The position of the posterior focus could be easily found by measuring the ultra-focal dis tance nF from one of the positions of the image towards the lens. The position of the nodal point of emergence would be given by measuring a further distance F towards the lens.
66. Where the only camera available is capable of only a small range of focus (which is the case of a large number of hand cameras) the above method is not possible, and the following method can be used (Debenham, 1879). Having focussed the image of a geometrical figure and determined the scale n, the total distance 1 between object and image is measured. This distance is the sum of the two ultra-nodal distances p and p' increased or diminished by the nodal interval i (separation of the nodal points) according as the nodal points are in the normal position or crossed (the nodal points are said to be crossed when the nodal point of emergence is the nearer to the anterior focus, which is opposite to the case of the systems is not large and if the angle between the second ary axis to the point object and the optical axis is never very great (Moessard, 1889).
To explain this, consider a lens (Fig. 49) which, for the sake of simplicity, we suppose to be reduced to the nodal planes The image of an infinitely distant object in the direction N on the axis is formed at the focus F. After rotation about an axis perpendicular to the optical axis through the nodal point of emergence the nodal point of incidence will move to The point object being infinitely distant, the secondary axis N'M' to this point is parallel to By virtue of the definition of the nodal points (§ 44) the two exterior parts of the secondary axis are parallel to one another ; The displacements of the image noticed when the angle of rotation is large enable us to deter mine the form of the focal surface point by point, and to study the various aberrations of the image.
69. Automatic Adjustment of Object and Image. The relations between the ultra-focal distances of two conjugate points, or of planes perpendicular to the axis passing through them, can be translated geometrically so that auto matic linkages between these planes can be made, so dispensing with all focussing in en larging or reproduction. The only adjustment to be made is that for the scale of reduction, obtained by the displacement of one of the conjugate planes, the image remaining sharp the secondary axis thus emerges from the lens in the direction NY.
This property, which is made use of in the greater number of panoramic cameras, can also be utilized to determine the position of the nodal points and the focal length directly, when the nodal point of emergence is within the mount (a condition which excludes telephoto and analogous lenses). The lens being mounted so that it can be moved to and fro on a platform which can rotate about a vertical pivot, the image is formed on a fixed screen and observed while the lens is moved on the platform until a position is found such that the images of distant points remain stationary while the lens is rotated. The nodal point is then on the axis of rotation and the distance of this axis from the screen is the focal length required (Motssard °Fourniquet, 1893). Turning the lens end for end, the other nodal point can be found similarly, and a second measurement made of the focal length, which gives a useful check on the first measurement.
throughout. Numerous solutions of this prob lem have been given ; we shall indicate only some of them, selected from the most charac teristic.
We shall suppose, in what follows, that the nodal points coincide with the optical centre. If this is not accurately true, it will be necessary to assign to one of the nodal points the position indicated by the centre, and move the conjugate point corresponding to the other nodal point in an appropriate direction by an amount equal to the nodal interval.
(1) Consider (Fig. 50) two points 0 and I, free to move in a slot parallel to the optical axis. At C, the intersection of the slot with the plane drawn through the optical centre at right angles to the optical axis, erect a perpendicular CD, of length equal to the focal length F. By making a bent lever pivoted at D, having slots of which the axes meet at right angles in D (J. Carpentier, 1898), rotate, it is possible to constrain two studs P and P' in the axial slot to move so that their distances d and di from the point C will always satisfy the relationship between the ultra-focal distances of two points, viz.' dd' = F2 It will then only be necessary to join P and P' to 0 and I respectively by two connecting rods, of length equal to F, to make certain that 0 and I are conjugate points, and consequently also the two planes perpendicular to the axis through them.