17,18,19 - Lens Power

Question 1

Components and optical principal of vertometer

Answer 1

• Light
• Target (mire)
• Standard lens
• Test lens
• Objective
• Graticule (for focus)
• Eyepiece (keplerian telescope)

In focus when light exits as parallel. This happens when target is located at point where standard lens creates the image at the test lens’ focal point.

Question 2

Describe the vertometer equation

Answer 2

F’T = xF’A^2

F’T = Testing lens power
x = distance
F’A^2 = Power of standard lens
Note: Distance and power of testing lens is linearly related.

Question 3

Factors affecting vertometer accuracy

Answer 3

• Depth of focus
• Rx
• Accommodation

Telescopes amplify vergence so 0.1D difference gives 5D difference at eye.

Question 4

What’s curvature, sag, and surface power?

Answer 4

Curvature = 1/r
Sag = Distance between a point on a circle and the midpoint of the chord (essentially the thickness of a lens)
Surface power = Depends on curvature and refractive indices.

Question 5

How to measure approximate power using a lens clock?
Problem in clinical setting?

Answer 5

Measure surface of front and back to find power of surfaces and add them.

Best for minus lenses (small centre thickness), but not clinically accurate enough.

Question 6

What’s equivalent power?
Problem in clinical setting?

Answer 6

Use thick lens equation to find an equivalent thin lens.

Can’t find principal planes easily and can be outside physical lens.

Question 7

Describe the equation for effective power

Answer 7

FB = FA/(1 - d * FA)
FB = Power required at new distance (D)
FA = Original power (D)
d = change in vertex distance (m)

Question 8

Describe notational power and it’s equation

Answer 8

Falpha = Fc * sin^2(α)
Fc = power of the curvature
alpha = angle from cyl axis
Falpha = Notational power at that angle.

Question 9

Describe adding sine^2 curves together method

Answer 9

• Plot sum of sin^2 curves on graph
• Height between peaks and troughs is cyl power
• Trough is sphere power

Question 10

Describe Stoke’s diagram method

Answer 10

• Convert both cyls to same sign (+ve or –ve)
• Assign F1 and F2 w/ angle (γ) in between
• Plot F1 along X
• Plot F2 at 2γ counterclockwise (proportional length)
• Complete parallelogram
• Draw C diagonal
• Length of C = cyl power, angle between C and F1 = 2θ where θ = resultant axis
• SR = (F1 + F2 - C)/2 for sphere resultant
• Sum initial sphere powers and SR for final sphere

Question 11

Describe Stoke’s mathematical model

Answer 11

tan2θ = (F2* sin2γ)/(F1 + F2 * cos2γ)
θ = angle between F1 and cyl
γ = angle between F1 and F2

C = (F2 * sin2γ)/sin2θ
C = cyl power

SR = (F1 + F2 - C)/2 for sphere resultant

Question 12

Describe astigmatic decomposition

Answer 12

It converts sphero-cyl notation into 3 components
- Mean sphere | M = S + C/2
- JCC at 180 and 90 | J0 = -(C/2)cos2α
- JCC at 45 and 135 | J45 = -(C/2)sin2α
Can be added or subtracted to other components from other cyl lenses
Can then be converted back into –ve cyl notation.
- Sphere | S = M + sqrt(J0^2 + J45^2)
- Cyl power | -2 * sqrt(J0^2 + J45^2)
- Cyl axis | α = 0.5tan^-1(J45/J0)
Note: Axis might be 90 degrees off, make sure to check.