yellow light (λ = 589 nm)? Give your answer in cm.

Challenge 2. An interferometric radio array has two dishes separated by 3000 km. It observes at a frequency of 1.4 GHz (neutral hydrogen line). (a) Calculate the wavelength. (b) Calculate the angular resolution and compare with the Hubble Space Telescope (D = 2.4 m, λ = 550 nm).

Challenge 3. A student claims a refractor with f_o = 2 m and f_e = 10 mm gives M = 200, but also that a longer telescope always gives more magnification. Evaluate this, and design a compact (tube length ≤ 500 mm) telescope with M ≥ 50 using a reflecting design. State all focal lengths chosen.