nodal point k" is the point from which the emergent ray c d appears to proceed; the direction of the emergent ray is, however, parallel to that of the incident

ray.

So long as the secondary axes make only small angles with the principal axis, all that has been said about the principal axis is applicable to them; that is, that rays of light emitted from a point P (Fig. 11) on the secondary axis PP', nearly coincide in the same point

of this axis P' and accordingly as the distance from the point P to the lens is greater or less than the principal focal distance, the focus will be either conjugate or virtual.

Formation of images in double convex lenses.In lenses the image of an object is the collection of the foci of each of its points; hence the images furnished by lenses are real or virtual in the same cases as their foci, and their construction resolves itself into determining a series of points.

Real image. Let A B (Fig. 13) be placed beyond the principal focus. If a secondary axis A a be drawn from the outside point A, any ray AC from this point will be twice refracted at C and D, and both times in the same direction, approaching the secondary axis which it cuts

at a. From what has just been said (p. 11), the other rays from the point A, will coincide in the point a,

which is accordingly the conjugate focus of the point A. If the secondary axis be drawn from the point B, it will be seen in like manner, that the rays from this point coincide in the point 6, and as the points between A and B have their foci between a and b, a real image of

A B will be formed at ab, which is inverted and smaller than the object A B.

Virtual image.-There is another case in which the object AB (Fig. 14) is placed between the lens and its

principal focus. If a secondary axis, Oa, be drawn through the point A, every ray AC after having been twice refracted, diverges in emerging from this axis, since the point A is at a less distance than the principal focus (see Fig. 7, p. 7). This ray continued in the opposite direction will cut the axis Oa in the point a, which is the virtual focus of the point A. Tracing the secondary axis of the point B, it will be found in the same manner that the virtual focus of this point is formed at b. There is, therefore, an image of AB at ab. This is a virtual image, it is in its right position, and is larger than the object.

Formation of images in double concave lenses. Double concave lenses give only virtual foci, whatever the distance of the object. Let AB (Fig. 15) be an

object placed in front of such a lens. If the secondary axis AO be drawn from the point A, all rays, AC, AI, from this point are twice refracted in the same direction, diverging from the axis AO; so that the eye receiving the emergent rays DE and GH, supposes them to proceed from the point where their continuations cut the secondary axis AO, in the point a.

In like manner drawing a secondary axis from the point B, the rays from this point form a pencil of diverging rays, the directions of which prolonged, coincide in the point b, on the secondary axis BO. Hence the eye sees at ab a virtual image of AB which is in its right position, and is smaller than the object,

CYLINDRICAL LENS.

A cylindrical lens convex or concave is ground upon a cylindrical surface and differs from a spherical in having what is known as an axis, in the direction of which there is no curvature; so that all rays of light passing through such a lens in the direction of its axis undergo no refraction, or at least only such as is experienced by rays passing through media with parallel surfaces (see Fig. 2, p. 2). All other rays passing through the lens are refracted; those in planes making small angles with the axis but little, those in planes making larger angles with the axis more, those in a plane at right angles to the axis most of all; so that we see the most powerful action of a cylindrical lens is in a direction at right angles to its axis. The direction of the refracted rays is either convergent or divergent according as the lens is convex or concave.

We can always ascertain the convex or concave curvature, as well as the axis of a cylindrical lens by allowing the light from a lamp situated at some six or eight feet distance to pass through it, and fall upon a screen placed from eight inches to three feet, or rather more, behind the lens according to its strength (nearer to it if the lens be strong, further from it if the lens be weak) and noticing the kind of figure formed upon the screen,

if the lens be convex the figure will have dark margins and a bright oval centre the long axis of the oval corresponding to the axis of the lens. If the lens be concave the figure will have a dark centre and bright edges forming altogether an oval, the long axis of which is at right angles to the axis of the lens.

REFRACTION OF THE EYE.

In the eye there are three refractive surfaces; the front of the cornea, the front of the lens and the front of the vitreous; we may consider these combined dioptric media as one biconvex lens, at the principal focus of which, in the normally shaped or emmetropic eye when its accommodation is relaxed the retina is situated; i.e. the emmetropic eye with accommodative rest is adapted for parallel rays.

Visual line and visual angle. The former signifies an imaginary line drawn from the yellow spot to the centre of the object looked at; the latter is the angle formed by two secondary axes drawn from what is known as the optical or more correctly the posterior nodal point of the eye (a point situated a little behind the crystalline lens) to the extremities of the object looked at. The visual line does not correspond with the optic axis, but cuts the cornea rather below and internal to its centre, and forms with the optic axis, an angle which varies in size according to the shape of the eyeball.

Conditions of normal vision. In order that an object may be seen distinctly, the following optical conditions must be fulfilled. A well defined inverted image must be formed in the yellow spot. The image