Help with Toric lens questions!

[Hannah Doidge]

Hi, I am a trainee Optometrist and I've only just started. This question keeps coming up in our practice questions and I don't know how to begin. Any pointers would be great. Sorry if it's a stupid question but I'd really appreciate help, our covering lecturer doesn't speak much English.

Two thin toric lenses are placed in contact with each other. What is the resultant sph-cyl prescription resulting from the two lenses in contact given that the first thin toric lens is made to the specification:
+5.50DC ×10 / +8.50DC ×100 −4.00
and the second thin toric lens is made to the specification:
+6.00____________________
−3.50DC ×115 / −5.50DC × 25
Express your answer in negative sph-cyl form

[MakeOptics]

Hi, I am a trainee Optometrist and I've only just started. This question keeps coming up in our practice questions and I don't know how to begin. Any pointers would be great. Sorry if it's a stupid question but I'd really appreciate help, our covering lecturer doesn't speak much English.

Two thin toric lenses are placed in contact with each other. What is the resultant sph-cyl prescription resulting from the two lenses in contact given that the first thin toric lens is made to the specification:
+5.50DC ×10 / +8.50DC ×100 −4.00
and the second thin toric lens is made to the specification:
+6.00____________________
−3.50DC ×115 / −5.50DC × 25
Express your answer in negative sph-cyl form

That -4.00 is not a standard notation, care to offer any clues? I could assume it's the back surface?

If that assumption is correct then your answer is:

6.92DS -4.84DC x 106°

Use this calculator http://makeoptics.com/harrychiling/b...nder-summation

[lensgrinder]

Hi, I am a trainee Optometrist and I've only just started. This question keeps coming up in our practice questions and I don't know how to begin. Any pointers would be great. Sorry if it's a stupid question but I'd really appreciate help, our covering lecturer doesn't speak much English.Two thin toric lenses are placed in contact with each other. What is the resultant sph-cyl prescription resulting from the two lenses in contact given that the first thin toric lens is made to the specification: +5.50DC ×10 / +8.50DC ×100 −4.00 and the second thin toric lens is made to the specification: +6.00____________________−3.50DC ×115 / −5.50DC × 25 Express your answer in negative sph-cyl form

It is a crossed cylinder question, but you need to first find the Rx. Your first Rx is a true plus cylinder cut on the front surface with a -4.00 sphere on the back. Add each surface:

+5.50 +(-4.00) = +1.50
+8.50 + (-4.00) = +4.50

The second one is a typical surface(i.e. plus on front ground wth minus cylinder)

+6.00 + (-3.50) = +2.50
+6.00 + (-5.50) = +0.50

Now we will put them both in the same format(plus or minus cylinder form)

The first Rx is +4.50 -3.00 X 10
The second Rx is +2.50 -2.00 X 25

We are only going to work with the cylinders first

A = -3.00
B = -2.00
Take the difference between the cylinder axes
= 15



Now find the angle that the axis of the resultant cylinder makes with the axis of A



Now we will find our sphere component



Add -4.92 to the sum of all the spheres

[latex]+4.50 + 2.50 + (-4.92) = 2.08[\latex]

Add to axis a.
5.96 + 10 = 15.96 or 16

Your Rx is +6.92 - 4.84 X 16

[lensgrinder]

That -4.00 is not a standard notation, care to offer any clues? I could assume it's the back surface?

If that assumption is correct then your answer is:

6.92DS -4.84DC x 106°

Use this calculator http://makeoptics.com/harrychiling/b...nder-summation

I assumed it was a front surface true cylinder form. Not really sure.

[HarryChiling]

I'm with you, interesting we used two different methods and ended up with two different axis. I will assume I am wrong on the axis.

[lensgrinder]

I'm with you, interesting we used two different methods and ended up with two different axis. I will assume I am wrong on the axis.

Assume nothing, my friend.

