American Board of Opticianry (ABO) Practice Test

A lens with a front curve of +6.50 requires what back curve to yield a corrective power of -1.00?

1. -7.50

2. -6.50

3. -2.00

4. -1.00

The correct answer is: -7.50

To determine the back curve of a lens required to achieve a specific power when given a front curve, one must apply the lensmaker's equation, which relates the front curvature, back curvature, and overall lens power. The power of a lens (P) is calculated by the formula: P = F1 + F2 Where F1 is the front surface power and F2 is the back surface power. The power of a lens is measured in diopters, and curvature is expressed as the reciprocal of the focal length in meters. In this scenario, the front curve has a power of +6.50 diopters. Since we need the total power of the lens to be -1.00 diopters, we can rearrange the lensmaker's equation: F2 = P - F1 Substituting the known values, we have: F2 = -1.00 - (+6.50) F2 = -1.00 - 6.50 F2 = -7.50 This calculation shows that to achieve an overall corrective power of -1.00 diopters with a front curvature of +6.50, the back curvature must indeed be -7.50 diopters. This relationship is critical