Reflecting Telescopes

Astrophysics Lesson 3

Homework

Collect last homework – feedback on Friday.

Past Paper Question for this Friday.

Learning Objectives

Draw ray diagram to show path of rays through the telescope as far as the eyepiece for a Cassegrain arrangement.

Describe the relative merits of reflectors and refractors.

Explain qualitatively what is meant the terms chromatic aberration and spherical aberration.

Question

In a telescope the eyepiece has a focal length of 2 cm and the objective has a focal length of 220 cm. 

What is the magnification?  If the moon subtends an angle of 8.8

× 10-3 rad to the naked eye, what would the angle be for the image of the moon observed through the telescope?

Assuming the Moon is at a distance of 384,400 km, calculate the radius of the Moon.

Answer

Magnification = fo/fe = 220/2 = 110Angle subtended by the Moon = 8.8

× 10-3 rad x 110 = 0.97 radD = rα = 384,400 km × 8.8 × 10-3

radians = 3382.72 kmSo the radius of the Moon = D/2 =

1690 km (3 s.f.)

Summary

Refracting telescopes use converging lenses

Lenses make images of objects that can be worked out using Ray diagrams

 Or the lens formula (1/f = 1/u + 1/v) The telescope consists of two lenses

set at a distance = fo + fe (normal adjustment)

 Magnification = β/α = fo/fe

Disadvantages of Refractors

They suffer from chromatic aberration. 

Bubbles and impurities in the glass absorb some of the light, large lenses are very difficult and expensive to make.

Large lenses are very heavy and can only be supported from their edges so their shape can become distorted.

To get a good magnification you need an objective lens with a very long focal length.  This can make the telescope very long.

Chromatic Aberration

Glass refracts different colours of light by different amounts (blue more than red).

The principal focus for each colour will be in a slightly different position and blurs the overall image.

Concave mirrors can be used to project a real image

Cassegrain System

Concave primary mirror, convex secondary mirror.

Cassegrain Arrangement

In 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.

Advantages of Reflectors

No chromatic aberration – mirrors do not refract light.

No spherical aberration – a parabolic mirror can be used to give perfect focusing.

No distortion – the mirror can be supported more strongly.

Better resolving power/greater brightness – mirrors can be larger.

More light gets through (brighter image) - a lens absorbs more light.

Spherical Aberration

The shape of the mirror must be parabolic to ensure that parallel rays converge at the same point.

If it isn’t quite parabolic the rays don’t converge and the image is blurred – spherical aberration.

Questions

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

(a) The light does not have to pass through glass, so will not suffer any chromatic aberration.  All colours are reflected by the same amount.

(b) The region lost by the presence of the secondary mirror is insignificant.  It would not matter if the dead space caused by the secondary mirror were removed.

Reflectors (further notes)

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.