Refracting Telescopes

The refracting telescope works by bending light with lenses.  The objective lens makes a small real image of the object so that the eyepiece lens can act as a magnifying glass and produce an enlarged image of the objective lens's image! 

The following factors are important in making a good quality instrument:

Lens quality - poor quality lenses produce a poor image - the curvature of the lens must be perfectly part of a sphere and the density of the glass uniform

Lens diameter - brightness and detail observed depends on the surface area of the lens.  A 12 cm lens can resolve detail nine times better than a 4 cm lens - area depends on the square of the diameter.

Angular magnification - the ratio of the angle subtended by the image of the object when using the instrument to view it, to the angle subtended at the eye of the observer when viewing the object without that instrument

The diagram shows the telescope when it is set up in normal adjustment - that means to view an object at infinity, therefore the focal point of both the eyepiece lens and the objective lens are set to coincide (see diagram below). Note that the length of the telescope is then set at the sum of the focal lengths of the two lenses. A very powerful telescope will have a big objective lens focal length. It will therefore be longer than a less powerful one.

 

Parallel rays of light from a distant object meet at the principal focus F_o of the objective lens.There it forms an intermediary real inverted image. The eyepiece is set so that the intermediary image is the focal length away from its principal focus F_e. Light from the intermediary image spreads out until it meets the eyepiece and forms an image at infinity - parallel rays emerge from the eyepiece and enter the eye of the observer. The observer traces the rays entering his/her eye back to infinity to form an inverted, virtual image of the original object.

A ray arrives at the objective at a small angle α to the axis.

The angle to the axis of the ray leaving the telescope is β.

The angular magnification can be worked out by the simple formula:

 

where α and β are small angles in radians.  

The angle α is the angle subtended by the object to the unaided eye.

The angle β is the angle subtended by the image to the eye.

 

The magnification can also be shown to be related to the focal lengths of the lenses by:

 

 

Where:

f_o is the focal length of the objective lens and

f_e is the focal length of the eyepiece lens

Disadvantages of using lenses in a telescope:

They refract light of different colours by different amounts.  See dispersion.  This leads to chromatic aberration.  The image is therefore colour-distorted.

They do not transmit 100 % of the light; some is lost (absorbed/reflected).

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 known is 20 m, with a 1 m wide objective lens.

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See reflecting telescpes