PAGE References to Optical Formulas Tutorial:  (first reference is to edition 1 / second reference is to edition 2).

We are going to take a look at the prescription +1.50 -0.50 x125. What are the major power/meridian combinations? In other words, what does it look like on the optical cross?

Well, the +1.50 and the axis 125 go together. +1.50 -0.50 = +1.00, and 125 - 90 = 035, so the other leg of the optical cross is +1.00 at 035. So we get the optical cross on the right.

Now lets take the prescription off of the optical cross in plus cylinder form. The power that is the least plus or the lowest on the power drum of the focimeter is +1.00, so the prescription will have +1.00 for the sphere and 035 for the axis. +1.50 - (+1.00) = +0.50, so the cylinder is +0.50. So the new prescription is +1.00 +0.50 x035.

We now have two prescriptions, both of which describe the exact same lens.
       +1.50 -0.50 x125 is the Rx is minus cylinder form.
       +1.00 +0.50 x035 is the Rx is plus cylinder form.
Notice that these two forms give the power and axis for each of the major meridians?

So we have two ways of describing the lens. We would like to have a way of changing from one form to the other without going through the optical cross. This method is called transposition.

The rules are:

That is all there is to it! So, lets look at that original Rx again. We had +1.50 -0.50 x125.

1. Add the sphere and cylinder amount. +1.50 -0.50 = +1.00. That is the new sphere.
2. Change the sign of the cylinder. Is was -0.50; now it becomes +0.50.
3. The axis is greater than 90, so we subtract 90 from it: 125 - 90 = 035.

As Opticians we are not allowed to change a prescription. Are we allowed to do this transposition? Yes, this is not changing the Rx, it is writing it in a different form. The lens that results from this Rx is exactly the same as the lens that results from the original Rx. You can see that from the optical cross. I may have changed the way the Rx is written, but I have not changed the lens.

There is a difference between making the lens in plus cylinder form versus making the lens in minus cylinder form. In the first case the toric surface is on the plus side of the lens, and in the second case the toric surface is on the minus side of the lens. Most Refractionists expect you to make the glasses in minus cylinder form regardless of the form that it is written in. If the lens is to be made in plus cylinder form the Refractionist will say so very specifically. So, in fact, the Refractionist is EXPECTING you to make the glasses in minus cylinder from even if it is given to you in plus cylinder form.

Lets do another example, then you get your exercises.

The Rx says -5.25 +1.50 x 053. You need to find the lens in your stock drawer, but they are all marked in minus cylinder form. So,

1. Add the sphere and cylinder: -5.25 +1.50 = -3.75.
2. Change the sign of the cylinder: -1.50.
3. The axis is less than 90, so we will add 90 to it: 053 + 90 = 143.

Here is another one: +2.50 -2.50 x 110. For some strange reason we are to transpose it to plus cylinder form. Why? I have no idea. This is school. We do not need reasons for the things that we do!

1. Add the sphere and cylinder: +2.50 -2.50 = 0.00.
2. Change the sign of the cylinder: +2.50.
3. Change the axis by 90 degrees: 110 - 90 = 20.

The Rx now reads pl +2.50 x020.

Read page (47-48 / 62-63) in Optical Formulas Tutorial, then do the exercises.  IGNORE Crossed Cylinders unless your instructor tells you to do it.

Transpose:

1. pl -1.25 x175
2. +1.25 +2.50 x123
3. -6.75 -2.50 x013
4. +0.25 -0.25 x036
5. -3.50 +1.25 x150
6. -0.25 +0.50 x089

Now, go to Systems for Ophthalmic Dispensing.  Read pages 392-397, and do exercises 10 and 11.  Then read pages 399-404 (up to Base Curves) and do exercises 1-7.