025 



MICROSCOPE. 



MICROSCOPE. 



628 



lines drawn from a similar arrow at twice the distance. The arrow A B 

 will therefore appear nearly twice as long as c D. beino; seen under 

 twice the angle, and in the same proportion for any greater or lesser 

 difference in distance. The angle in question is called the angle of 

 vision, or the visual angle. 



The angle of vision must however not be confounded with the angle 

 of the pencil of light by which an object is seen, and which is explained 

 in fi'j. 2. Here we have drawn two arrows placed in relation to the 



eye as before, and from the centre of each have drawn lines exhibiting 

 the quantity of light which each point will send into the eye at the 

 respective distances. 



Now if E F represent the diameter of the pupil, the angle E A F shows 

 the size of the cone or pencil of light which enters the eye from the 

 point A, and in like manner the angle E B F is that of the pencil 

 emanating from B, and entering the eye. Then, since E A F is double 

 KBF, it U evident that A is seen by four times the quantity of light 

 which could be received from an equally illuminated point at B ; so 

 that the nearer body would appear brighter if it did not appear larger ; 

 but as its apparent area is increased four times, as well as its light, uo 

 difference in this respect is discovered. But if we could find means to 

 send into the eye a larger pencil of light, as for instance that shown by 

 the lines GAH, without increasing the apparent size in the same 

 proportion, it is evident that we should obtain a benefit totally distinct 

 from that of increased magnitude, and one which is in some cases of 

 even more importance than size in developing the structure of what we 

 wish to examine. This, it will be hereafter shown, is sometimes done ; 

 for the present, we wish merely to explain clearly the distinction 

 between apparent magnitude, or the angle under which the object is 

 seen, and apparent brightness, or the angle of the pencil of light by 

 which each of its points is seen, and with these explanations we shall 

 continue to employ the common expressions magnifying glass and 

 magnifying power. 



The magnifying power of a single lens depends upon its focal length, 

 the object being in fact placed nearly in its principal focus, or so that 

 the light which diverges from each point may, after refraction by the 

 Ions, proceed in parallel lines to the eye, or as nearly so as is requisite 

 for distinct vision. In fy. 3, A B is a double convex lens, near which 



r -. ::. 



i.i a small arrow to represent the object under examination, and the 

 cones drawn from its extremities are portions of the rays of light 

 diverging from those points and falling upon the lens. These rays, if 

 mitfered to fall at once upon the pupil, would be too divergent to 

 permit their being brought to a focus upon the retina by the optical 

 arrangements of the eye. But being first passed through the lens, they 

 are bent into nearly parallel lines, or into lines diverging from some 

 points within the limits of distinct vision, as from c and D. Thus 

 altered, the eye receives them precisely as if they emanated from a 

 larger arrow placed at c D, which we may suppose to be ten inches from 

 the, eye, and then the dilference between the real and the imaginary 

 arrow is called the magnifying power of the lens in question. 



From what has been said it will be evident that two pel-sous whose 

 eyes differed as to the distance at which they obtained distinct vision, 

 would give different results as to the magnifying power of a lens. 

 To one who can see distinctly with the naked eye at a distance of five 

 inches, the magnifying power would set m (and would indeed be) only 

 half what we have assumed. Such instances are however rare ; the 

 focal length of the eye usually ranges from six to twelve or fourteen 

 inches, so that the distance we iirst assumed of ten inches is very 

 near the true average, and is a convenient number, inasmuch as a 

 cipher added to the denominator of the fraction which expresses 

 the focal length of a lens gives its magnifying power. Thus a lens 

 whose focal length is one-sixteenth of an inch is said to magnify 160 

 times. 



ARTS AND SCI. DIV. VOL. V. 



When the focal length of a lens is very small it is difficult to measure 

 accurately the distance between its centre and its object. In such 

 cases the best way to obtain the focal length for parallel or nearly 

 parallel rays is to view the image of some distant object formed by the 

 lens in question through another lens of one inch solar focal length, 

 keeping both eyes open and comparing the imige presented through 

 the two lenses with that of the naked eye. The proportion between 

 the two images so seen will be the focal length required. Thus if the 

 image seen by the naked eye is ten times as large as that shown by the 

 lenses, the focal length of the lens in question is one-tenth of an inch. 

 The panes of glass in a window, or courses of bricks in a wall, are con- 

 venient objects for this purpose. 



