from naître; L. part ii., p. 96.-g. l'auront, have without doubt. -h. from mourir; L. S. 60, R. 2; also L. part ii., p. 96.-i. pieds de devant, fore-feet.-j. from rire; L. part ii., p. 104.

thence it suffices to know the angle of refraction A and the angle of minimum deviation d, to deduce the index of refraction of a vacuum, which has been designated, the absolute index. To obtain the absolute index of any gas besides air, the gas is to be passed in, after exhausting the tube; then measuring the angles A and d, the 4th of the preceding formula will discover the index of refraction of gas. Knowing already the index of a vacuum, the ratio of these two indices gives the index of a void filled with gas-in other words, its absolute index.

LENSES, THEIR EFFECTS.

Different kinds of Lens.-We give the name of lenses to transparent media, which, from the curvature of their surface, have the property of converging or diverging the rays of light which pass through them. According to the nature of the curve, the lenses are called spherical, cylindrical, eliptical, and parabolic. The spherical lenses are the only ones used for optical instruments. They are generally made of crown glass, or of flint glass, the latter having more refracting power than the other. There are six species of lenses, represented in fig. 288. The first A, is called bi-contex; the second B,

Fig. 288.

the normal, at the point of incidence B, and in deviating at the point of emergence D, is refracted twice towards the axis, which it strikes at F. All the rays parallel to the axis being refracted in the same manner, they pass through the same point r, as long as the arc в E does not exceed 10 to 12 degrees. It is this point which is the principal focus, and the distance FA, is the principal focal distance. It is constant with the same lens, but variable with the ray of curvature and the index of refraction. In the ordinary lenses, which are made of crown glass, the principal focus coincides very nearly with the centre of the

we compare the course of the divergent ray LB with that of the ray s B, parallel to the axis, we shall perceive that the first makes with the normal an angle LBn greater than the angle s B; it ought, therefore, to make an angle of refraction greater; whence it results that after having passed through the lens, it encounters the axis at a point 7, more distant than the principal focus F. All the rays departing from the point L, coming thus to concur sensibly at the same point L, this last is the conjugal focus of the point L. This denomination expresses here, the same as in mirrors, the relation which exists between the two points L and 7, such relation that if the luminous point is transferred to 1, the focus passes reciprocally to L.

planoconvex; the third c, concave-convex-convergent; the fourth D, bi-concave; the fifth E, plano concave; and the last F, concave-convex divergent. The lens c, is also called meniscus convergent, and F, meniscus divergent. The three first, which are thicker at the centre than at the ends, are convergents; the three latter, which are thinner at the centre than the ends, are divergents. In the first group it will be sufficient to consider the bi-convex lens, and in the second the bi-concave. In the In proportion as the object L approaches the lens, the diverlenses whose two faces are spherical, the centres of these sur-gence of the emergent rays augments, and the focus becomes faces are called centes of curvature; and a right line drawn more remote; when the object L coincides with the principal through these two centres is the principal axis. focus, the emergent rays from the other side of the lens are parallel to the axis, and then there is no focus, or, which is the same thing, it is at an infinite distance. In this case the refracted rays being parallel, the intensity of the light decreases very slowly, and a single lamp may then give light at great distances. For that purpose it is sufficient to place it in the focus of a bi-convex lens, as shown in fig. 291. Fig. 291.

In order that we may be able to compare the passage of the luminous rays in lenses with that which takes place in prisms, we may make the same hypothesis as for curved mirrors. According to this hypothesis, we can always conceive, at the points of incidence and emergence, two plain surfaces more or less inclined, and producing thus the effect of the prism. In pursuing this comparison, we may liken the three lenses A, B, C, fig. 288, to a series of prisms united by their basis, and the lenses D, E, F, to a series of prisms united by their summits, which shows how the former must cause the rays to converge, and the latter to diverge, as we have seen that when a ray passes through a prism it deviates towards the

base.

The Foci in Bi-convex Lenses.-In lenses, as in mirrors, we give the name of focus to the point in which the refracted rays or their prolongations meet. Bi-convex lenses present the same kind of foci as concave mirrors, namely, the principal focus, the conjugal focus, and the virtual focus.

1. The Principal Focus.-This is formed by the rays, which, before their incidence, are parallel to the principal axis, as shown in fig. 289. In this case the ray LB, in approaching

Fig. 289.

