330 LECTURE XXXVI. 



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'br 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 

 subtends at the centre of the lens : and since this angle may 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 micro- 

 scope ; 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 dis- 

 tance 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 mag- 

 nitude may be increased 17 times instead of 16, and 9 times instead of 8. 

 (Plate XXVII. Fig. 395, 396.) 



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

 focus, it is usual to employ the minutest lenses that can be ground, and 

 sometimes a small globule is formed by fusion in a lamp. Even a drop of 

 water, placed in the perforation of a plate, makes a tolerable magnifier ; 

 and it has been proposed to substitute for water a transparent varnish, 

 which is less liable to evaporate. 



Supposing the whole light that proceeds from a distant object, and falls 

 on a lens or speculum, to be collected in the image, its intensity must be 

 increased in the ratio of the surface of the lens or speculum to that of the 

 image. The image is greater in proportion as the object is greater ; conse- 

 quently the degree of condensation produced by any lens is the greater as 

 the object is smaller, thus if the diameter of a lens were an inch, and the 

 image of the sun formed by it were also an inch in diameter, the density of 

 the light would be unaltered ; but the image of a star would be infinitely 

 brighter than the direct light of the star falling on the lens. The illumina- 

 tion of any image formed by a lens or mirror, supposing no light to be 

 lost, is always the same as would be produced by the direct light of the 

 surface of the lens or mirror, if it were equally luminous with the surface 

 of the object which emits the light. It may also be shown, that when two 

 lenses are of similar forms, their focal lengths being proportional to their 

 diameters, they must produce the same degree of illumination in the image : 

 but as far as the heat excited may be supposed to be a measure of the 



