Lens clock

A lens clock is a mechanical dial caliper measuring dioptric power of a lens curvature. It is a specialized version of a spherometer.

A lens clock is used to read from a scale calibrated in diopter strength. The mechanical caliper is placed upon the surface of a lens of known refractive index. See the mathematical equations below for a further description.

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Measuring diopter power from lens curvature

A dispensing optician works with various tools to measure the power of a lens. Suppose you have a lens clock caliper instrument in your optical dispensing kit that takes measurements of surface power for the front and back of spectacle lenses. The usual lens clock is calibrated to measure the power of a curvature of Royal Crown glass with a refractive index of 1.523 and for comparison, the refractive index of air is 1, by convention.

Example

Estimating lens power of lens with high refractive index

If a lens is prescribed with a higher refractive index to reduce the edge thickness, then you can still use the lens clock diopter power reading, and estimate the lens power using a mathematic surface power equation to convert the calibrated powers to the higher index powers. In this example, the lens measured is made of high index flint glass (a known 1.7 index), and the lens clock is calibrated for Royal Crown glass (a known 1.523 index).

The following example from the diagram is for clarification only, to demonstrate the math formula, and variables. The opposite sides of the biconcave lens read measurements of -3.0, and -7.0 diopters sphere from the lens clock caliper. Remember the caliper is calibrated for another index. But, we have measurements from the caliper that are still useful.

Calibrated 1st side radius length

surface power = (glass index - 1)/(radius of curvature)

SP = (n - 1)/r

the lens clock uses a known index of 1.523

-3.0 = (1.523 - 1)/r

solving for r using 0.523/f where f = -1/3.0 (reciprocal of surface power)

r = -0.1743

Let us set this number aside for a moment...

This number represents a vertex distance in meters of the radius of curvature. This approximates a distance of about 17.4 centimeters. It equals the distance from the center to the circumference of a circle of this radius.

Remember the dial read -3.0 for the first side, but is calibrated for an index of Royal Crown Glass (1.523).

Calibrated 2nd side radius length

our surface power equation, the same as above

SP = (n - 1)/r

taking the -7.0 measured from the lens clock on the 2nd curvature

-7.0 = (1.523 - 1)/r

solve for r using -7.0 from 2nd side measurement

r = -0.0747 Let us also set this number aside for a moment...

A thin lens diopter power can now be estimated using the high refractive index of the specially ordered flint glass lens having a refractive index of 1.7 (relative to air = 1).

Estimated total lens power in diopters

P = (n - 1)[(1/r) + (1/ŕ)] (by convention side 1 uses r, and side 2 uses ŕ

Plug in the variables we set aside above, and you get

P = (1.7 - 1) x [(1/-.1743) + (1/-0.0747)] solve for P

Remember the lens was biconcave, so both r and ŕ are negative numbers as you see in the equation above.

= -0.7[5.737 + 13.387]

solve for P; the combined biconcave curvature power in diopters

P = -13.4 diopters sphere

This is within 0.1 diopter of the power actually read off a vertometer (lensometer). So, consider certain tolerances using the thin lens equations while doing bench work for your patients.

Concluding comment

This example shows that curvature power -3.0 and -7.0 don't necessarily give a -10.0 power lens. The estimated lens power in this example was -13.4, even though the lens clock caliper read -3.0 and -7.0 diopters. The difference is in the higher refractive index of flint glass (1.7), and the conventional calibration using index of Royal Crown glass (1.523) for the lens clock caliper. An understanding of these principles help develop geometrical optics for use in many applications.

Using a lens clock to estimate the approximate thickness of a GP (gas permeable) contact lens

Hard and gas permeable (GP) contact lens thicknesses are best measured with a contact lens dial thickness gauge. However, since most ophthalmic practices do not have this tool, but they do have a lens clock, the lens clock can be used to measure the approximate thickness of the contact lens.

This is how to perform this measurement with a lens clock, as described on the Art Optical web site: Place the contact lens, concave side up, on a clean, flat, hard surface, such as a desk or countertop. Place the center prong of the lens clock in the absolute center of the contact lens, this will leave the other two prongs on the flat surface on the outside of the contact lens. Take the reading off the dial of the lens clock and divide by two. This will approximate the thickness of the RGP contact lens.

Example: Lens clock reads +2.50 diopters, divide by 2 = 1.25, move the decimal point one place to the left = .125, this will equal the approximate center thickness of the contact lens in millimeters.

See also

• Astigmatism
• Eyeglasses prescription
• Corrective lens
• Diopter
• Galileo
• Lensometer
• Optical power
• Optics
• Optometry
• Refractive error
• Vertex
• Vertometer

Suggested reading of other articles

internal workings of clock gears
mathematical models of gear ratio

References

Geometrical Optics, UHCO, R. Weldon Smith
Corning Museum of Glass
Art Optical [1]