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# Lens clock

A lens clock is a mechanical dial caliper that is used to measure dioptric power of a lens. It is a specialized version of a spherometer. A lens clock measures the curvature of a surface, but gives the result in diopters, assuming the lens is made of a material with a particular refractive index.

How it works

The lens clock has three pointed probes that make contact with the surface of the lens. The outer two probes are fixed while the center one moves, retracting as the instrument is pressed down on the lens's surface. As the probe retracts, the hand on the face of the clock turns by an amount proportional to the distance.

The optical power $phi$ of the surface is given by :$phi = \left\{2 \left(n-1\right)s over \left(D/2\right)^2\right\},$where $n$ is the index of refraction of the glass, $s$ is the vertical distance ("sagitta") between the center and outer probes, and $D$ is the horizontal separation of the outer probes.

A typical lens clock is calibrated to display the power of a crown glass surface, with a refractive index of 1.523. If the lens is made of some other material, the reading must be adjusted to correct for the difference in refractive index.

Measuring both sides of the lens and adding the surface powers together gives the approximate optical power of the whole lens. (This approximation relies on the assumption that the lens is relatively thin.)

The radius of curvature $R$ of the surface can be obtained from the optical power given by the lens clock using the formula:$R=\left\{\left(n-1\right) over phi\right\},$where $n$ is the index of refraction "for which the lens clock is calibrated", regardless of the actual index of the lens being measured. If the lens is made of glass with some other index $n_2$, the true optical power of the surface can be obtained using:$phi=\left\{\left(n_2-1\right) over R\right\}.$

Examples

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.

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).

"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.

Estimating the thickness of a 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. [cite web |url=http://www.artoptical.com/contact/read/94 |title=Checking the center thickness of a GP with a lens clock |work=Art Optical |accessdate=27 October 2007]

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 twenty. This will approximate the thickness of the GP 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.

ee also

*Astigmatism
*Eyeglasses prescription
*Corrective lens
*Galileo
*Lensometer
*Optics
*Optometry
*Refractive error
*Vertex (optics)
*Vertometer
*Clock
*Gear ratio

References

Wikimedia Foundation. 2010.

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