# Optical Forums > Ophthalmic Optics >  Help with prisms!

## Whitwoo

Hi guys,

I'm going through a few questions in my book. For the following, I don't understand differential prisms or really anything in these questions. It doesn't seem to be anywhere in my books! Can anyone do them, so I can see the working, or can someone point me in the direction of formulas etc pleeease?
There are as follows:

5) A prescription reads:

RE 3.5 base up, 1.5 base out
LE 6.5 base down, 7.5 base out

I need to equally divide the prism between the 2 eyes.

6) Another prescription reads:

RE 5 base up
LE 9 base out

I need to equally divide the prism between the 2 eyes.

7) Calculate the total prism in each eye, and the differential prism, when the wearer of the following prescription looks at an object through points 12mm to the left (from the wearer's perspective) and 8mm up from the distance optical centres.

RE +6.75D
LE +1.50D

8) Calculate the total prism in each eye, and the differential prism, when the wearer of the following prescription looks at an object through points 10mm to the right (from the wearer's perspective) and 8mm up from the distance optical centres.

RE -2.25D
LE -5.50D

9) Calculate the total prism in each eye, and the differential prism, when the wearer of the following prescription looks at an object through points 6mm to the right (from the wearer's perspective) and 10mm up from the distance optical centres.

RE -3.50D
LE +2.50D

10) A prescription reads RE +5.00D, LE+5.00D. If the wearer os this prescription looks through a point 8mm above the optical centres, will she or he experience any differential prism? If so, how much? If not, why not?

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## HarryChiling

Questions 5 and 6 you can sum up the prism and then divide by 2




> 5) A prescription reads:
> 
> RE 3.5 base up, 1.5 base out
> LE 6.5 base down, 7.5 base out
> 
> I need to equally divide the prism between the 2 eyes.


3.5 up and 6.5 down = 10 total difference
1.5 out and 7.5 out = 9 total difference

So:

RE 5.0 up 4.5 out
LE 5.0 up 4.5 out




> 7) Calculate the total prism in each eye, and the differential prism, when the wearer of the following prescription looks at an object through points 12mm to the left (from the wearer's perspective) and 8mm up from the distance optical centres.
> 
> RE +6.75D
> LE +1.50D


well it's 12 to the left and 8 up so:

RE = +6.75 * 12 / 10 = 8.1 out
RE = +6.75 * 8 / 10 = 5.4 down

RE 8.1 out 5.4 down

LE = +1.50 * 12 / 10 = 1.8 in
LE = +1.50 * 8 / 10 = 1.2 down

LE 1.8 in 1.2 down

The trick here is that the prism in reference to the side of the eye is going to chage your bases orientation on the horzontal but on the vertical 90 is up and 270 is down no matter how you slice it.

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## Memoir

> 10) A prescription reads RE +5.00D, LE+5.00D. If the wearer os this prescription looks through a point 8mm above the optical centres, will she or he experience any differential prism? If so, how much? If not, why not?


The wearer will not experience any differential prism as his/her eyes are in balance.

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## Memoir

> 9) Calculate the total prism in each eye, and the differential prism, when the wearer of the following prescription looks at an object through points 6mm to the right (from the wearer's perspective) and 10mm up from the distance optical centres.
> 
> RE -3.50D
> LE +2.50D


Begin by working out the vertical (v) and horizontal (h) components of prism in each eye, presenting them side by side helps (however the nature of this post i have to just do one eye after another. I've also attached a drawing from your parameters which aids in working out the base direction in your workings, have a look!

The triangles I've drawn on, represents the prism of a plus and minus lens (R minus, L plus respectively) relative to the vertical and horizontal. The base is the *bold* lines. And thus you can work out its direction away from the oc from your point (in your case, 6mm to the right and 10mm up). 

To calculate prism, use Prentice Rule P = cF where, c = distance away from optical centre IN CENTIMETRES (ie, 10mm = 1cm), F is power of lens in Dioptres.

RE 
Pv = cF 
= 1 x 3.5
*Pv = 3.5Δ Base UP* 

Ph = cF 
= 0.6 x 3.5
*Ph = 2.1Δ Base OUT* 


LE
Pv = cF 
= 1 x 2.5
*Pv = 2.5Δ Base DOWN*


Ph = cF 
= 0.6 x 2.5
*Ph = 1.5Δ Base OUT* 


Then calculate the differential prism effect, by compounding them together. You should have info in your texts for 'how to'.. but if you're stuck, 
up and down = add together (ie 1 up R 3 down L = 1+3 = 4)
out and out = add together (ie 1 out R and 3 out L = 1+3 = 4)
in and in = add together (ie 1 in R and 3 in L = 1+3 = 4)
in and out = subtract (ie 1 in R and 3 out L = 3-1 = 2 Base Out L)

In this question, you still have to associate the Base Up direction to an eye, it is safe to pick the eye with the most prism component when labelling the Vertical DPE (in this case, the R eye had 3.5, so more than L eye which had 2.5 prism dioptres). 

You do not need to specify an eye when giving Horizontal DPE. 

V DPE = RE Pv + LE Pv
= 3.5 + 2.5
*V DPE = 6Δ Base UP RE*

H DPE = RE Ph + LE Ph
= 2.1 + 1.5
*H DPE = 3.6Δ Base OUT*

The answers are in bold, however be sure to provide your workings with your assignments.

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## EyeFitWell

> So:
> 
> RE 5.0 up 4.5 out
> LE 5.0 up 4.5 out


 This is a once in a lifetime opportunity to correct Harry Chiling!  I believe the left eye would be 5.0 down b/c up and down are the compounding directions for vert. prism.
Whew, that was fun! ;)
:cheers::cheers:

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## Rafael

You right the left eye will be base down

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## HarryChiling

> This is a once in a lifetime opportunity to correct Harry Chiling! I believe the left eye would be 5.0 down b/c up and down are the compounding directions for vert. prism.
> Whew, that was fun! ;)
> :cheers::cheers:


I'd give you a positive for that but it says I got to spread some around, that was a typo nice catch.

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## EyeFitWell

I figured it was an oversight/typo rather than a lack of knowledge.  :::bows to your optigenius:::

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