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The facts behind the PD measurement – prismatic effect


Everybody in optics know the meaning of PD – right? But do you know what the significance is behind the measurement of the pupillary distance? Do you know Prentice’s Rule?

To come to grips with it, we have to take a step back and look at the principles of refraction.

Light is only refracted when it strikes a material at an angle, such as the curved surface of a spectacle lens. If it strikes a surface at 90 degrees, it will carry straight on the same path.

Refraction is the bending of light when it goes from one medium to another so, when a ray of light passes from air through a glass prism, refraction of light occurs both, when it enters the prism as well as when it leaves the prism. Since the refracting surfaces are not parallel, therefore, it strikes the surfaces at an angle.


Light passing through a prism will always be bent towards to base of the prism, but the image will appear to come from a point towards the apex. It is this principle of refraction that allows us to use lenses to bend light so that the focus falls on the retina, correcting refractive errors.

Spectacle lenses are made from a combination of prisms like this:


A plus lens has the bases together and a minus lens the apexes. If light passes through the centre of the lens (at 90 degrees), there will be no deviation, but anywhere outside the centre, the light will be deviated towards the base of the prism.

Setting up a pair of spectacles, we want the pupils to coincide exactly with the optic centres of the lenses. That is why we measure the PD. Should the PD not coincide with the optic centres of the specs, there will be prismatic effect.

In the diagram below, the interpupillary distance of the eyes is less than the optical centres of the lenses. The result is that the object appears to be at position B when it is actually at position A. This means that the eyes must converge more than expected, which can cause discomfort.


In the drawing below the opposite applies. This results in less convergence being required, because the object viewed is at A but appears to be at B. This places a demand for diverging the eyes, which is not a natural movement and more difficult than turning the eyes in.


So, in practical terms, when you dot the optic centres in the vertometer, and the measurement between them is not the same as the PD, the patient is at risk of suffering discomfort, even if the Rx is spot on. So, how much prismatic effect is acceptable? How do we calculate it? We use Prentice’s Rule.

Fig.5 – PD versus the optical centres

Prentice’s Rule states: The power of the prism is equal to the power of the lens in dioptres times the amount of decentration in millimeters divided by 10. dec = decentration or distance in mm away from the optical centre of the lens.

Prismatic Effect = the distance in centimeters X the power of the lens in the horizontal meridian

P = c x F


Rx –  R + 4,00  L +3,00

Pd = 64mm

Optic centres = 70mm (how the spectacles turned out)

70 -64 = 6 = 3mm per eye

P = c X F

R – P = ,3 cms X 4 = 1,2 Base out

However, in a Sphero cylindrical Rx, we need to understand how to determine the power in the horizontal plane. Again, we have to take a step back to come to grips with the optics.

A spherical lens has the same bending power in all directions, whereas a cyl only has power in the meridian at 90 degrees to the axis.

+2,00 – 1,00 X 90 = total power in the horizontal plane is +1,00

-4,00 – 2,00 X 180 = total power in horizontal plane is -4,00

Light can only be bent by a material if it strikes is at an angle. That’s why lenses are curved. However, a cylinder lens is only curved in one plane. In the figure below, the axis is at 90 degrees and the bending power is in the horizontal plane. In the vertical plane the material is flat with no bending power but in the horizontal it is curved with bending power.


Now that we have calculated prismatic effect – what next? There is a table of tolerances, which in my opinion cannot be seen as the be all and end all.


Base-Out – 2 prism dioptres

Base-In – 0,5 prism dioptres

Vertical – 0,5 prism dioptres

What we do know, is that it is easier to overcome base out prism (Fig3) than it is to overcome base in prism (Fig 4). This is simply because it is easier to converge or willfully turn our eyes in, but not so easy to turn them out at will.

The most important factor to take into account is the binocular vision status of the patient. If the patient has an exophoria, base-in will assist and with an esophoria base-out will assist. At the end of the day, it is for the optometrist to make the decision, taking into account the clinical findings and the binocular status of the patients.

It would be excellent for the optical dispenser to report the problem to the optometrist in prism dioptres – 2 base-in or 0,75 base up R.

From Prentice’s Rule, it is clear that the higher the prescription power in the horizontal plane, the more critical it becomes to have the optic centres spot on. With this information on board, one can now at a glance see that a Rx – Pl – 4,50 X 180 poses no problem if the centres are out.