Telescopes and Astronomical Observation

Telescopes and Astronomical Observation

Telescopes collect and focus electromagnetic radiation from astronomical objects. Different types of telescope observe different parts of the electromagnetic spectrum, each revealing different physical processes.

Refracting Telescopes

A refracting telescope uses two converging lenses:

• Objective lens: Large diameter, long focal length (f_o). Collects light and forms a real, inverted, diminished image at its focal point.
• Eyepiece lens: Small diameter, short focal length (f_e). Acts as a magnifying glass to produce a virtual, magnified image for the eye.

In normal adjustment (final image at infinity, relaxed eye): the lenses are separated by f_o + f_e, and the intermediate image forms at the common focal point.

Angular magnification in normal adjustment:

M = angle subtended by image / angle subtended by object = f_o / f_e

Worked Example

A refracting telescope has an objective lens of focal length 1.20 m and an eyepiece of focal length 0.025 m. Find the angular magnification and the telescope length in normal adjustment.

M = f_o/f_e = 1.20/0.025 = 48×

Length = f_o + f_e = 1.20 + 0.025 = 1.225 m

Limitations of Refractors

• Chromatic aberration: Different wavelengths refract by different amounts, causing colour fringing. Partially corrected with achromatic doublets (two lenses of different glass types).
• Size limitation: Large lenses are heavy, can only be supported at the edges (sag under gravity), and must be made from flawless glass throughout
• Absorption: Glass absorbs some light, especially UV and IR

Reflecting Telescopes

A reflecting telescope uses a concave (parabolic) primary mirror to collect and focus light, and a secondary mirror or lens arrangement to direct the image to the eyepiece or detector.

Cassegrain design: A convex secondary mirror reflects light back through a hole in the primary mirror.

Newtonian design: A flat secondary mirror at 45° reflects light to an eyepiece on the side.

Advantages of Reflectors Over Refractors

• No chromatic aberration (reflection does not depend on wavelength)
• Can be made much larger — mirrors can be supported from behind
• Lighter — only one surface needs to be polished
• All wavelengths reflected equally — can observe UV, visible, and IR
• Cheaper per unit area for large apertures

Collecting Power

The collecting power of a telescope is proportional to the area of the objective:

Collecting power ∝ πD²/4 ∝ D²

where D = diameter of the objective lens or primary mirror.

Doubling the diameter increases the collecting power by a factor of 4, allowing fainter objects to be observed.

Resolving Power (Angular Resolution)

The Rayleigh criterion gives the minimum angular separation at which two point sources can just be resolved:

θ_min = 1.22 λ/D (in radians)

where:

• θ_min = minimum resolvable angle (rad)
• λ = wavelength of observation (m)
• D = diameter of the aperture (m)

Larger apertures give better (smaller) angular resolution. This is why large telescopes can see finer detail.

Worked Example

The Hubble Space Telescope has a mirror diameter of 2.4 m. Find its angular resolution at λ = 550 nm.

θ = 1.22 × 550 × 10⁻⁹ / 2.4 = 2.80 × 10⁻⁷ rad = 0.058 arcseconds

Radio Telescopes

Radio telescopes detect radio waves (λ ≈ mm to m) from astronomical sources.

Design: A large parabolic dish focuses radio waves onto a receiver at the focal point.

Advantages: Can observe through clouds and dust; can observe day and night; radio sources reveal different physics (pulsars, quasars, CMB).

Disadvantage: Very poor angular resolution because λ is large. Even a 76 m dish at λ = 21 cm:

θ = 1.22 × 0.21 / 76 = 3.4 × 10⁻³ rad ≈ 0.19° (very poor compared to optical)

Solution — Interferometry: Combining signals from multiple dishes separated by a baseline distance B gives an effective resolution of θ ≈ λ/B. Very Long Baseline Interferometry (VLBI) uses dishes on different continents.

Space-Based Telescopes

Advantages of placing telescopes in space:

• No atmospheric absorption: Earth's atmosphere blocks most UV, X-ray, gamma ray, and much IR radiation. Only visible light, some IR, and radio waves reach the ground.
• No atmospheric turbulence: Eliminates "twinkling" (scintillation) that blurs ground-based images
• No light pollution: Can observe faint objects
• No weather: Continuous observation

Examples: Hubble (visible/UV/near-IR), James Webb Space Telescope (IR), Chandra (X-ray), Fermi (gamma ray)

Disadvantages: Extremely expensive to launch and maintain; difficult to repair; limited lifetime.

Charge-Coupled Devices (CCDs)

CCDs are electronic detectors that convert light into electrical signals:

• Quantum efficiency: ~80–90% (compared to ~1–2% for photographic film)
• Linear response: Output signal proportional to light intensity
• Digital output: Easy to store, process, and transmit electronically
• Wide wavelength range: Sensitive from UV to near-IR
• Can record very faint objects with long exposure times (charge accumulates)

CCDs work by the photoelectric effect: Photons liberate electrons in silicon pixels, and the accumulated charge in each pixel is read out to produce a digital image.

Atmospheric Windows

The Earth's atmosphere is transparent in two main "windows":

• Optical window: Visible light (~400–700 nm)
• Radio window: Radio waves (~1 mm to ~20 m)

Other wavelengths are absorbed by atmospheric gases: water vapour and CO₂ absorb IR; ozone absorbs UV; the ionosphere reflects long radio waves. This is why UV, X-ray, gamma ray, and far-IR astronomy must be done from space or high-altitude balloons.