Page 140 - Nov- Dec 2024

We have:
S = +6, C = -3, θ = 140, x = +0.25, y = +1.1 Big News!

P = y.S + C cos θ (x sin θ + y cos θ)
V
= 1.1 x 6 - 3 cos 140 (0.25 sin 140 + 1.1 cos 140) Your go-to optics

= +5.03Δ or 5.03 base up since P is positive.
V
P = x.S + C sin θ (x sin θ + y cos θ) magazine is now
H
= 0.25 x 6 - 3 sin 140 (0.25 sin 140 + 1.1 cos 140) online. Get the latest

= +2.81Δ or 2.81 base out since P is positive. insights, trends, and
V
These formulae can be transformed to find updates instantly.
the vertical and horizontal decentrations (y and x)
required to produce a prescribed prismatic effect, VISIT
P and/or P . The same sign convention is used.
H
V
tionet.in
We have, from above, by expansion:
2
P = y (S + C cos θ) + x C sin θ cos θ and never miss a beat!
V
and P = y C sin θ cos θ + x (S + C sin θ).
2
H
Solving this pair of simultaneous equations
we find
y = P (S + C sin θ) - P C sin θ cos θ / S (S + C) EXAMPLE:
2
V
H
(decentre up when y is positive), Find the vertical and horizontal
and x = P (S + C cos θ) - P C sin θ cos θ / S (S + C) decentrations required to produce 3Δ base
2
v
H
(decentre out when x is positive). 0 and 4Δ base in with the lens R -2.50 /
+3.00 x 60.
We have:
S = -2.5, C = +3, θ = 60, P = +3, P = - 4
V
H
y = 3 (-2.5 + 3 sin2 60) + 4 x 3 sin 60 cos 60 /
-2.5 (-2.5 + 3)
= -3.56 cm or decentre 3.56 cm down.

x = P (S + C cos θ) - P C sin θ cos θ / S (S + C)
2
H
v
= -4 (-2.5 + 3cos 60) - 3 x 3sin 60 cos 60) /
2
-2.5 (-2.5 + 3)
= -2.48 cm or decentre 2.48 cm in.
The required decentrations are 3.56 cm
down and 2.48 cm in.
REFERENCE

1. Jalie M (2021), Principles of Ophthalmic
FIGURE 2 - PRISMATIC EFFECT Lenses (6 Ed.) ABDO, Godmersham.
th
AT POINT R

134 | THE INDIAN OPTICIAN | NOV-DEC 2024 LENS TALK