if the entrance pupil is increased. It then comprises all points
reached by principal rays. The same relations apply to the image-space,
in which there is an exit luke, which, seen from the middle
of the exit pupil, appears under the smallest angle. It is the image
of the entrance luke produced by the whole system. The image-side
field of view 2w′ is the angle comprised by the principal rays
reaching the edge of the exit luke.
Fig. 18.
Most optical instruments are used to observe object-reliefs (three-dimensional objects), and generally an image-relief (a three-dimensional image) is conjugate to this object-relief. It is sometimes required, however, to represent by means of an optical instrument the object-relief on a plane or on a ground-glass as in the photographic camera. For simplicity we shall assume the intercepting plane as perpendicular to the axis and shall call it, after von Rohr, the “ground glass plane.” All points of the image not lying in this plane produce circular spots (corresponding to the form of the pupils) on it, which are called “circles of confusion.” The ground-glass plane (fig. 18) is conjugate to the object-plane E in the object-space, perpendicular to the axis, and called the “plane focused for.” All points lying in this plane are reproduced exactly on the ground-glass plane as the points OO. The circle of confusion Z on the plane focused for corresponds to the circle of confusion Z′ on the ground-glass plane. The figure formed on the plane focused for by the cones of rays from all of the object-points of the total object-space directed to the entrance pupil, was called “object-side representation” (imago) by M von Rohr. This representation is a central projection. If, for instance, the entrance pupil is imagined so small that only the principal rays pass through, then they project directly, and the intersections of the principal rays represent the projections of the points of the object lying off the plane focused for. The centre of the projection or the perspective centre is the middle point of the entrance pupil C. If the entrance pupil is opened, in place of points, circles of confusion appear, whose size depends upon the size of the entrance pupil and the position of the object-points and the plane focused for. The intersection of the principal ray is the centre of the circle of confusion. The clearness of the representation on the plane focused for is of course diminished by the circles of confusion. This central projection does not at all depend upon the instrument, but is entirely geometrical, arising when the position and the size of the entrance pupil, and the position of the plane focused for have been fixed. The instrument then produces an image on the ground-glass plane of this perspective representation on the plane focused for, and on account of the exact likeness which this image has to the object-side representation it is called the “representation copy.” By moving it round an angle of 180°, this representation can be brought into a perspective position to the objects, so that all rays coming from the middle of the entrance pupil and aiming at the object-points, would always meet the corresponding image-points. This representation is accessible to the observer in different ways in different instruments. If the observer desires a perfectly correct perspective impression of the object-relief the distance of the pivot of the eye from the representation copy must be equal to the nth part of the distance of the plane focused for from the entrance pupil, if the instrument has produced a nth diminution of the object-side representation. The pivot of the eye must coincide with the centre of the perspective, because all images are observed in direct vision. It is known that the pivot of the eye is the point of intersection of all the directions in which one can look. Thus all these points represented by circles of confusion which are less than the angular sharpness of vision appear clear to the eye; the space containing all these object-points, which appear clear to the eye, is called the depth. The depth of definition, therefore, is not a special property of the instrument, but depends on the size of the entrance pupil, the position of the plane focused for and on the conditions under which the representation can be observed.
 |
| After von Rohr. |
| Fig. 19. |
If the distance of the representation from the pivot of the eye be altered from the correct distance already mentioned, the angles of vision under which various objects appear are changed; perspective errors arise, causing an incorrect idea to be given of the depth. A simple case is shown in fig. 19. A cube is the object, and if it is observed as in fig. 19a with the representation copy at the correct distance, a correct idea of a cube will be obtained. If, as in figs. 19b and 19c, the distance is too great, there can be two results. If it is known that the farthest section is just as high as the nearer one then the cube appears exceptionally deepened, like a long parallelepipedon. But if it is known to be as deep as it is high then the eye will see it low at the back and high at the front. The reverse occurs when the distance of observation is too short, the body then appears either too flat, or the nearer sections seem too low in relation to those farther off. These perspective errors can be seen in any telescope. In the telescope ocular the representation copy has to be observed under too large an angle or at too short a distance: all objects therefore appear flattened, or the more distant objects appear too large in comparison with those nearer at hand.
 |
 |
| After von Rohr. | After von Rohr. |
| Fig. 20. | Fig. 21. |
 |
| After von Rohr. |
| Fig. 22. |
From the above the importance of experience will be inferred. But it is not only necessary that the objects themselves be known to the observer but also that they are presented to his eye in the customary manner. This depends upon the way in which the principal rays pass through the system—in other words, upon the special kind of “transmission” of the principal rays. In ordinary vision the pivot of the eye is the centre of the perspective representation which arises on the very distant plane standing perpendicular to the mean direction of sight. In this kind of central projection all objects lying in front of the plane focused for are diminished when projected on this plane, and those lying behind it are magnified. (The distances are always given in the direction of light.) Thus the objects near to the eye appear large and those farther from it appear small. This perspective has been called by M von Rohr[1] “entocentric transmission” (fig. 20). If the entrance pupil of the instrument lies at infinity, then all the principal rays are parallel and the projections of all objects on the plane focused for are exactly as large as the objects themselves. After E. Abbe, this course of rays is called “telecentric transmission” (fig. 21). The exit pupil then lies in the image-side focus of the system. If the perspective centre lies in front of the plane focused for, then the objects lying in front of this plane are magnified and those behind it are diminished. This is just the reverse of perspective representation in ordinary sight, so that the relations of size and the arrangements for space must be quite incorrectly indicated (fig. 22); this representation is called by M von Rohr a “hypercentric transmission.” (O. Hr.)
LENT (O. Eng. lencten, “spring,” M. Eng. lenten, lente, lent; cf.
Dut. lente, Ger. Lenz, “spring,” O. H. Ger. lenzin, lengizin, lenzo,
probably from the same root as “long” and referring to “the
lengthening days”), in the Christian Church, the period of
fasting preparatory to the festival of Easter. As this fast
falls in the early part of the year, it became confused with the
season, and gradually the word Lent, which originally meant
spring, was confined to this use. The Latin name for the fast,
Quadragesima (whence Ital. quaresima, Span. cuaresma and Fr.
carême), and its Gr. equivalent τεσσαρακοστή (now superseded
by the term ἡ νηστεία “the fast”), are derived from the Sunday
which was the fortieth day before Easter, as Quinquagesima
and Sexagesima are the fiftieth and sixtieth, Quadragesima
being until the 7th century the caput jejunii or first day of
the fast.
The length of this fast and the rigour with which it has been observed have varied greatly at different times and in different countries (see Fasting). In the time of Irenaeus the fast before Easter was very short, but very severe; thus some ate nothing for forty hours between the afternoon of Good Friday and the morning of Easter. This was the only authoritatively prescribed fast known to Tertullian (De jejunio, 2, 13, 14; De oratione, 18). In Alexandria about the middle of the 3rd century it was already
- ↑ M von Rohr, Zeitschr. für Sinnesphysiologie (1907), xli. 408–429.
