The Jackson Cross Cylinder
The Jackson cross cylinder is a spherocylindrical lens used in clinical refraction (see Chapter 3). It is the combination of a plus cylinder and a minus cylinder having axes 90° apart and equal power.
The cross-cylinder lens itself is usually ground in the spherocylindrical form. It has a cylindrical surface on one side and a spherical surface on the other side that has half the power and is of opposite sign to those of the cylindrical surface; thus, its spherical equivalent is zero.
Use of the Jackson cross cylinder to determine both the power and axis of the astigmatic correction for an eye is discussed in Chapter 3. The specific power (eg, ±0.25 D, ±0.37 D, ±0.50 D) of cross cylinder selected for use in clinical testing depends on the patient’s visual acuity. For 20/30 and better, the ±0.25 D cross cylinder is appropriate. The ±0.50 D cross cylinder is useful for visual acuities between 20/40 and 20/70, and so forth.
Prisms
Prism Diopter
Prism power is defined by the amount of deviation produced as a light ray traverses the prism. The deviation is measured as the number of centimeters of deflection measured at a distance of 100 cm from the prism (Fig 1-58) and expressed in prism diopters (Δ).
Figure 1-58 Definition of prism diopter. The power of the prism, when held in this particular position, is defined to be the number of centimeters of deflection of a ray, measured 100 cm after passage through the prism and expressed in prism
diopters. (Illustration developed b y Edmond H. Thall, MD, and Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
For angles less than 100Δ (45°), each change in deviation by 2 prism diopters is approximately equal to a change of 1°. For larger angles, increasingly more prism diopters are required for an equivalent change by 1°.
Glass prisms are calibrated to be held in the Prentice position, that is, with one of the faces of the prism perpendicular to the light rays. A glass prism, then, is correctly held with the back face parallel to the plane of the iris—the direction the eye is turned. All of the refraction occurs at the opposite face and is greater than the minimum deviation for that prism. This is the manner in which prism in spectacle lenses of any material is measured on a lensmeter, with the back surface of the spectacle lens flat against the nose cone of the lensmeter. If the rear surface of a 40Δ glass prism is erroneously held in the frontal plane of the subject’s face, only 32Δ of effect will be achieved.
Plastic prisms and prism bars, on the other hand, are calibrated according to the angle of
minimum deviation. To approximate this angle clinically, these prisms are held with the rear surface in the frontal plane of the subject’s face (Fig 1-59).
Figure 1-59 Correct positions for holding orthoptic glass and plastic prisms. (Illustration developed b y Edmond H. Thall, MD, and
Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
The path of a pencil of rays passing through a prism is bent toward the base of the prism to form a real image, which is shifted in the direction of the base of the prism. If you put a prism in front of your vision chart projector with the apex pointed toward the left side of the room, the letters on the screen will be shifted in the direction you are pointing the base of the prism—that is, to the right (Fig 1-60).
Figure 1-60 Real images are displaced by the prism toward the base of the prism. (Illustration developed b y Edmond H. Thall,
MD, and Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
On the other hand, if I am looking at a letter on the chart, a real object, and you interpose in front of my eye the same prism with its apex pointed toward the left side of the room, the prism will create a virtual image, which is displaced with respect to the original object, toward the apex of the prism. My eye sees those diverging rays as coming from an optically real object, which my eye brings to focus as a real image on my retina. To me, the letter will appear to have jumped to the left (Fig 1-61).
Figure 1-61 The prism forms a virtual image of a real object, and that virtual image is displaced, compared with the
original object, toward the apex of the prism. (Illustration developed b y Edmond H. Thall, MD, and Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
Prismatic Effect of Lenses and the Prentice Rule
A spherical lens obviously has prismatic power at every point on its surface that bends light rays toward the optical axis (plus lenses) or away from the optical axis (minus lenses). Prismatic power is zero at the optical center of the lens and increases away from the center, proportional to both the dioptric power of the lens and the distance from the center of the lens. This relationship is expressed by the Prentice rule, which states that the prismatic power of a lens (in prism diopters, Δ) at any point on its surface is equal to the distance from the optical center (in centimeters) times the power of the lens (in diopters) (Fig 1-62).
Figure 1-62 The Prentice rule. See text for explanation. D = power of the lens in diopters; Fp = focal point; h = distance
from the optical center, in centimeters. (Illustration developed b y Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
The prismatic effect of lenses becomes clinically important for patients with anisometropia
(unequal lens power) in the vertical meridian, as different prismatic effects are produced for the 2 eyes in the reading position, and a vertical misalignment of the visual axes is produced. Thus, the effects of prismatic image displacement and prismatic image “jump” are taken into account in the design of bifocal lens segments.
A prism may be effectively “added” to a spectacle lens simply by decentering the lens in the frame so that the patient’s visual axis in primary position passes through an off-center portion of the lens. Whether the desired amount of prism can be added by such decentration depends on the power of the lens and the size of the lens blank. For example, adding 5Δ of base-out prism to a +1.00 D spherical spectacle lens would require decentering the lens temporally by 5 cm, which is farther than the edge of the lens blank; in this case, prism would need to be ground into the lens.
How can one quickly tell with a lensmeter whether a spectacle lens has been decentered or prism has been ground into the lens? The determination can be made simply by locating the optical center by moving the lens around until the lensmeter target is centered. If the greatest distance from the optical center to the edge of the lens is more than half the 60-mm diameter of the usual lens blank, then prism must have been ground into the lens.
Remember that prism in a spectacle lens is read at the position of the wearer’s visual axis in primary position. A washable felt-tip pen is helpful in marking this position before transferring the glasses from the subject’s face to the lensmeter. The lensmeter target, being a real image, is displaced in the direction of the base of the prism being measured. Therefore, if the optical centers appear in the lensmeter to be laterally displaced, for instance, the glasses have base-out prism.
If we need a certain amount of vertical prism and another of horizontal prism, we can add the 2 as vectors to find the obliquely angled prism that accomplishes both requirements (Fig 1-63). However, if we hold 2 loose prisms together, we will not have a prism whose power is equal to the sum of the 2, as the light path is already bent before it hits the second prism. For our purpose, we can add the powers by holding 1 prism in front of each eye.
Figure 1-63 Vector addition of 2 prisms. A, The magnitude of the sum vector is 
. B, The angle of the sum vector
is arctan (6/8). BU = base up; BO = base out. (Illustration developed b y Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
When prescribing an oblique prism, it is important to specify the direction of the base clearly, by writing, for instance, “base up and out, in the 37° meridian” or “base down and in, in the 37° meridian.”