3. The Virtual Focus.-With bi-convex lenses the focus is virtual, when the luminous object L is placed between the len and the principal focus, as seen in fig. 292. In this case Fig. 292.

incident rays L I forming with the normal greater angles than those formed by the rays F1 emitted from the principal focus, it follows that after emergence the former rays become more remote from the axis than the latter, and form a divergent pencil, HKG M. These rays, then, cannot give place to a real focus; but their prolongations converge at the same point 1, situated on the axis, and this point is the virtual focus of the point L.

Foci in the Bi-concave Lenses.-Bi-concave lenses form only virtual foci, whatever be the position of the object, First, let there be a pencil of rays parallel to the axis, fig. 293. Any

Fig. 293.

H

distance FD, because of the similitude of the triangles rab and FA B.

In bi-concave lenses, as well as in the convex, at least when they are in crown glass, the principal focus coincides sensibly with the centre of the curve.

Optic Centre-Secondary Axes.-In every lens there is a point, named the optic centre, which is situated on the axis, and possesses this property, that no ray of light, passing through it, experiences the angular deviation, that is, the ray of emergence is parallel to the ray of incidence. In order to demonstrate the existence of this point, in a bi-convex lens let two parallel rays be brought to its two surfaces, CA and d'A' (fig. 296). The two planes of the surface of the lens, A and A'

7

ray 8 1, will be refracted at the point of incidence 1, in approaching the normal c1. At the point of emergence G it is refract d anew, but in departing from the normal G c', so that it is b nt twice in the same direction in escaping from the axis cc'. The same thing occurring with any other ray S'KM N, it follows that after passing through the lens, the rays form a divergent pencil G HM N. The prolongations of these rays converge in the point F, which is the virtual focus. In the case where the rays depart from the point L, fig. 294,

Fig. 294.

situated upon the axis, we ascertain by the same construction that they form a virtual focus in 7, which is between the principal focus and the lens.

Experimental Determination of the Principal Focus of Lenses.In order to determine the principal focus of a bi-concave lens, it is sufficient to expose it to the rays of the sun, taking care that its principal axis should be parallel to them. Admitting then the convergent pencil on a screen of polished glass, we easily determine the point where the rays converge; this is the principal focus.

If the lens is bi-concave, we cover the surface a D b, fig. 295,
Fig. 203.

with an opaque body, reserving on the same plane of the meridian, and at an equal distance from the axis, two little disks a and b, not darkened, which will allow the light to pass; then we receive on the other surface of the lens, parallel to the axis, a pencil of solar light, the screen P, which receives the emergent rays, being made to advance or recede so that the images AB of the little openings 6 should be distant from one another the double of a 6. The interval p1 is then equal to the focal

being parallel, as perpendicular to two parallel right lines, we perceive that the refracted ray A A' passes through the middle of the parallel surfaces. Consequently, the ray which arrives at a with such an inclination that, after refraction, it follows the direction A A', must issue parallel to its first direction; the point o where the right line A A' strikes the axis, is then the optic centre. In order to determine the position of this point, where the curve of the two surfaces is the same, which is the ordinary case, it suffices to observe that the angles co A, and c' o A are equal, and that we have oc=oc, whence o BOB'. By this we discover the point o.

If the curves are not equal, the triangles, coa and c'o A are similar, and from this we deduce co or c'o, and, by consequence, the point o.

In bi-concave or concave-convex lenses, the optic centre is determined by the same construction. In lenses which have a plain surface, this point is the intersection of the axis by the surface of the curve.

Every right line Pr' fig. 297, which passes the optic centre

Fig. 297.

without passing the centres of the curve, is a secondary axis. Following the property of the optic centre, every secondary axis represents a ray of light passing by this point; for, owing to the small thickness of lenses, the rays which pass through the optic centre keep a right line, that is, they avoid the slight deviation which rays experience, though remaining parallel, when they obliquely traverse the centre between parallel surfaces, fig. 297.

Though the secondary axis make but a small angle with the principal axis, we may apply to them all that has just now been said of the principal axis, that is to say, the rays emitted from a point P, fig. 297, situated on the secondary axis Pr' come very nearly to converge at the same point r' of this axis; and according as the distance from the point P to the lens is greater or less than the principal focal distance, the focus thus formed is conjugal or virtual. Tais principle is the basis of that which follows on the formation of images.

Formation of Images in Bi-convex Lenses.-In lenses, as well as in mirrors, the image of an object is the combination of the foci of all its points; whence it follows, that the images fur nished by lenses are real or virtual, the same as the foci.