Part 5
The ray A C is called the INCIDENT RAY; and the ray C B, the REFRACTED RAY.
The angle A C I is called the ANGLE OF INCIDENCE, and the angle B C K is called the ANGLE OF REFRACTION.
If from the point A upon the right line C I, there be let fall the perpendicular A D, that line is called the sine of the angle of incidence.
In the same manner, if from the point B, upon the right line I K, there be let fall the perpendicular B E, that line will be the sine of the angle of refraction.
The sines of the angles are the measures of the refractions, and this measure is constant; that is, whatever is the sine of the angle of incidence, it will be in a constant proportion to the sine of the angle of refraction, when the mediums continue the same. A general idea of refraction may be formed from the following experiments.
EXPERIMENT 1. Let A B C D, Fig. 3. Plate I. represent a vessel so placed, with respect to the candle E, that the shadow of the side A C may fall at D. Suppose the vessel to be now filled with water, and the shadow will withdraw to d; the ray of light, instead of proceeding to D, being refracted or bent to d. And there is no doubt but that an eye, placed at d, would see the candle at e, in the direction of the refracted ray d A. This is also confirmed by the following pleasing experiment.
2. Lay a shilling, or any piece of money, at the bottom of a bason; then withdraw from the bason, till you lose sight of the shilling; fill the bason nearly with water, and the shilling will be seen very plainly, though you are at the same distance from it.
3. Place a stick over a bason which is filled with water; then reflect the sun’s rays, so that they may fall perpendicularly on the surface of the water; the shadow of the stick will fall on the same place, whether the vessel be empty or full.
What has been said of water, may be applied to any transparent medium, only the power of refraction is greater in some than in others. It is from this wonderful property, that we derive all the curious effects of glass, which make it the subject of optics. It is to this we owe the powers of the microscope and the telescope.
To produce these effects, pieces of glass are formed into given figures, which, when so formed, are called lenses. The six following figures are those which are most in use for optical purposes.
1. A PLANE GLASS, one that is flat on each side, and of an equal thickness throughout. F, Fig. 13. Plate I.
2. A DOUBLE CONVEX GLASS, one that is more elevated towards the middle than the edge. B, Fig. 13. Plate I.
3. A DOUBLE CONCAVE is hollow on both sides, or thinner in the middle than at the edges. D, Fig. 13. Plate I.
4. A PLANO CONVEX, flat on one side, and convex on the other. A, Fig. 13. Plate I.
5. A PLANO CONCAVE, flat on one side, and concave on the other. C, Fig. 13. Plate I.
6. A MENISCUS, convex on one side, concave on the other. E, Fig. 13. Plate I.
It has been already observed, that light proceeds invariably from a luminous body, in strait lines, without the least deviation; but if it happen to pass from one medium to another, it always leaves the direction it had before, and assumes a new one. After having taken this new direction, it proceeds in a strait line, till it meets with a different medium, which again turns it out of its course.
A ray of light passing obliquely through a plane glass, will go out in the same direction it entered, though not precisely in the same line. The ray C D, Fig.4. Plate I. falling obliquely upon the surface of the plane glass A B, will be refracted towards the glass in the direction D E; but when it comes to E, it will be as much refracted the contrary way. If the ray of light had fallen perpendicularly on the surface of the plane glass, it would have passed through it in a strait line, and not have been refracted at all.
If parallel rays of light, as a b c d e f g, Fig. 6. Plate I. fall directly upon a convex lens A B, they will be so bent, as to unite in a point C behind it. For the ray d D which falls perpendicularly upon the middle of the glass, will go through it without suffering any refraction: but those which go through the sides of the lens, falling obliquely on its surface, will be so bent, as to meet the central ray at C. The further the ray a is from the axis of the lens, the more obliquely it will fall upon it. The rays a b c d e f g will be so refracted, as to meet or be collected in the point C, called the principal focus, whose distance, in a double convex lens, is equal to the radius or semi-diameter of the sphere of the convexity of the lens. All the rays cross the middle ray at C, and then diverge from it to the contrary side, in the same manner as they were before converged.
If another lens, of the same convexity, as A B, Fig. 6. Plate I. be placed in the rays, and at the same distance from the focus, it will refract them, so that after going out of it, they will all be parallel again, and go on in the same manner as they came to the first glass A B, but on the contrary sides of the middle ray.
The rays diverge from any radiant point, as from a principal focus: therefore, if a candle be placed at C, in the focus of the convex lens A B, Fig. 6. Plate I. the rays diverging from it will be so refracted by the lens, that after going out of it, they will become parallel. If the candle be placed nearer the lens than its focal distance, the rays will diverge more or less, as the candle is more or less distant from the focus.
