422 LECTURE XXXVI. 



ally; and these are cither microscopes or telescopes, which present us with 

 great diversity in their arrangements, and in the appurtenances subservient to 

 their uses. 



It is a general rule, that when an image of an actual object is formed by 

 any lens or speculum, if the rays converge to an actual focus, the image 

 is inverted; but erect, if they diverge from a virtual focus, and the object and 

 image subtend equal angles at the centre of the lens or speculum. Hence, 

 a convex lens and a concave mirror form an inverted image, smaller than the 

 object, whenever the object is at a greater distance than twice the principal 

 focal length; but larger, when the object is within this distance; and when 

 it is within the principal focal distance, the magnified image is virtual and 

 erect, and may be seen by looking into the concave mirror, or by looking 

 through the lens towards the object. But a concave lens and a convex 

 mirror always form a virtual image of a real object, which is erect, and 

 smaller than the object. (Plate XXVII. Fig. 390 . . 394.) 



When the object is precisely in the principal focus of a convex lens or a 

 concave mirror, the virtual image becomes infinitely distant; so that from 

 whatever point in the neighbourhood of the lens it may be viewed, it must 

 •subtend the same angle, which is always equal to that which the object sub- 

 tends at the centre of the lens: and since this angle ma/y easily be much 

 greater than that under which the object can be conveniently viewed by the 

 naked eye, such a lens or mirror is often used as a simple microscope; and 

 its magnifying power may be ascertained from a comparison of the angles 

 which the object and image subtend. Thus, if a person cannot see a minute 

 object with the naked eye at a distance less than eight inches, a lens of half 

 an inch focal length will represent it to him in an angle 16 times as great: 

 but if he can see it without the lens at the distance of four inches, the lens 

 will magnify it to his eye but eight times. Supposing, however, the eye to 

 be applied close to the lens, the object may be viewed a little within 

 the focal distance, and its apparent angular magnitude may be increas- 

 ed 17 times instead of l6, and 9 times instead of 8. (Plate XXVII. 

 rig. 395, 596.) 



Since the magnifying power of a lens is the greater, the smaller its focus, 



