Part e -- Resolving prism formulas
 

Patient:  Mrs. Y         .              Rx: OD -- 2D BI, added to what is there. Dr. X             .

Believe it or not, I got  a prescription that looked just like that once.  Now, if it just happened that I'd made the glasses that Mrs. Y was wearing, I would have known just how much prism to order.  Unfortunately, the glasses were made elsewhere, to an Rx that was not Dr. X's Rx, and so my next step was to see what was in the glasses.  Wouldn't it have been nice if what was there was just BI or BO?  Nope.

Let's suppose that I neutralize Mrs. Y's glasses, and the prism that I read in the lensometer is 2.5 BU&I at 35 degrees.  Now what do I do?

Believe it or not, in the old ABO study guide, under questions for preparation for the ABO Master's exam, there was a problem where they asked you to combine two different prism amounts, both at axis that were not 0, 90, 180 or 270.  What to do?

The answer to both of these questions is to first resolve the prism into the horizontal (BI or BO) and vertical (BU or BD) components, combine horizontals and verticals, and then resolve to the new prism amount and direction.

Take a look at this diagram from several lessons ago.  When you combined the 1.5 UP and the 2 IN, you got 2.5 @ 37.  What we need to do is take that 2.5 @ 37 that we started with this time and resolve it back to the original vertical and horizontal components.

Remember that the formula for the angle when we were finding the resultant prism was TAN angle = Vertical/Horizontal?  Now, look on your calculator.  Of the functions sine (SIN), cosine (COS), and tangent (TAN), what is first?  Sine.  So, SIN goes with Vertical and COS goes with Horizontal.

The formula is:
                    Vertical = (prism) (sin angle)
                    Horizontal = (prism) (cos angle)
To do this, start with the angle that you are given:  in this case, we are resolving 2.5 @ 35.  So, the angle here is 35, and the prism amount is 2.5.

• Vertical = (prism) (sin angle) = 2.5 (sin 35)
= (2.5)(0.573576....) = 1.43... = 1.4 vertical prism.
• Horizontal = (prism) (cos angle) = 2.5 (cos 35)
= (2.5)(0.819152....) = 2.04... = 2.0 horizontal prism.

What is left is to find out what directions are vertical and horizontal.  Right lens, original axis of 35, so it is in quadrant I where the base direction is U&I.  So vertical is UP and horizontal is IN.  The answer to what was originally in the glasses is 1.4 UP and 2.0 IN.

Now,  Dr. X asked that I give Mrs. Y  2 more IN than she had.  So, the new glasses will have 1.4 UP and 4.0 IN.  Go ahead, find the resultant prism for that for the new glasses.  What is it?

---

If you got 4.2 U&I at 19 degrees, you did it correctly.

---

Let's look at a potential  ABO Master's exam problem.

Combine:  OS, 3.5 @ 135 with 1.0 @ 75.
First:  Resolve each of those into horizontal and vertical.

OS, 3.5 @ 135

Vertical = P(sin a) = 3.5(sin 135) =
             = (3.5)(0.7071) = 2.5
Horizontal = P(cos a) = 3.5(cos 135)
            = (3.5)(0.7071) = 2.5
Left lens, 135 is Quadrant II, which is U&I, so 2.5 U and 2.5 I

OS,  1.0 @ 75

Vertical = P(sin a) = 1.0(sin 75) =
             = (1.0)(0.9659) = 1.0
Horizontal = P(cos a) = 1.0(cos 75)
            = (1.0)(0.2588) = 0.25
Left lens, 75 is Quadrant I, which is U&O, so 1.0 U and 0.25 O

Next:  Combine the horizontals and the verticals.

2.5 U and 1.0 U for 3.5 U
2.5 I and 0.25 O combines to 2.25 I

Last, find the resultant prism for OS, 3.5 BU and 2.25 BI.  What is it?

---

If you got 4.2 BU&I @ 123, then you are correct.

---

Let's do some less complex resolving prism exercises, then come back and review the ones above again.

1.  Resolve:  OD 3.5  @ 290.

1. V = P(sin a) = 3.5 (sin 290) = (3.5)(0.9397) = 3.3
2. H = P(cos a) = 3.5(cos 290) = (3.5)( 0.3420) = 1.2

---> Notice that I ignored minus signs in the calculator when doing the sine and cosine of the angle.
---> Also notice that I used the meridian just as it was -- no need to convert;  but you will have to determine the quadrant now, to find what direction the vertical is and what direction the horizontal is.  So,

3. OD at 290 is Q IV, which is Down and In, so the vertical, 3.3 is DOWN and the horizontal, 1.2 is IN.  So, the answer is:  3.3 BD and 1.2 BI.

The way to check your answer is to do the resultant prism formula, chart or table, and see if you get the original amount of  OD 3.5 @290.

2.  Resolve:  OS 4.0 BD&I @ 25

1. V = P(sin a) = 4.0(sin 25) = (4.0)(0.4226) = 1.69 = 1.7
2. H = P(cos a) = 4.0(cos 25) = (4.0)(0.9063) = 3.63 = 3.6
3. OS BD&I is QIII which is. . . D & I.  So, 1.7BD and 3.6 BI
.

USING THE GRAPH:
If you understood how to do resultant prism with the graph, then this is just doing the opposite.  Suppose I ask you to resolve 2.2 @ 27  into the vertical and horizontal components.  First, you look ONLY at the bicycle spokes -- find the one that goes in the direction of the meridian given.

Once you find the spoke, determine where on or between the circles the amount of prism is.
Now, go straight down to the horizontal line and straight over to the vertical line, and see where you come out.

---

How about OS 3.2 @ 219 ?

1. Find the bicycle spoke that is at 219, then the 3 ring, and go almost 1/2 way to the 3.5 ring.

1. Draw straight up to the center line -- looks like 2.5 on that drawing.  Since this is an OS, that is IN.
2. Draw straight across to the center line -- looks like 2 on the drawing.  That is DOWN.

So, the answer is 2.5 BI and 2 BD.  Yes?

USING THE TABLE:
This is not practical.  It is very hard to find any particular prism/axis combination on the table.  So, although you can use this to check if your answer is reasonable, I do not recommend it as a method to find that answer.

STEPS FOR RESOLVING PRISM:

Practice:

1. OD 6.7 @ 077
2. OS 3.4 @ 153
3. OD 3.75 BD&I @ 127
4. OS 4.6 BD&I @ 029
5. OD 7.6 @ 212
6. OS 7.1 @ 293
7. OD 2.8 @ 100
8. OS 6.5 @ 004
9. OD 4.9 BU&I @ 045
10. OS 5.0 BD&I @ 053
11. OS 4.1 BD&O @ 166
12. OD 1.8 BU&O @ 124
13. OS 1.5 @ 090
14. OS 3.0 @ 180

The answers are here. Call or e-mail your instructor if you have questions.