Page 106 - The Indian Optician Digital Edition September-October 2022

the prism base direction and the coordinates x Note that using the sign convention, y =
and y.
When P = +2Δ (i.e., 2Δ base up),
V
+2 = 2 cos 30 (x sin 30 + y cos 30)
or, +1 = 0.433 x +0.75 y.
Now we know that the iso-V-prism line is a
straight line parallel with the cylinder axis so it
passes through a point on the x-axis where y =
zero and a point on the y-axis where x = zero.
Putting x, and then y, equal to 0, we have:
when x = 0, 1 = 0.75 y
from which, y = +1.333 cm,
and when y = 0, +1 = 0.433 x
from which, x = +2.309cm.
FIGURE 3 - 2Δ ISO-V-PRISM ZONES FOR +2.00 D
PLANO-CYLINDRICAL LENSES
FIGURE 4 - 2Δ ISO-V-PRISM ZONE FOR
PLANO-CYLINDER, +2.00 DC X 30
102 | THE INDIAN OPTICIAN | SEPT-OCT 2022
+1.333, means the point lies below the origin, so
the 2Δ base up iso-V-prism line passes through
the coordinates (0,+1.333) and through (+2.309,0)
as shown in red in Figure 5.
The 2Δ base down iso-V prism line is
equidistant but on the opposite side of the
30° meridian and must pass through points (0,
-1.333) and (-2.309, 0). Note that these
co-ordinates are given in cm.
The perpendicular distance from the
cylinder axis to the 2Δ iso-V-prism line is seen
to be given by 2.309 x sin 30 which is 1.154cm or
11.54mm. The band width is, therefore 23.08mm.
Now these results could also have been
found from a carefully drawn graphical
construction as shown in Figure 6, in which, OV,
whose length represents P , (2Δ in the example
V
in hand) has been resolved along the power
meridian of the cylinder, (OR along 120°) and
the length, OR, represents the power of the
prism along 120 which gives rise to 2Δ base up.
By measurement, OR = 2.31Δ up @ 120.
The decentration along 120 which gives rise
to this prism is
c = P 120 / F = 2.31/2 = 1.155cm or 11.55mm.
120
120
Point J has been marked off (in red) 11.55mm
along the 120° meridian and the 2Δ base down
iso-V-prism line drawn parallel with the cylinder
axis through J.
Point K has been marked off 11.55mm along
the 120° meridian below the cylinder axis and
the 2Δ base up iso-V-prism line drawn parallel
with the cylinder axis through K.
In the case of a sphero-cylindrical lens
with axis 90 or 180, the vertical power of the
lens is known, so the iso-V-prism zone can be
determined without difficulty and is found to
be a horizontal band, just as in the case of a
spherical lens.
For example, with the lens -4.00 / -1.00 x 180,
the power of the lens in the vertical meridian is
-5.00 D and the 2Δ iso-V-prism zone is a band
8mm wide parallel with the 180 meridian, since
LENS TALK