## Sunday, May 21, 2006

### Lens Effectivity

Lens effectivity is the change in vergence of light that occurs at different points along its path. This is related to vertex distance.

Formula: Fnew = Fcurrent/(1-dFcurrent) where F is in Diopters and d is in meters.

When providing a “distance correction”, the principle focal point F2 of the correcting lens must coincide with the far point of the eye. The lens power depends on its location in front of the eye. The closer to the eye the lens is mounted, the shorter is its focal length in the case of hyperopia, and the longer its focal length in the case of myopia. Because of this, plus power has to be added in both cases. Therefore, myopes need less minus and hyperopes need more plus when going from spectacles to contact lenses.

For spectacles, pushing a minus lens closer to the eyes increases the effective power of the lens (more -). Moving a plus lens away from the eyes increases the effective power of the lens (more +).

Question: A +12.00 diopter lens mounted 12mm in front of the cornea would require what contact lens power?

Answer: Fnew = Fcurrent/(1-dFcurrent) = +12.00/(1-0.012(+12.00)) = +14.02D

Question: For a myopic eye that can be corrected with a –12.00 diopter lens mounted 12 mm in front of the cornea would require what contact lens power?

Answer: Fnew = Fcurrent/(1-dFcurrent) = -12.00/(1-0.012(-12.00) = -10.49D

Question: An object is placed 0.3m in front of a +5.00D lens. (Figure 11) What lens power could be used 0.2m from the image to achieve the same effectivity?

Click on image to enlarge.

Answer: First, we need to know where the image will be focused.

Using the equation U + D = V where

u = object distance = -30cm

U = object vergence = 100/u = 100/-30cm = -3.33D

D = lens power = +5.00D

V = image vergence = U + D = -3.33D + (+5.00D) = +1.66D

v = image distance = 100/V = 100/+1.66D = 60cm to the right of the lens. Therefore the image is 30cm + 60cm = 90cm from the object and the new lens will be 90cm – 20cm = 70cm from the object.

For the new lens, use the equation U + D = V where

u = -70cm

U = object vergence = 100/-70 = -1.43D

v = image distance = +20cm

V = image vergence = 100/+20cm = +5.00D

D = new lens power = V – U = +5.00D – (-1.43D) = + 6.43D (the lens power needed to achieve the same effectivity).