In whichever way the focal length of the lens is ascertained, the 

 rules given for deducing its magnifying power are not rigorously 

 correct, though they are sufficiently so for all practical purposes, par- 

 ticularly as the whole rests on an assumption in regard to the focal 

 length of the eye, and as it does not in any way affect the actual 

 measurement of the object. To calculate with great precision the 

 magnifying power of a lens with a given focal length of eye, it is neces- 

 sary that the thickness of the lens be taken into the account, and also 

 the focal length of the eye itself. 



We have hith rto considered a magnifying lens only in reference to 

 its enlargement of the object, or the increase of the angle under which 

 the object is seen. A further and equally important consideration is 

 that of the number of rays or quantity of light by which eveiy point 

 of the object is rendered visible. The naked eye as shown in jig. 2, 

 admits from each point of every visible object a cone of light having 

 the diameter of the pupil for its base, and most persons are familiar 

 with that beautiful provision by which in cases of excessive brilliancy 

 the pupil spontaneously contracts to reduce the cone of admitted light 

 within bearable limits. This effect is still further produced in the 

 experiment already described, of looking at an object through a 

 needle-hole in a card, which is equivalent to reducing the pupil to the 

 size of a needle-hole. Seen in this way the object becomes compara- 

 tively dark or obscure, because each point is seen by means of a very 

 small cone of light, and a little consideration will suffice to explain the 

 different effects produced by the needle-hole and the lens. Both change 

 the angular value of the cone of light presented to the eye, but the 

 lens changes the angle by bending the extreme rays within the limits 

 suited to distinct vision, while the needle-hole effects the same purpose 

 by cutting off the rays which exceed those limits. 



It has been shown that removing a brilliant object to a greater distance 

 will reduce the quantity of light which each point sends into the eye, 

 as effectually as viewing it through a needle-hole ; and magnifying an 

 object^by a lens has been shown to be the same thing in some respects 

 as removing it to a greater distance. We have to see the magnified 

 picture by the light emanating from the small object, and it becomes 

 a matter of difficulty to obtain from each point a sufficient quantity of 

 light to bear the diffusion of a great magnifying power. We want 

 to perform an operation just the reverse of applying the card with 

 the needle-hole to the eye we want in some cases to bring into 

 the eye the largest possible pencil of light from each point of the 

 object. 



Referring to fiij. 3, it will be observed that if the eye could see the 

 small arrow at the distance there shown without the intervention of 

 the lens, only a very small portion of the cones of light drawn from 

 its extremities would enter the pupil ; whereas we have supposed that 

 after being bent by the lens the whole of this light enters the eye as 

 part of the cones of smaller angle whose summits are at c and D. 

 The.se cones will further explain the difference between large and 

 small pencils of light ; those from the small arrow are large pencil* ; 

 the dotted cones from the large arrow are small pencils. 



In assuming that the whole of this light could have been suffered to 

 enter the eye through the lens A B, we did so for the sake of not per- 

 plexing the reader with too many considerations at once. He must 

 now learn that so large a pencil of light passing through a single lens 

 would be so distorted by the spherical figure of the lens, and by the 

 chromatic dispersion of the glass, as to produce a very confused and 

 imperfect image. This confusion may be greatly diminished by 

 reducing the pencil ; for instance, by applying a stop, as it is called, 

 to the lens, which is neither more nor less than the needle-hole 

 applied to the eye. A small pencil of light may be thus transmitted 

 through a single lens without suffering from spherical aberration or 

 chromatic dispersion any amount of distortion which will materially 

 affect the figure of the object; but this quantity of light is insufficient 

 to bear diffusion over the magnified picture, which is therefore too 

 obscure to exhibit what we most desire to see those beautiful and 

 delicate markings by which one kind of organic matter is distinguished 

 from another. With a small aperture these markings are not seen at 

 all ; with a large aperture and a single lens they exhibit a faint 

 nebulous appearance enveloped in a chromatic mist, a state which is of 

 course utterly valueless to the naturalist, and not even amusing to the 

 amateur. 



It becomes therefore a most important problem to reconcile a large 

 aperture with distinctness, or, as it is called, dffnitian ; and this has 

 been done in a considerable degree by effecting the required amount of 

 refraction through two or more lenses instead of one, thus reducing 

 the angles of incidence and refraction, and producing other effects 



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