If any object, A B, Fig. 7. Plate I. be placed beyond the focus of the convex lens E F, some of the rays which flow from every point of the object, on the side next the glass, will fall upon it, and after passing through it, they will be converged into as many points on the opposite side of the glass; for the rays a b, which flow from the point A, will converge into _a b_, and meet at C. The rays c d, flowing from the point G, will be converged into _c d_, and meet at g; and the rays which flow from B, will meet each other again at D; and so of the rays which flow from any of the intermediate points: for there will be as many focal points formed, as there are radiant points in the object, and consequently they will depict on a sheet of paper, or any other light-coloured body, placed at D g C, an inverted image of the object. If the object be brought nearer the lens, the picture will be formed further off. If it be placed at the principal focus, the rays will go out parallel, and consequently form no picture behind the glass.
To render this still plainer, let us divest what has been said of the A’s and B’s, and of the references to figures. When objects are viewed through a flat or plane glass, the rays of light in passing through it, from the object to the eye, proceed in a strait direction and parallel to each other, and consequently the object appeared at the same distance as to the naked eye, neither enlarged or diminished. But if the glass be of a convex form, the rays of light change their direction in passing through the glass, and incline from the circumference towards the center of convexity, in an angle proportional to the convexity, and meet at a point at a less or greater distance from the glass, as it is more or less convex. The point where the rays thus meet is called the focus; when, therefore, the convexity is small, the focus is at a great distance, but when it is considerable, the focus is near; the magnifying power is in proportion to the change made in the rays, or the degree of convexity, by which we are enabled to see an object nearer than we otherwise could; and the nearer it is brought to the eye, the larger will be the angle under which it appears, and consequently the more it will be magnified.
The human eye is so constituted, that it can only have distinct vision, when the rays which fall on it are parallel, or nearly so; because the retina, on which the image is painted, is placed in the focus of the crystalline humor, which performs the office of a lens in collecting rays, and forming the image in the bottom of the eye.
As an object becomes perceptible to us, by means of the image thereof which is formed on the retina, it will, therefore, be seen in that direction, in which the rays enter the eye to form the image, and will always be found in the line, in which the axis of a pencil of rays flowing from it enters the eye. We from hence acquire a habit of judging the object to be situated in that line. Note; as the mind is unacquainted with the refraction the rays suffer before they enter the eye, it judges them to be in the line produced back, in which the axis of a pencil of rays flowing from it is situated, and not in that in which it was before the refraction.
If the rays, therefore, that proceed from an object, are refracted and reflected several times before they enter the eye, and these refractions or reflections change considerably the original direction of the rays which proceed from the object, it is clear, that it will not be seen in that line, which would come strait from it to the eye; but it will be seen in the direction of those rays which enter the eye, and form the image thereof on it.
We perceive the presence and figure of objects, by the impression each respective image makes on the retina; the mind, in consequence of these impressions, forms conclusions concerning the size, position, and motion of the object. It must however be observed, that these conclusions are often rectified or changed by the mind, in consequence of the effects of more habitual impressions. For example, there is a certain distance, at which, in the general business of life, we are accustomed to see objects: now, though the measure of the image of these objects changes considerably when they move from, or approach nearer to us, yet we do not perceive that their size is much altered; but beyond this distance, we find the objects appear to be diminished, or increased, in proportion as they are more or less distant from us.
For instance, if I place my eye successively at two, at four, and at six feet from the same person, the dimensions of the image on the retina will be nearly in the proportion of 1, of ¹⁄₂, of ¹⁄₃, and consequently they should appear to be diminished in the same proportion; but we do not perceive this diminution, because the mind has rectified the impression received on the retina. To prove this, we need only consider, that if we see a person at 120 feet distance, he will not appear so strikingly small, as if the same person should be viewed from the top of a tower, or other building 120 feet high, a situation to which we had not been accustomed.
From hence, also, it is clear, that when we place a glass between the object and the eye, which from its figure changes the direction of the rays of light from the object, this object ought not to be judged as if it were placed at the ordinary reach of the sight, in which case we judge of its size more by habit than by the dimensions of the images formed on the retina; but it must be estimated by the size of the image in the eye, or by the angle formed at the eye, by the two rays which come from the extremity of the object.
If the image of an object, formed after refraction, be greater or less than the angle formed at the eye, by the rays proceeding from the extremities of the object itself, the object will appear also proportionably enlarged or diminished; so that if the eye approach to or remove from the last image, the object will appear to increase or diminish, though the eye should in reality remove from it in one case, or approach toward it in the other; because the image takes place of the object, and is considered instead of it.
