9.1.4 Advantages of large diameter telescopes

1. Collecting Power:

• Collecting power is the ability of a telescope's lens or mirror to gather incoming electromagnetic radiation (EM).
• A telescope's collecting power is directly proportional to the area of its objective lens or mirror. This means that as the size of the objective lens or mirror increases, so does its ability to collect light.
• Since $area = π(diameter/2)²$, collecting power $∝ (objective \ diameter)²$.
• The larger the collecting power, the brighter the image produced by the telescope, which enhances observation capabilities.

2. Resolving Power:

• Resolving power is the telescope's ability to distinguish between objects that are close together in the sky.
• To resolve two objects, the angle (θ) between them as observed from Earth must be greater than or equal to the minimum angular resolution (θ) of the telescope.
• Minimum angular resolution in radians is given by:

$$\theta = \frac{\lambda}{D}$$

Where:

• $λ$ is the wavelength of the observed radiation,
• $D$ is the diameter of the objective lens or mirror.
• This criterion is known as the Rayleigh Criterion, which states that two objects will be unresolved if any part of the central maximum of either object's image overlaps with the first minimum diffraction ring of the other.
• Light diffracts as it passes through a telescope, creating a central bright spot surrounded by dark rings known as an airy disc.

3. Charge-Coupled Devices (CCDs):

• CCDs are arrays of light-sensitive pixels that become charged when exposed to light via the photoelectric effect.
• Advantages of CCDs over the human eye:
  • Quantum Efficiency: CCDs capture about 80% of incoming photons compared to 4-5% for the human eye.
  • Spectral Range: CCDs detect infrared, ultraviolet, and visible light, while the human eye detects only visible light.
  • Pixel Resolution: CCDs typically have around 50 megapixels, which allows for fine detail, though the human eye has a higher effective resolution.
  • Spatial Resolution: CCDs have a spatial resolution of around 10 μm, compared to 100 μm for the human eye, allowing finer details to be captured.
  • Convenience: Images from CCDs are digital, enabling storage and sharing, whereas the human eye cannot retain images directly.

Comparison Table: CCD vs Human Eye

Feature	CCD	Human Eye
Quantum Efficiency	~80%	4-5%
Spectral Range	Infrared, UV, Visible	Only Visible Light
Pixel Resolution	~50 Megapixels	~500 Megapixels
Spatial Resolution	10 μm	100 μm
Convenience	Digital, sharable	Immediate but non-recordable