If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.
He points out - (I) that a telescope with an objectglass so divided still produces a single image of any object to which it may be directed, provided that the optical centres of the segments are in coincidence (i.e.
This instrument has a superb objectglass of 72 in.
This lens is divided and mounted like a heliometer objectglass; the separation of the lenses produces the required double image, and is measured by a screw.
James Bradley, on 27th December 1722, actually measured the diameter of Venus with a telescope whose objectglass had a focal length of 2124 ft.
Huygens contrived some ingenious arrangements for directing such telescopes towards any object visible in the heavens - the focal adjustment and centring of the eyepiece being preserved by a braced rod connecting the objectglass and eye-piece.
But all his efforts to produce an actual objectglass of this construction were fruitless - a failure which he attributed solely to the difficulty of procuring lenses worked precisely to the requisite curves (Hem.
In these telescopes the photographic objectglass has an aperture of 13 in.