The apparent distance of an object from the eye, is not measured by the real distance from the last image; for, as the apparent distance is estimated principally by the ideas we have of their size, it follows, that when we see objects, whose images are increased or diminished by refraction, we naturally judge them to be nearer or further from the eye, in proportion to the size thereof, when compared to that with which we are acquainted. The apparent distance of an object is considerably affected by the brightness, distinctness, and magnitude thereof. Now as these circumstances are, in a certain degree, altered by the refraction of the rays, in their passing through different mediums, they will also, in some measure, affect the estimation of the apparent distance.
In the theory of vision it is necessary to be cautious not to confound the organs of vision with the being that perceives, or with the perspective faculty. The eye is not that which sees, it is only the organ by which we see. A man cannot see the satellites of Jupiter but by a telescope. Does he conclude from this, that it is the telescope that sees those stars? By no means; such a conclusion would be absurd. It is no less absurd to conclude, that it is the eye that sees. The telescope is an artificial organ of sight, but it sees not. The eye is a natural organ of sight, by which we see; but the natural organ sees as little as the artificial.
The eye is a machine, most admirably contrived for refracting the rays of light, and forming a distinct picture of objects upon the retina; but it sees neither the object nor the picture. It can form the picture after it is taken out of the head, but no vision ensues. Even when it is in its proper place, and perfectly sound, it is well known, that an obstruction in the optic nerve takes away vision, though the eye has performed all that belongs to it.[25]
[25] Reid on the Intellectual Powers of Man, p. 78.
OF THE SINGLE MICROSCOPE.
The single microscope renders minute objects visible, by means of a small glass globule, or convex lens, of a short focus. Let E Y, Fig. 11. Plate I. represent the eye; and O B a small object, situated very near to it; consequently, the angle of its apparent magnitude very large. Let the convex lens R S be interposed between the eye and the object, so that the distance between it and the object may be equal to the focal length; and the rays which diverge from the object, and pass through the lens, will afterwards proceed, and consequently enter the eye parallel: after which, they will be converged, and form an inverted picture on the retina, and the object will be clearly seen; though, if removed to the distance of six inches, its smallness would render it invisible.
When the lens is not held close to the eye, the object is somewhat more magnified; because the pencils, which pass at a distance from the center of the lens, are refracted inward toward the axis, and consequently seem to come from points more remote from the center of the object, as may be seen in Fig. 12. Plate I. where the pencils which proceed from O and B are refracted inwards, and seem to come from the point i and m.
Fig. 8. Plate I. may, perhaps give the reader a still clearer view, why a convex lens increases the angle of vision. Without a lens, as F G, the eye at A would see the dart B C under the angle b A c; but the rays B F and C G from the extremities of the dart in passing through the lens, are refracted to the eye in the directions f A and g A, which causes the dart to be seen under the much larger angle D A E (the same as the angle f A g.) And therefore the dart B C will appear so much magnified, as to extend in length from D to E.
The object, when thus seen distinctly, by means of a small lens, appears to be magnified nearly in the proportion which the focal distance of the glass bears to the distance of the objects, when viewed by the naked eye.
To explain this further, place the eye close to the glass, that as much of the object may be seen at one view as is possible; then remove the object to and fro, till it appear perfectly distinct, and well defined; now remove the lens, and substitute in its place a thin plate, with a very small hole in it, and the object will appear as distinct, and as much magnified, as with the lens, though not quite so bright; and it appears as much more magnified in this case, than it does when viewed with the naked eye, as the distance of the object from the hole, or lens, is less than the distance at which it may be seen distinctly with the naked eye.
From hence we see, that the whole effect of the lens is to render the object distinct, which it does by assisting the eye to increase the refraction of the rays in each pencil; and that the apparent magnitude is entirely owing to the object being seen so much nearer the eye than it could be viewed without it.
Single microscopes magnify the diameter of the object,[26] as we have already shewn, in the proportion of the focal distance (to the limits of distinct vision with the naked eye) to eight inches. For example, if the semi-diameter of a lens, equally convex on both sides, be half an inch, which is also equal to its focal distance, we shall have as ¹⁄₂ is to 8, so is 1 to 16; that is, the diameter of the object in the proportion of sixteen to one. 2. As the distance of eight inches is always the same, it follows, that by how much the focal distance is smaller, there will be a greater difference between it and the eight inches; and consequently, the diameter of the object will be so much the more magnified, in proportion as the lenses are segments of smaller spheres. 3. If the object be placed in the focus of a glass globule or sphere, and the eye be behind it in the focus, the object will be seen distinct in an erect situation, and magnified as to its diameter, in the proportion of ³⁄₄ of the diameter of the globule to eight inches; thus suppose the diameter of the sphere to be ¹⁄₁₀ of an inch, then ³⁄₄ of this will be equal to ³⁄₄₀; consequently, the real diameter of the object to the apparent one, as ³⁄₄₀ to 8, or as 3 to 320, or as 1 to 106 nearly.