My reasoning was:

• Sphere = Base Curve + Sphere Curve
• Cylinder = Cross Curve - Base Curve
• Axis = Axis of cross curve

First:

+5.50 BC
+8.50 CC
-4.00 sphere curve

Second

-3.50 BC
-5.50 CC
+6.00 sphere curve(we call it the base curve as well, but for ease of confusion)


First Power
Sphere = 5.50+(-4.00) = +1.50
Cylinder = 8.50 - 3.50 = +3.00
Axis = 100

Minus Cylinder +4.50 - 3.00 X 10

Second Power
Sphere = -3.50 + 6.00 = +2.50
Cylinder = -5.50 - (-3.50) = -2.00
Axis = 25

+2.50 -2.00 X 25

[Hannah Doidge]

Yeah, the -4.00 was meant to be on the bottom. Thank you so much, I'm going to try your steps right now on my others ��

[HarryChiling]

Assume nothing, my friend.

My reasoning was:

• Sphere = Base Curve + Sphere Curve
• Cylinder = Cross Curve - Base Curve
• Axis = Axis of cross curve

First:

+5.50 BC
+8.50 CC
-4.00 sphere curve

Second

-3.50 BC
-5.50 CC
+6.00 sphere curve(we call it the base curve as well, but for ease of confusion)


First Power
Sphere = 5.50+(-4.00) = +1.50
Cylinder = 8.50 - 3.50 = +3.00
Axis = 100

Minus Cylinder +4.50 - 3.00 X 10

Second Power
Sphere = -3.50 + 6.00 = +2.50
Cylinder = -5.50 - (-3.50) = -2.00
Axis = 25

+2.50 -2.00 X 25

I knew I could count on you, my assumption is correct (I WAS WRONG) :-). I looked at the problem this morning and I didn't cross the axis in the crossed cylinder notation. It's been a few nights no sleep and redbull. Thanks for throwing up your example. I knew from the axis my conversion step was off. I like that you converted to lenses and powers before adding. I took a different approach, converting to cyl@045 cyl@180 and MRE for each surface and then adding them all together and converting back. Astigmatic Decomposition, I have been found of this method lately since I can add hundreds of lenses together simply and programming it reduces to a few lines of code.

Decomposition
MRE = Sph + Cyl/2
C045 = Cyl * sin(2*axis)
C180 = Cyl * cos(2*axis)

Back to Sphero-Cyl land
Cyl = Sqrt(C045^2 + C180^2)
Sph = MRE - Cyl/2
Axis = Arctan(C045/C180)/2

It's a bit easier to memorize for me since all the formulas are simple and compact and make sense when looking at them, it's literally the same as thompsons just breaking it down into modularized steps. Brent, I can't wait to show you our project. It's coming along and I'd love your opinion from an educator/professional perspective.

An interesting note as well since they are thin lenses, the surfaces can be in any order and the result is the same.

[Hannah Doidge]

Hi, I get everything apart from the final sphere value. How did you get from 2.08 to +6.92? Many thanks

[Hannah Doidge]

Ah, do you just add D and C together?

[lensgrinder]

I knew I could count on you, my assumption is correct (I WAS WRONG) :-). I looked at the problem this morning and I didn't cross the axis in the crossed cylinder notation. It's been a few nights no sleep and redbull. Thanks for throwing up your example. I knew from the axis my conversion step was off. I like that you converted to lenses and powers before adding. I took a different approach, converting to cyl@045 cyl@180 and MRE for each surface and then adding them all together and converting back. Astigmatic Decomposition, I have been found of this method lately since I can add hundreds of lenses together simply and programming it reduces to a few lines of code.

Decomposition
MRE = Sph + Cyl/2
C045 = Cyl * sin(2*axis)
C180 = Cyl * cos(2*axis)

Back to Sphero-Cyl land
Cyl = Sqrt(C045^2 + C180^2)
Sph = MRE - Cyl/2
Axis = Arctan(C045/C180)/2

It's a bit easier to memorize for me since all the formulas are simple and compact and make sense when looking at them, it's literally the same as thompsons just breaking it down into modularized steps. Brent, I can't wait to show you our project. It's coming along and I'd love your opinion from an educator/professional perspective.

An interesting note as well since they are thin lenses, the surfaces can be in any order and the result is the same.

Interesting method Harry, I am going to look at when I have more time. Thanks.

I am looking forward to seeing the project. I will swing by in NY and take a look.

Ah, do you just add D and C together?

Sorry I was not clear, I have a tendency to skip steps in my head.

To find the sphere components, since I transported to minus cylinder(i.e. C = -4.84), you would



Now take the sum of all spheres

4.50+2.50+(-0.08)=+6.92