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THIS ARTICLE IS BEST READ ON A PDF.
Any object viewed through a prism appears to be displaced towards the apex, with the amount of deviation dependent on the prism's power. CF Prentice suggested a way of quantifying this power. The unit 'prism dioptre' is where the tangent of the angle of deviation (d) is 1/100. The image is deviated by 'y' over a distance 'x' (Figure 1). So if the deviation is 1cm (y) at a distance of 1m (x) the prism has a power of 1 prism dioptre, 2cm deviation over 1m has a power of 2?. The symbol we use for prism dioptre is ?.
Prentice's rule can be derived from Figure 2.
Remembering the tangent of the angle of deviation for 1? is 1/100, the unit for c must be centimetres if the unit for f is metres. Working with power rather than focal length is easier, so this becomes
P = cF
Spectacle lenses behave in the same way as a prism, and can be considered as numerous prisms of differing apical angles. In positive lenses the apical angle of the consecutive prisms decreases towards the periphery of the lens, and in minus lenses the angle increases (Figure 3).
At the centre of the lens there is no prismatic effect, and light passes straight through, undeviated. This point on a lens is known as the optical centre. When a patient looks away from the optical centres (up, down etc) there will be some induced prismatic effect. For a patient with the same prescription right and left, the images will be deviated by the same amount, both images fall on corresponding points on the retina and are perceived as a single image.
If the prescription in each eye is dissimilar, the two images may fall outside Panum's fusional area, resulting in diplopia. This is an issue only when viewing away from the optical centres of the lens, and if the vertical differential prism at that point is greater than 2?. This is a theoretic value in practice much larger differences can be well tolerated. Likewise, some people may not tolerate as much as 2?.
Although this diplopia can occur at all directions of gaze, we tend to only to reduce (or remove) it in lower gaze, to make near vision more comfortable. Anisometropia is due to the distance prescription only, unless the add is different right and left.
To remove the differential prism at the near visual point, it is necessary to know how much unwanted prism there is. We drop our eyes to read, by about 8mm. When the eye is in the primary position the patient should be viewing through the optical centre of the lens. So we are concerned with the vertical prismatic effects at points 8mm below the optical centres. We rarely need to worry about horizontal differential prism as horizontal fusional reserves are large.
It's easy to employ P=cF to determine the effective prism in each lens. As we are concerned that the resultant differential prism is less than 2? it is possible to round values to enable faster mental arithmetic.
We can round up the axis to more manageable numbers
175° @ 180° @ 5°
46° @ 45° @ 42°
39° @ 35° @ 32°
and assume that the near vision point is 10 below the optical centre
So P=cF becomes P=F
Example
-6.00 x 180 6?down -6.00 x 90 zero prism +6.00 x180 6?up
Example for a spherical Rx
So for the following prescription
R -6.00DS P=cF P=1 x 6, P = 6 base down
L -1.00DS P=cF P=1 x 1, P = 1 base down
If you have problems with the base direction then visualise the lens. A plus lens will be base up and a minus will be base down. Had both eyes been -1.00, there would have been no differential prism. The right eye has 5 dioptres more prism than that, so there are 5 dioptres of base down differential prism in the right eye (or 5 dioptres base up in the left).
For toric lenses we are only concerned with vertical power and the resulting prism. Remember that if the axis is horizontal, then the power is vertical and vice versa. Logically at any other axis the prismatic power is going to be somewhere in between. As the axis changes from vertical to horizontal the effective power in the vertical will increase until it is at its maximum. Sadly it is not a linear relationship - an axis half way does not give you half the prism. Once the prism from the sphere has been calculated it can be added to the prism from the cyl, calculated by using trigonometry.
Where:
(Sin axis) x (power of the cyl) = power in the vertical meridian.
Easy to remember approximation
Example
R -3.00/-2.00x180 L -1.00/-1.00x180
Example
The anisometropia may be obvious such as R -2.00 and L -5.00, but watch out for odd Rx's such as:
R-2.00/-4.50x45 L-5.00/-4.00x90
There are at least two good software programs on the web to help you determine the prismatic effect at a particular point on a lens. You would need to run it for both lenses and work out the differential prism yourself. Pocketsoft Optical Utilities is probably the better of the two listed, as it covers many of the calculations in this series (www.thomson-software-solutions.com/html/optometritoolbox.html) (http://pocketsoft.co.uk/).
Janet Carlton is dispensing manager at the Fight For Sight Optometry Clinic, City University