Measurement of the Magnifying Power of a Telescope - Second Method

The magnifying power of a telescope for an infinitely distant object may be taken as the ratio of the focal length of the object-glass to that of the eye-piece, and may be found by the following method:

Focus the telescope for parallel rays as follows:

(1) Focus the eye-lens by sliding in the socket until the cross-wires are seen distinctly.

(2) Direct the telescope to the most distant object visible from an open window - a vane is generally a convenient object - and move the eye-piece and cross-wires together as one piece (there is generally a screw for doing this, but sometimes it has to be done by pulling out the tube by hand) until the distant object is clearly seen as well as the cross-wires, and so that there is no parallax, i.e. so that on moving the eye across the aperture of the eye-piece the cross-wires and image do not move relatively to each other. This will be the case when the image of the distant object formed by the object-glass is in the plane of the cross-wires. The telescope is then said to be focussed for infinity or for parallel rays.

Next, screw off the cover of the eye-piece - without altering the focus - and screw out the object-glass and substitute for it an oblong-shaped diaphragm, the length of which must be accurately measured: let it equal L. The measurement can be easily effected by means of a pair of dividers and a fine scale.

The distance of this from the optical centre of the eyepiece is F+f, F and f being the focal lengths of the object-glass and eye-piece respectively. An image of this oblong aperture will be formed by the eye-piece at a distance v on the other side of its optical centre, where

Now measure the length of this image by bringing up to it a micrometer scale engraved on glass, such as is made for use in a microscope, graduated to tenths of a millimetre and having a lens mounted in front of it to facilitate the reading. Place the micrometer in a clip, and adjust the height and distance until the scale and the image of the aperture are both distinctly seen on looking through the lens attached to the micrometer. In this way the length of the image of the diaphragm can be determined in terms of millimetres and tenths. Let this be l. Of course any other convenient form of micrometer may be used for this purpose.

Then the magnifying power F/f = L/l

For if LL' (fig. 31) be the diaphragm aperture, so that LL' = L, M the micrometer, and ll' the image formed, c the optical centre of the eye-piece, then

But

In measuring the length of the image by the micrometer scale, the aperture should not be too brightly illuminated, or the image may be blurred and indistinct. The telescope should on this account be pointed at a sheet of grey filter-paper or other slightly illuminated uniform surface, giving just light enough for reading the micrometer scale.

Experiment. - Determine the magnifying power of the given telescope.

Enter results thus:

Telescope No. 2.
Length of aperture: 2.18 cm
Length of image: 0.16 cm
Magnifying power: 13.6