Physics - Telescopes - Astrophysics

What is a principal axis?

For a single converging lens, the line that passes through the centre of the lens at right angles to it is called the principal axis or optical axis.

What is the principal focus?

Light rays that are essentially parallel to the principal axis converge to a point called the principal focus.

What is focal length?

The distance from the centre of the lens to the principal focus.

The shorter the focal length the more the stronger the lens converges its lenses.

What are optical telescopes?

Telescopes that receive light from the visible part of the light spectrum.

What are refracting telescopes?

Telescopes that focus light rays by refraction through lenses.

What lenses does a simple refracting telescope contain?

A converging objective lense

A converging eyepiece lense

What is normal adjustment and give a diagram showing this.

In normal adjustment the final image appears at infinity, this means the rays coming out of the telescope are parallel, this reduces strain on the eye.

Explain the ray diagram representing normal adjustment.

• Light from the edge of an object enters the objective lens at an angle β to the principal axis, and forms an intermediate image in between the lenses.

• The angle β is the angle subtended by the object to the unaided eye and is a very small angle.

• In normal adjustment parallel light rays emerge from the eyepiece lens.

• This occurs when the focus of the eyepiece lens (focal length f_e) is coincident with that of the objective lens (focal length f_o)

• When looking through the eyepiece, the angle subtended by the image to the eye, α, has now increased.

What is an object’s angular size?

The angle between the lines of sight to its two opposite ends and is a measure of how big the object appears to the unaided eye.

What is angular magnification?

M = (angle subtended by image at eye)/ (angle subtended by object by unaided eye) = α/β

M = f_o/f_e

What is chromatic aberration?

An objective lens focuses the different colours over a range of focal lengths, a deficiency known as chromatic aberration.

What is spherical aberration?

Because of the curvature of the lens, spherical aberration results in light rays in a parallel beam being focused at slightly different positions.

What is the Cassegrain arrangement of a reflecting telescope?

The large primary mirror has a parabolic shape. A convex secondary mirror with a hyperbolic shape is used, which sends the rays down an opening in the primary mirror (usually in the centre), where the image is brought to a focus using an eyepiece or an imaging camera.

What are the disadvantages of refracting telescopes?

• Mounting of the lens and support can only be made using the edge of the lens

• Using glass of sufficient clarity and purity and free from defects to make large-diameter telescopes is extremely difficult

• Large-diameter lenses are heavy and tend to distort under their own weight

• Suffer from chromatic aberration and spherical aberration

• Heavy and difficult to manoeuvre quickly

• Difficult to mount heavy observing equipment and associated electronics

• Large magnifications require large objective lenses and very long focal lengths

What are the advantages of reflecting mirrors?

• Large single mirrors can be made, which are light and easily supportable from behind

• Mirror surfaces can be made just a few nanometres thick, giving excellent image properties

• Mirrors use only the front surface for reflection, so removing many of the problems associated with lenses

• No chromatic aberration, and no spherical aberration when using parabolic mirrors

• Relatively light mirrors allow rapid response to astronomical events

• Smaller segmented mirrors can be used to form a large composite objective mirror

How can the atmosphere impact telescopes?

The atmosphere can absorb different wavelengths meaning it would be useless to observe some wavelengths of light from the surface of earth as they would be absorbed by the atmosphere.

What is resolving power?

This is its ability to produce separate images of closely spaced objects.

What is an Airy disc?

A telescope may not focus a star to a perfect point but to a disc instead, called an Airy disc

What is the Rayleigh criterion? + extra note on how θ can be changed

The Rayleigh criterion states that two point objects can be resolved if their angular separation is at least

θ = λ/D

where λ is the wavelength of light in metres, D is the diameter of the mirror or lens in metres and θ is the angular position in radians.

The angle θ is known as the minimum angular resolution of the instrument at a particular wavelength λ.

Extra note:

This gives us the important result that the width of the central maximum can be reduced by making the diameter, D, of the mirror or lens as large as possible, for a fixed value of the wavelength. Also, the shorter the wavelength, the smaller the width of the disc.

What are arcminutes and arcseconds?

1 arcminute = 1’ = 1/60 of 1°

1 arcsecond = 1’’ = 1/60 of 1’ = 1/3600 of 1°

What is the collecting power of a telescope?

It is a measure of its ability to collect incident electromagnetic radiation. It is directly proportional to the square of the diameter of its objective.

What are the similarities and differences of radio telescopes compared to optical telescopes? structure, positioning and use, together with comparisons of resolving and collecting powers.

Feature	Radio telescopes	Optical telescopes
Structure	Large parabolic dish focuses radio waves onto a receiver; signal amplified.	Lens or mirror focuses visible light to form an image.
Positioning/use	Ground-based; work day and night; isolated areas avoid radio interference.	Often ground-based; usually observe at night; affected by clouds and daylight.
Resolving power	Lower; long wavelengths require a much larger aperture.	Higher for the same diameter; visible light has shorter wavelengths.
Collecting power	Large dishes collect weak radio signals.	Larger mirrors/lenses collect more light.
Similarity	Both collect electromagnetic radiation and focus it to detect astronomical objects.	Both collect electromagnetic radiation and focus it to detect astronomical objects.

What are the different types of telescopes and they features?

Telescope type	Structure	Positioning	Main use
Optical	Lenses or mirrors; detects visible light.	Ground-based; usually night-time.	Observes stars and galaxies in visible light.
Radio	Large parabolic dish and receiver.	Ground-based; day and night, away from interference.	Detects radio waves; can see gas through dust clouds.
Infrared (IR)	Mirrors/lenses and cooled IR detector.	Mainly space or high altitude; some wavelengths observable from ground.	Studies cool objects, gas and star formation.
Ultraviolet (UV)	Mirrors and UV-sensitive detectors.	Space-based, as atmosphere absorbs most UV.	Studies hot young stars, very hot gas and the solar corona.
X-ray	Special mirrors using grazing incidence; X-ray detectors.	Space-based, as atmosphere absorbs X-rays.	Studies extremely hot gas, black holes, neutron stars and supernova remnants.
Gamma-ray	Special detectors; no mirrors.	Space-based.	Detects very high-energy events, such as gamma-ray bursts and pulsars.

Comparison	Key point
Resolving power	\(\theta \approx \lambda/D\): shorter wavelengths or larger apertures give better resolution. Radio telescopes need very large dishes.
Collecting power	Larger apertures collect more radiation and give stronger signals.
Interferometers	Link multiple telescopes to improve resolving power; radio telescopes can use very long baselines.

What is a charge-coupled device (CCD)?

Is a semiconductor device in which light is converted directly into digital information. CCD’s are divided into small regions called pixels.

What is quantum efficiency (QE)?

(number of photons detected)/(number of photons incident) x100

The quantum efficiency tells us how well a detector can capture photons and make them available for further amplification and imaging.

Compare the eye and CCD as detectors in terms of quantum efficiency, resolution and convenience of use.

Quantum efficiency:

Eyes have a quantum efficiency of roughly 4%-5% while CCD’s can be in excess of 80%. So CCD’s require shorter exposure times and CCD’s generally have a larger spectral range.

Resolution:

For CCD’s resolution depends on pixel size, smaller pixels give better resolution, while for the eye, resolution depends on the spacing of light sensitive cells in the retina.

CCD is more convenient for astronomy as it has a better resolution and quantum efficiency.