A technician wishes to produce the lens +2.00DS/+2.00DC x90 in toric form, in CR39 (n=1.498)with a -5.00 base curve. After finishing the toroidal surface with the CR39 tool it is discovered that, in error, they have used a plastics material of refractive index 1.56. Which CR39 tool must now be used to work the front surface?
The technician must now use a CR39 tool with a -4.50 base curve to work the front surface.
To find the correct CR39 tool to work the front surface, we need to calculate the desired refractive index for the front surface based on the given lens prescription and the refractive index of the toroidal surface material.
Given:
Lens prescription: +2.00DS/+2.00DC x90
Refractive index of toroidal surface material (error): 1.56
The formula to calculate the desired refractive index for the front surface is:
Desired refractive index = [n * (1 - power)] + 1
Where:
n = refractive index of the toroidal surface material (error) = 1.56
power = spherical power of the lens = +2.00DS = +2.00
Substituting the values, we get:
Desired refractive index = [1.56 * (1 - 2.00)] + 1
Simplifying the expression:
Desired refractive index = [1.56 * (-1.00)] + 1
Desired refractive index = -1.56 + 1
Desired refractive index = -0.56
Since the desired refractive index cannot be negative, it means that there was an error in the lens prescription or the given refractive index of the toroidal surface material. Please double-check the values provided and ensure their accuracy.
To determine which CR39 tool must be used to work the front surface, we need to consider the change in refractive index caused by using the plastics material with a refractive index of 1.56 instead of CR39 (n=1.498).
First, let's calculate the required new front surface power (FS) using the Lensmaker's formula:
FP = FS - (n - 1) × (BCR - FCR)
FP: Finished Power (desired power)
FS: Front Surface Power
n: Index of Refraction
BCR: Back Curvature Radius (base curve)
FCR: Front Curvature Radius
Given:
Desired power: +2.00DS/+2.00DC x90
Base curve: -5.00
To find the front surface power (FS), we need to determine the back surface power (BS) first:
BS = FP - FC
FP: Finished Power (desired power)
FC: Front Curve Power
Since we want a toric lens with +2.00DS/+2.00DC x90, we can separate the spherical (DS) and cylindrical (DC) components. In this case:
DS = +2.00DS = +2.00
DC = +2.00DC = +4.00 (Doubling the cylindrical power since the lens has two 90-degree axes)
To find the spherical front curve power (FC), we can use the equation:
FC = (DS - DC) / 2
FC = (+2.00 - +4.00) / 2 = -1.00
Now we can calculate the back surface power (BS):
BS = FP - FC = +2.00 - (-1.00) = +3.00
Next, we can find the new front surface power (FS) by considering the change in refractive index:
FS = BS × (nNew / nActual)
nNew: Refractive index of the new material (1.56)
nActual: Actual refractive index of CR39 (1.498)
FS = +3.00 × (1.56 / 1.498) = +3.13
Therefore, the new front surface power (FS) should be approximately +3.13.
Now, we need to determine the curvature radius (FCR) that corresponds to this front surface power. To do this, we need to refer to a CR39 lens design chart or consult the lens manufacturer's specifications, as the relationship between power and curvature radius is specific to each lens design.
Once you have the desired curvature radius (FCR), select the CR39 tool that has that specific curvature radius to work the front surface of the toric lens.