Theory — Telescopes and Image Analysis

The single most important number for a telescope is its aperture D, the diameter of its main lens or mirror. Aperture controls both how much light is collected and how fine the detail that can be resolved.

1. Refractors and reflectors

A refractor uses a lens to bend light to a focus; a reflector uses a curved mirror. Almost all large research telescopes are reflectors, because large mirrors are easier and cheaper to make and support than large lenses.

2. Light-gathering power

The light collected grows with the area of the aperture, which scales as the square of the diameter:

Light-gathering ratio Ratio = (D1 / D2)2
Doubling the aperture collects four times as much light.

3. Resolving power

Diffraction sets the finest detail a telescope can separate. The Rayleigh criterion gives the smallest resolvable angle:

Resolving power (Rayleigh) θ (arcsec) = 2.52 × 105 × λ / D
  with λ and D in the same units (e.g. metres)
A larger aperture (or shorter wavelength) resolves finer detail.

This comes from θ = 1.22 λ / D in radians, converted to arcseconds with the 206265 factor.

4. The atmosphere and why we go to space

Turbulence in the air blurs images, a limit called seeing that is usually about 1 arcsecond from the ground no matter how large the telescope. Space telescopes escape this blur, and they also reach wavelengths (ultraviolet, most infrared, X-ray) that the atmosphere blocks. Detectors called CCDs record the image digitally so it can be measured.

Apparatus

Observing uses instruments to collect, focus, and record light. In the simulation these are modelled, but the readings match what each instrument would give.

Refractor
A lens telescope: the objective lens bends light to a focus at the eyepiece.
Newtonian reflector
A mirror telescope: a curved primary mirror focuses light to a small flat secondary and out to the eyepiece.
CCD detector
A digital sensor that records the brightness at each pixel, producing a measurable image.
Eyepiece
A small lens that magnifies the focused image for the eye.
Equatorial mount
A mount aligned to the celestial pole so one motion tracks the stars as the sky turns.
Radio dish
A large parabolic dish that focuses radio waves to a receiver at its focus.

Instructions

Work through both tabs. Calculate first by hand, then press the button to compare.

Part A — Resolving power

Part B — Light-gathering power

Simulation

Telescope BenchCalculate first, then check against the simulation.

Team Questions

1. A 10 m telescope collects how many times more light than a 2.5 m telescope?
2. To resolve finer detail you should:
3. Space telescopes are used partly because the atmosphere:

Example Report

Worked example: resolution of the Hubble Space Telescope

Hubble has an aperture of about D = 2.4 m, observing green light at λ = 5.5 × 10-7 m.

θ = 2.52 × 105 × λ / D = 2.52 × 105 × (5.5 × 10-7) / 2.4 ≈ 0.058 arcsec.

Hubble’s resolution is about 0.05 arcsecond, far better than the roughly 1 arcsecond that atmospheric seeing allows from the ground. Computing this and comparing is the calculate-then-compare core of the lab.

Practice Questions

1. A 1 m telescope in green light (5.5 × 10-7 m) resolves about:
2. Most large research telescopes are reflectors because:
3. Ground-based image sharpness is usually limited to about 1 arcsecond by: