Telescopes: Principles, Types, and Properties in Physics

Telescopes in Physics

Systems for Measuring Radiation

Modern telescopes are part of systems designed to measure electromagnetic radiation from astronomical sources. These systems typically include:

• Telescope: Collects and focuses incoming radiation.

• Radiation "sorter": Separates radiation by wavelength or type.

• Detector: Senses and records radiation in specified wavelength regions.

• Historic Examples: Ancient observatories like Machu Picchu and Stonehenge used basic principles of radiation measurement.

Basic Ideas of Telescopes

Telescopes are designed to collect and focus light from distant sources to form images. Their two main jobs are:

• Collecting Light: Gathering as much light as possible from a source.

• Focusing Light: Directing the light to form a clear image.

Calculating Light Collecting Area:

The area $A$ of a telescope's aperture determines how much light it can collect:

$A = \frac{\pi d^2}{4}$

where $d$ is the diameter of the aperture.

Telescope Parts

• Eye piece

• Finderscope

• Focuser

• Mount

• Optical Tube

• Aperture

Mounts

Mounts are essential for stabilizing and orienting telescopes:

• Alt-Az (Altitude-Azimuth): Simple design, but cannot follow Earth's rotation.

• Equatorial: More complex, allows tracking of celestial objects by aligning with Earth's axis.

Telescope Types

• Refractor: Uses lenses to focus light at a focal point. Typically smaller and used in earlier models (e.g., Yerkes Observatory).

• Reflector: Uses mirrors to focus light. Larger, modern telescopes; can be designed for various applications.

Types of Reflector Telescopes

• Prime Focus: Light is focused directly in the middle of the telescope tube.

• Newtonian: Uses a diagonal mirror to direct light to the side of the tube.

• Cassegrain: Light is reflected through a hole in the primary mirror to a compact focus point.

• Coude: Multiple mirrors direct light to a fixed point away from the telescope.

Segmented Mirrors

Large telescopes may use multiple smaller mirror segments instead of a single large mirror. Example: James Webb Space Telescope (JWST).

Detectors

• Early detectors used glass plates with light-sensitive emulsions.

• Modern detectors use CCD (Charge-Coupled Devices), also called "light buckets".

• CCDs are composed of silicon squares that act as electron "wells".

• Pixel response is proportional to the number of photoelectrons collected.

• Modern CCDs have quantum efficiency exceeding 100%.

Quantum Efficiency Equation:

$QE = \frac{N_{\text{electrons}}}{N_{\gamma}}$

Spectrometers

• Photometry: Measures brightness over a wide range of wavelengths.

• Spectrometry: Measures brightness as a function of wavelength (e.g., color).

• Main components: Prism or diffraction grating.

Telescope Properties

• Focal Length (F): Distance from mirror/lens to focal point. Image forms at the focal plane.

• Angular Size: The apparent size of an object as seen through the telescope.

Angular size formula:

$D = \frac{ed}{206265} = \theta$ in radians

Plate Scale: Relates angular size to focal length and physical size:

$F\theta = d$

Shorter focal length yields brighter images but lower resolution.

Field of View

• Amount of sky visible at a given time through the telescope.

• Fullness of view is often measured in degrees.

• Larger field of view is useful for surveys; smaller field for detailed observation.

Advantages of Telescopes

• Light Gathering Power

• Resolution

• Magnification

Light-Gathering Power

• Luminosity: Total power emitted by a source, independent of distance.

• Absolute/Intrinsic Brightness: True brightness of an object.

• Flux: Apparent brightness as seen by an observer, depends on distance.

Flux equation:

$F = \frac{L}{4\pi r^2}$

Inverse square law: Brightness decreases as the square of the distance increases.

Signal to Noise Ratio (SNR)

• Light arrives as discrete photons; detection is subject to statistical fluctuations.

• Poisson distribution governs photon arrival.

• Longer exposure times reduce randomness.

• Noise is the remaining randomness in the signal.

• SNR measures the "cleanliness" of the measurement.

Key Calculations:

$SNR = \sqrt{N}, \ N = \text{number of photons}$

$SNR = \sqrt{\frac{FAt\theta_{\text{eff}}\langle S \rangle}{hc}}$, \text{solve for time}$

Resolution

• Ability to distinguish between two close objects.

• Diffraction limits resolution; larger apertures improve it.

• Point Source Function (PSF): Describes the light pattern from a point source.

• For circular apertures, the ideal PSF is an Airy Disk.

Resolving Two Point Sources

Minimum angular separation $\theta$ that can be resolved:

$\theta = \frac{1.22\lambda}{D}$

where $D$ is the aperture diameter.

Atmospheric Effects

• Atmosphere blocks many wavelengths; only certain windows (IR, Optical, Radio) are accessible.

• Scintillation (star twinkling) and turbulence degrade resolution.

• Best seeing conditions: 0.2 arcseconds; ordinary: 1 arcsecond; poor: >3 arcseconds.

Adaptive Optics

• Compensates for atmospheric distortions by changing mirror shapes.

• Space telescopes avoid atmospheric issues; limited only by diffraction.

Active Optics

• Large mirrors are difficult to maintain due to environmental factors.

• Hundreds of pistons underneath the primary mirror help maintain its shape.

Summary Table: Telescope Types and Properties

Type	Optical Element	Size	Example
Refractor	Lens	Small/Early	Yerkes
Reflector	Mirror	Large/Modern	JWST

Most Important Feature

The diameter of the telescope is the most important feature, as it determines both light-gathering power and resolution.

Additional info: Some equations and explanations have been expanded for clarity and completeness.