Part d -- Resultant prism tables

Now for the third method. The table for this method is in Clifford Brooks' Understanding Lens Surfacing, pages 310-311, or they are available here to print. Dr. Brooks went up to 6.5 where I only went up to 6, and he did the amount and angle all on one table, where I separated them into two tables. I needed to do tables that you could print easily in case you did not have the book yet, so mine are separated. This is the amount table and this is the meridian (axis) table. Print each one if you do not have the book.

The tables are simply giving you the result of the equations, only they are set up on quarter of prism diopter increments. If you ever do one of this type of problem where the prism amount is not in an even quarter you will have to round to the nearest quarter to use the table. When I give you a problem on the test and ask you to use the table I will give you the question in quarters, as I have done for all of the exercises. If you are ever in a position to do a lot of resultant prism and want the tables in tenths it is possible to fairly quickly generate a new table.

Let's do the problem that we started with last time: OD 2 IN and 1 UP. As with the formulas you need to identify which is vertical and which is horizontal; and you need to decide what the quadrant is. In this case vertical is 1 and horizontal is 2, and it is quadrant I. As with the formulas, in Q I we use the meridian as we get it from the formula.

On the table on pages 310-311 of Understanding Lens Surfacing, or on the 'RESULTANT PRISM AMOUNT' table, the vertical amount is found vertically down the side of the table and the horizontal amount is found horizontally across the top of the table. Find 1.0 down the side and 2.0 across the top, and find where the row and column meet.

On my table they meet at 2.2. On Dr. Brooks' table they meet at 2.24, with a 27 under it. Going to my table that says 'RESULTANT PRISM AXIS' you find that same 27 at the intersection of the 1.0 row and the 2.0 column. I rounded amounts to tenths instead of hundredths because this is about all the accuracy we can get in the lensometer. It does not matter to me whether you give me the answer of 2.2 or 2.24.

Using the rules that you learned with the formulas, the answer to this problem is 2.2 BU&I @ 027 or 2.2 @ 027.

How about OS 4.25 BO and 3.75 BD?

1. Determine what is horizontal and what is vertical, and determine the quadrant.
   1. V = 3.75
   2. H = 4.25
   3. OS D&O is Q IV.
   4. On the table(s) locate the intersection of the row for the vertical amount and the column for the horizontal amount.
   
         The 3.75 row and the 4.25 column intersect at 5.7 (5.67) and 41 degrees. So the amount is 5.7 and the angle is 41.
   5. In the fourth quadrant we subtract the angle from 180. Dr. Brooks has you subtract it from 360. So you get 180 - 41 = 139, or 360 - 41 = 319. These are the two meridians, depending on whether you are using 180 or 360 notation.

   
   

   The answer is 5.7 BD&O @ 139 or 5.7 @ 319.

   

   OK, here is that same set of exercises for you to do. Do them with the table.  Remember, the rules for the axis are the same rules that we used when we did this with the formulas.
    

   1. OD 5.5BU & 1.5BI
   2. OS 1.5BU & 3.0BI
   3. OD 3.0BD & 2.25BI
   4. OS 2.25BD & 4.0BI
   5. OD 4.0BD & 4.5BO
   6. OS 5.0BD & 2.75BO
   7. OD2.75BU & 0.5BO
   8. OS 0.5BU & 5.5BO
   9. OD 3.5BI & 3.5BU
   10. OS 3.0BI & 4.0BD
   11. OS 4.0BO & 1.0BD
   12. OD 1.0BO & 1.5BU
   13. OD 1.5BU
   14. OS 3.0BI
   15. OD 5.5BD & 2.25BO
   16. OS 4.25BU & 3.0BI
   Numbers 15 and 16 are to be submitted to your instructor by e-mail.

   
   Here are all of the answers..