[26] Cyclopedia, Article Microscope.
OF THE DOUBLE OR COMPOUND MICROSCOPE.
In the compound microscope, the image is viewed instead of the object, which image is magnified by a single lens, as the object is in a single microscope. It consists of an object lens N L, Fig. 5. Plate I. and an eye glass F G. The object B O is placed a little further from the lens than its principal focal distance, so that the pencils of rays proceeding from the different points of the object through the lens, may converge to their respective foci, and form an inverted image of the object at Q P; which image is viewed by the eye through the eye glass F G, which is so placed, that the image may be in its focus on one side, and the eye at the same distance on the other. The rays of each pencil will be parallel, after passing out of the glass, till they reach the eye at E, where they will begin to converge by the refractive powers of the humours; and after having crossed each other in the pupil, and passed through the crystalline and vitreous humours, they will be collected in points on the retina, and form a large inverted image thereon.
It will be easy, from what has been already explained, to understand the reason of the magnifying power of a compound microscope. The object is magnified upon two accounts; first, because if we viewed the image with the naked eye, it would appear as much larger than the object, as the image is really larger than it, or as the distance f R is greater than the distance f b; and secondly, because this picture is again magnified by the eye glass, upon the principle explained in the foregoing article on vision, by single microscopes.
But it is to be noted, that the image formed in the focus of a lens, as is the case in the compound microscope, differs from the real object in a very essential particular; that is to say, the light being emitted from the object in every direction, renders it visible to an eye placed in any position; but the points of the image formed by a lens, emitting no more than a small conical body of rays, which arrives from the glass, can be visible only when the eye is situate within its confine. Thus, the pencil, which emanates from o in the object, and is converged by the lens to D, proceeds afterwards diverging towards H, and, therefore, never arrives at the lens F G, nor enters the eye at E. But the pencils which proceed from the points o and b, will be received on the lens F G, and by it carried parallel to the eye; consequently, the correspondent points of the image Q P will be visible; and those which are situate farther out towards H and I, will not be seen. This quantity of the image Q P, or visible area, is called the field of view.
Hence it appears, that if the image be large, a very small part of it will be visible; because the pencils of rays will for the most part fall without the eye glass F G. And it is likewise plain, that a remedy which would cause the pencils, which proceed from the extremes B and O of the object, to arrive at the eye, will render a greater part of it visible: or, in other words, enlarge the field of view. This is effected by the interposition of a broad lens D E, Fig. 5, of a proper curvature, at a small distance from the focal image. For, by those means, the pencil D N, which would otherwise have proceeded towards H, is refracted to the eye, as delineated in the figure, and the mind conceives from thence the existence of a radiant point at Q, from which the rays last proceeded. In like manner, and by a parity of reason, the other extreme of the image is seen at P, and the intermediate points are also rendered visible. On these considerations it is, that compound microscopes are usually made to consist of an object lens N L, by which the image is formed, enlarged, and inverted; an amplifying lens D E, by which the field of view is enlarged, and an eye glass or lens, by which the eye is allowed to approach very near, and consequently to view the image under a very great angle of apparent magnitude. It is now customary to combine two or more lenses together at the eye glass, in the manner of Eustachio Divinis and M. Joblot; by which means the aberration of light from the figure is in some measure corrected, and the apparent field increased.
OF THE SOLAR MICROSCOPE.
In this instrument, the image of the object is refracted upon a screen in a darkened room. It may be considered under two distinct heads: 1st, the mirror and lens, which are intended to reflect and transmit the light of the sun upon the object; and 2dly, that part which constitutes the microscope, or which produces the magnified image of the object, Fig. 10. Plate I. Let N O represent the side of a darkened chamber, G H a small convex lens, fixed opposite to a perforation in the side N O, A B a plane mirror or looking glass, placed without the room to reflect the solar rays on the lens C D, by which they are converged and concentrated on the object fixed at E F.
2. The object being thus illuminated, the ray which proceeds from E will be converged by the lens G H to a focus K, on the screen L M; and the ray which comes from F will be converged to I, and the intermediate points will be delineated between I and K; thus forming a picture, which will be as much larger than the object, in proportion as the distance of the screen exceeds that of the image from the object; a small object, such as a mite, &c. may be thus magnified to eight or ten feet in diameter.