We can simplify the first part of the problem,
+7.00DCx135/+9.50DCx45:
Code:
+9.50 -2.50 x 135
(+) -3.50
------------------------
+6.00 -2.50 x 135
Now your question is what gets added to this prescription to result in +2.25DS/-3.75DCx135
Code:
+6.00 -2.50 x 135
(+) X
-----------------------
+2.25 -3.75 x 135
This is an algebraic equation:
Code:
+2.25 -3.75 x 135
(-) +6.00 -2.50 x 135
-----------------------
X
Luckily the axis are the same, so your task is easier, however if they weren't you could use Thompson's (yuk), a better way to add or in this case subtract two prescriptions is breaking them down into their MRE, C45, C180 components which all add and subtract simple then use, the trace and discriminant to compute the resulting spherocylinder I will post a link at the end to give you a better easier formula to remember assuming you are comfortable with matrix mathematics. For now, we march on and turnt he above into an addition so it's easier to comprehend:
Code:
+2.25 -3.75 x 135
(+) -6.00 +2.50 x 135
-----------------------
-3.75 -1.25 x 135
There is your answer: -3.75 -1.25 x 135
Here is your link with calculator and explanation:
https://makeoptics.com/harrychiling/...nder-summation
PS - to check your answer add the three powers (since they are thin lens) in the caculator and the result should be equal:
Code:
+9.50 -2.50 x 135
(+) -3.50
(+) -3.75 -1.25 x 135
---------------------
+2.25 -3.75 x 135
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