A technician wishes to produce the lens +2.00DS/+2.00DC x90 in toric form, in CR39 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?
To determine the CR39 tool that needs to be used to work the front surface of the toric lens, we need to calculate the required base curve.
First, let's understand the concept of the base curve. The base curve refers to the front surface curve of a lens, specifically the curvature measured in diopters (D). The base curve determines the overall shape of the lens and how light is refracted when it passes through the lens.
In this case, the technician wants to produce a toric lens with a power of +2.00DS and a cylindrical power of +2.00DC x90. The back surface of the lens has already been finished with a -5.00 base curve using a CR39 tool.
Now, let's calculate the required front surface base curve using the lens powers and the given refractive index of 1.56 for the plastics material (in this case, CR39).
The formula to calculate the lens power is:
Lens Power (P) = (n2 - n1) / R
Where:
- P is the lens power in diopters (D)
- n1 is the refractive index of air (approximately 1.00)
- n2 is the refractive index of the lens material (1.56 in this case)
- R is the radius of curvature of the lens surface
To calculate the required front surface base curve, we need to find the radius of curvature for the front surface.
For the toric lens, the front surface will have a spherical curve along the x-axis (along the power meridian) and a toroidal curve along the y-axis (along the cylindrical meridian).
Since the lens power is +2.00DS/+2.00DC x90, the spherical power is +2.00DS and the cylindrical power along the y-axis (toroidal curve) is +2.00DC.
For the spherical curve, we can use the formula:
Lens Power (P) = (n2 - n1) / R
Substituting the values:
2.00 = (1.56 - 1.00) / R
Simplifying the equation:
2.00R = 1.56 - 1.00
2.00R = 0.56
R = 0.56 / 2.00
R = 0.28
So, the radius of curvature for the spherical curve on the front surface is approximately 0.28.
Now, let's calculate the required base curve for the toroidal (cylindrical) curve along the y-axis.
The formula to calculate the base curve for the toroidal curve is:
Base Curve (BC) = power x (1/n)
Where:
- BC is the base curve in diopters (D)
- power is the cylindrical power along the y-axis for the lens (+2.00DC)
- n is the refractive index of the lens material (1.56 in this case)
Substituting the values:
BC = 2.00 x (1/1.56)
BC ≈ 1.2821
So, the required base curve for the toroidal curve of the lens along the y-axis is approximately 1.2821.
Therefore, to work the front surface of the toric lens denoted by +2.00DS/+2.00DC x90 using a plastics material with a refractive index of 1.56, a CR39 tool with a base curve of approximately -1.2821D should be used.