78 



OF OPTICAL INSTRUMENTS. 



the SIM, or as xy%', y being the cosine : but the angular 

 dissipation after reflection is as the product of twice %' and 

 the sine of twice the arc z, since the light forms twice as 

 great an angle with the axis after reflection as before. But 

 the sine of twice the arc z is lyx, and the product Axyz' is 

 ilways proportional to the former product xyz', expressing 

 the space in which the light was uniformly spread before re- 

 flection ; it will therefore be uniformly spread after reflection. 

 Scholium. If the quantity of light reflected varied ac- 

 cording to any given function of the obliquity, the density of 

 the reflected light would vary according to the same law, 

 considering the obliquity as determined by half the angular 

 distance of the reflected light from the axis. The density 

 of the light reflected by a cylinder varies as the cosine y, 

 supposing none to be lost. 



444. Definition. Iu telescopes and 

 compound microscopes, the image formed by 

 one lens or mirror stands in the place of a 

 new object for another. 



445. Definition. In the astronomical 

 telescope, the object glas.s first forms an ac- 

 tual inverted image nearly in the principal 

 focus of the eyeglass, and the eyeglass a se- 

 cond virtual and inverted image of the first. 



446. Theorem. Tite inagnifying power 

 of the astronomical telescope is expressed 

 by the quotient of the focal lengths of the 

 glasses. 



For the object 

 and image subtend 

 equal angles at the 

 centre of theobject 

 glass ; and the an- 

 gles subtended by the image at the centre of the eyeglass 

 and object glass are ultimately in the inverse ratio of the 

 distances (199, I4l). 



447. Definition. The double mlcro- 

 scrope resembles in its construction the astro- 

 nomical telescope, excepting that the dis- 

 tance of the lenses much exceeds their joint 

 focal length. 



448. Theorem. Tlie angular magnitude 

 of an object viewed through a double micro- 

 scope is greater than wiien viewed through 

 the eyeglass alone, in the ratio of the dis- 

 tances of the object and first image, from 

 the object glass. 



For the first 

 image may be con- 

 sidered as a new 

 object in the focus 

 of the eyeglass (424). 



449. Definition. In the Galilean te- 

 lescope, or opera glass, a concave eyeglass is 

 placed so near the object glass, that the first 

 image would be formed beyond it, and near 

 its principal focus. 



450. Theorem. In the Galilean tele- 

 scope, the second virtual image, formed by 

 the eyeglass, is inverted with respect to this 

 image, and erect with respect to the object; 

 and the magnifying power is the quotient of 

 the focal lengths. 



Since, for a con- 



cave lens —zz— 

 e d 



— (421), when d is little greater than/, e becomes very 



'large ; and the two images are on different sides of the eye- 

 glass. The magnifying power is ultimately the quotient of 

 the distances of the glasses from the first image. 



451. Definition. In day telescopes, 

 one or more eyeglasses are added, in order 

 to restore the image to its natural position. 



Scholium. In the common day telescopes of Rheita, 

 two eyeglasses are employed, of nearly equal focus, and so 

 placed, as scarcely to affect the magnifying power ; but in 

 either case, they may be so disposed as to Vary it at plea- 

 sure ; for such an eye piece is a species of compound rai- 

 croscope. 



