1. ## Prisms

Hi friends,

Need a little help here . How do I solve these?

1. Find the vertical and horizontal prismatic effects produced by decentring the lens R-2.50DS / +5.00DC @135 12mm upwards.

Do I take x as 0 while using the formula method ?

How does it correlate while solving by the graphical method?

2. How much prism must be incorporated in the lens L-4.00 DS / -2.00 DC @ 140 in order to shift the optical centre 6mm inwards ?

Do both the problems incorporate the same concept? Pls pls kindly help

Rekha

2. Both problems are dealing with the same concept. You'll need to first find the power in specific meridians (vertical or horizontal) with the formula R=sin2θ (this is for curvature, but it works well enough for power). Then, you'll need to use the Prentice Rule (Δ=cF) to figure out the prism. You may have to work backwards, depending on the question asked, but everything you need is there.

variables:
R: curvature or power
θ: angle between lens cylinder axis and desired axis (90 for vertical, 180 for horizontal)
Δ: Prism
c: decentration in cm
F: power (in whichever meridian the decentration is occurring)

[Note: I know that I will get some backlash for helping you on this, but I figure "what the hell" - as long as I'm not flat out giving you the answer]

3. Originally Posted by musicvirtuoso
You'll need to first find the power in specific meridians (vertical or horizontal) with the formula R=sin2θ (this is for curvature, but it works well enough for power). Then, you'll need to use the Prentice Rule (Δ=cF) to figure out the prism.
Unfortunately, the sine-squared formula, alone, will not work for accurately determining the horizontal and vertical components, which is most likely what is expected for these problems.

Originally Posted by Rekha
1. Find the vertical and horizontal prismatic effects produced by decentring the lens R-2.50DS / +5.00DC @135 12mm upwards... Do I take x as 0 while using the formula method ?
Your instructor most likely assigned a book that describes the formulaic and graphical methods in detail, like Jalie's "Principles of Ophthalmic Lenses." I prefer the elegant mathematical approached proposed by Keating (in "Geometric, Physical, and Visual Optics"):

You would first determine the three power components of the prescription, the horizontal (FX) power, the vertical (FY) power, and the "torsional" power (FT):

$F_X = Sph + Cyl \cdot sin^2 Ax$
$F_Y = Sph + Cyl \cdot cos^2 Ax$
$F_T = -C \cdot sin Ax \cdot cos Ax$

The horizontal and vertical prismatic effects induced by horizontal (X) and vertical (Y) decentration in centimeters are then given by:

$\Delta_X = F_X \cdot X + F_T \cdot Y$
$\Delta_Y = F_Y \cdot Y + F_T \cdot X$

You would have to pay attention to the sign of your answer. For the right eye, positive would be base up (for vertical) or base in (for horizontal). Your second problem would be solved using similar mathematics.

Originally Posted by Rekha
How does it correlate while solving by the graphical method?
Again, you would have to consult a textbook on ophthalmic optics for the details regarding the graphical approach, which involves drawing the decentration components relative to the center of the lens, and then dropping a perpendicular to the cylinder axis. The formulaic approach is certainly faster.

You can also verify your answers using the Induced Prism Calculator at OptiCampus.com. For the first problem, for instance, 3.0 prism diopters base is induced with 12 mm of decentration up for a -2.50 DS +5.00 DC x 135 lens.

Best regards,
Darryl

4. You know, when I wrote that, I totally had a brain fart. lol. I thought for a moment that might be too simple. .
Now that I've been discredited (haha) this may not be super useful, but I think the graphical method of solving this is also in "Systems of Ophthalmic Dispensing"... if memory serves (which it obviously often doesn't)

5. Originally Posted by musicvirtuoso
Now that I've been discredited (haha) this may not be super useful, but I think the graphical method of solving this is also in "Systems of Ophthalmic Dispensing"... if memory serves (which it obviously often doesn't)
I wouldn't say "discredited" at all: Your sine-squared formula would work adequately enough for estimating the amount of vertical prism imbalance at near, for instance. But optical assignment problems like these generally want an exact answer with both the horizontal and vertical components.

"System for Ophthalmic Dispensing" definitely provides a good presentation on the topic of prism by decentration, with both the formulaic and graphical approaches, assuming that Rekha hasn't already been instructed to purchase a specific textbook from the ABDO or something.

Best regards,
Darryl

6. Thanks a lot friends for the reply . And Darryl u r right . We do follow the prescribed textbooks which are - Opthalmic optics by Jalie and Optics by Tunnacliffe.

I did refer Boorish but was not of any help when it came to the graphs . The values obtained by the graphical method and by formula should match both in finding the prismatic effect and the decentration which posed some problems . (Not to mention how much it has put me behind in my assignments ) .

Right now working on stokes construction again by graph hope it goes on well !!!!!

thanks once again

Regards,
Rekha.

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