Topic 2 The Reflecting Telescope

In the exam you are expected to know about:

• Reflecting telescopes 

• Focal point of concave mirror

• Cassegrain arrangement, ray diagram to show path of rays through the telescope as far as the eyepiece

• Relative merits of reflectors and refractors including a qualitative treatment of spherical and chromatic aberration

• Resolving power;

• Appreciation of diffraction pattern produced by circular aperture,

• Airy disc

• Resolving power of telescope, Rayleigh criterion,

• 

• Charge coupled device: Structure and operation of the charge coupled device

• Quantum efficiency of pixel > 70%

Reflecting Telescopes

Lenses suffer a major drawbacks:

• They refract light of different colours by different amounts.  You can see that when light is split into a spectrum with a prism.  This leads to chromatic aberration.  The image is distorted.

• They do not transmit 100 % of the light; some is lost.

• Large lenses are very difficult to make.

• To get a good magnification you need an objective lens with a very long focal length.  This can make the telescope very long.  The largest is 20 m, with a 1 m wide objective lens.

Concave mirrors can be used to project a real image:

The advantages of a concave mirror that is front-silvered are:

• it can be made bigger (large diameter lenses are very hard to make);

• there is no chromatic aberration in reflection.

The focal length of a concave mirror is half the radius of curvature.  Spherical mirrors are easy to produce, but the image can be distorted by spherical aberration, so a parabolic shape is used to give perfect focusing.  The diagrams show the two kinds of reflecting telescope:

This is called the Newtonian system.  Light is reflected to an eyepiece at the side of the telescope.

This telescope uses the Cassegrain system.  The eyepiece is at the back of the telescope.  The hole in the centre of the mirror does not affect the viewing ability.  Both kinds are found in observatories.  

All large telescopes use the reflecting system.   The largest telescope in the world has a 5 metre diameter concave mirror which requires many tonnes of glass, a considerable cooling time, and many hundred of hours of grinding to get it to a perfect shape.  It was silvered with a few grams of aluminium.

Question 1 Suggest reasons for the following:

(a) The silvering on a telescope mirror is on the top surface.

(b) The hole in the centre of the mirror of the Cassegrain system does not affect the viewing ability of the instrument.  ANSWER

Resolving Power

The resolving power of any optical instrument is an indication of how good it is at distinguishing two objects close to one another.  For example, at a long distance two car headlights appear as a single blob of light.  At about 5 km, we can tell that they are two separate lights.  This is because the eye can resolve down to an angle about 3 x 10^-4 radians.

Astronomers use angles in radians or degrees:

• There are 2 p radians in a circle = 360^o.

• I rad is approximately 57^o.

• Degrees are subdivided into arc-minutes (1^o = 60 arc-minutes [60'])

• and arc-seconds (1' = 60 arc seconds [60''])

Radians have the advantage that for small angles:

sin q = tan q = q

This makes trigonometrical functions easier.  However astronomers tend to use arc-seconds which are useful for describing very small areas of sky.

Question 2 The Moon has a diameter of about 3500 km and is about 400 000 km from the Earth.  What is the angle in radians that the Moon subtends to an observer on the Earth? What is this in degrees?  ANSWER

Question 3 Entirely coincidentally the angle subtended by the Sun is exactly the same as the angle subtended by the Moon.  The distance between the Earth and the Sun is 150 x 10⁶ km.  What is the diameter of the Sun?  ANSWER

The observation of objects in space is made difficult because the atmosphere is turbulent.  This results in the twinkling or scintillation of stars.  Light pollution from street lights does not help either.  Dust in the atmosphere causes scattering of light. Major observatories have moved as far away as possible from cities and are situated on high mountains. 

The best images of them all come from the Hubble Telescope, a Cassegrain instrument which is in orbit above the Earth.  There are no problems with distortion of the atmosphere up in space, but doing routine maintenance is not very easy.  The quality of pictures produced has been very high.

Diffraction Effects

When light enters a telescope, it is passing through a gap.  It spreads out by the process of diffraction.  You will remember from Module 4 how when light passes through a single slit, dark and bright fringes are made.  (You might want to break off and revise that bit  Go to Topic 6.)  The resulting pattern is called a Fraunhofer Diffraction pattern:

Fraunhofer diffraction also occurs with circular openings.  If we use a circular aperture we get an effect like this:

The central bright spot is called an Airy Disc.

The physicist Lord Rayleigh studied the effect of overlapping of fringes and came up with the Rayleigh's Criterion.  (His Lordship did most of his thinking in the lavatory, according to his butler.)  The angular separation is given by the formula:

[q - angular separation (rad); l - wavelength (m); D - aperture width (m)]

To improve the resolution of a telescope, we need to have a large aperture and a short wavelength.

Question 4 What is the resolving power of a telescope of diameter 15 cm at a wavelength of 600 nm?  ANSWER

In practice, although telescopes have much better resolution that the eye, this is limited by the atmosphere.  Telescopes have large apertures to allow as much light to get in as possible.

Light Detectors

Once we have got a good image down the telescope, we need to have a way of recording it.  In early astronomy the human eye was used, and the results depended on the artistic ability of the astronomer.  Photographic techniques were used from the middle of the Nineteenth Century.

The resolution depends not just on the Rayleigh Criterion, but also on the emulsion of the film.  Very fine grain films are used for astronomical observation.  The quality of the picture needed to be high and precision mechanisms were essential for tracking individual stars across the sky.  If the grains of film are larger than the resolution of the telescope, than that is the limiting factor.

More recently a charged coupled device is used and is connected to a computer.  The computer can quickly do comparisons of images which would take a skilled astronomer several days.  The CCD is constructed like this:

The picture below shows a CCD.

The CCD is about the size of a postage stamp and can have many millions of pixels on it.  They work on the principles of quantum physics.  They have these advantages over film:

• They are sensitive;

• Their quantum efficiency is about 70 %.  A film has a quantum efficiency of about 4 % which means that 25 photons are needed to deposit a grain of silver.

• They are getting cheaper all the time.

• The CCD can detect radiations that are beyond the visible spectrum.

The graph below shows the quantum efficiency of the CCD:

The eye has a quantum efficiency of only 1 %.

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