Lens clock
Encyclopedia
A lens clock is a mechanical dial indicator
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 as an optical power
in diopters, assuming the lens is made of a material with a particular refractive index
.
The optical power
of the surface is given by
where
is the index of refraction of the glass, 
is the vertical distance (sagitta
) between the center and outer probes, and
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
.)
of the surface can be obtained from the optical power given by the lens clock using the formula
where
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 
, the true optical power of the surface can be obtained using
with an index of 1.7 is measured with a lens clock calibrated for crown glass with an index of 1.523. If the lens clock gives surface powers of −3.0 and −7.0 diopters (dpt), the optical power of the lens is obtained as follows:
First, the radii of curvature are obtained:
Next, the optical powers of each surface are obtained:
Finally, if the lens is thin the powers of each surface can be added to give the approximate optical power of the whole lens: −13.4 diopters. The actual power, as read by a vertometer
or lensometer, might differ by as much as 0.1 diopters. The optical power of the lens is not merely the sum of the surface powers given by the clock, −10 diopters, because the clock is calibrated for glass with a different index of refraction.
. Ideally, a contact lens dial thickness gauge would be used for this, but a lens clock can be used if a dial thickness gauge is not available. To do this, the contact lens is placed concave side up on a table or other hard surface. The lens clock is then brought down on it such that the center prong contacts the lens as close to its center as possible, and the outer prongs rest on the table. The thickness of the lens is then the sagitta
in the formula above, and can be calculated from the optical power reading, if the distance between the outer prongs is known.
Dial indicator
Dial indicators, also known as dial gauges and probe indicators, are instruments used to accurately measure small linear distances, and are frequently used in industrial and mechanical processes...
that is used to measure dioptric power of a lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
. It is a specialized version of a spherometer
Spherometer
A spherometer is an instrument for the precise measurement of the radius of a sphere. Originally, these instruments were primarily used by opticians to measure the curvature of the surface of a lens....
. A lens clock measures the curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
of a surface, but gives the result as an optical power
Optical power
Optical power is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. The dioptre is the most common unit of measurement of optical power...
in diopters, assuming the lens is made of a material with a particular refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
.
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 dial turns by an amount proportional to the distance.The optical power
of the surface is given bywhere
is the index of refraction of the glass, is the vertical distance (sagittaVersine
The versine or versed sine, versin, is a trigonometric function equal to and 2sin2. It appeared in some of the earliest trigonometric tables and was once widespread, but it is now little-used...
) between the center and outer probes, and
is the horizontal separation of the outer probes.A typical lens clock is calibrated to display the power of a crown glass
Crown glass (optics)
Crown glass is type of optical glass used in lenses and other optical components. It has relatively low refractive index and low dispersion...
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
Thin lens
[Image:Lens1.svg|thumb|A lens can be considered a thin lens if d [Image:Lens1.svg|thumb|A lens can be considered a thin lens if d [Image:Lens1.svg|thumb|A lens can be considered a thin lens if d...
.)
Radius of curvature
The radius of curvatureRadius of curvature (optics)
Radius of curvature has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located in either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis...
of the surface can be obtained from the optical power given by the lens clock using the formulawhere
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 , the true optical power of the surface can be obtained usingExample—correcting for refractive index
A biconcave lens made of flint glassFlint glass
Flint glass is optical glass that has relatively high refractive index and low Abbe number. Flint glasses are arbitrarily defined as having an Abbe number of 50 to 55 or less. The currently known flint glasses have refractive indices ranging between 1.45 and 2.00...
with an index of 1.7 is measured with a lens clock calibrated for crown glass with an index of 1.523. If the lens clock gives surface powers of −3.0 and −7.0 diopters (dpt), the optical power of the lens is obtained as follows:
First, the radii of curvature are obtained:
Next, the optical powers of each surface are obtained:
Finally, if the lens is thin the powers of each surface can be added to give the approximate optical power of the whole lens: −13.4 diopters. The actual power, as read by a vertometer
Vertometer
Vertometer was the trade name of an instrument made by Bausch & Lomb and later by Reichert.Lensometer was the trade name of the nearly similar instrument made by American Optical.Neither the Vertometer or the Lensometer is now being made....
or lensometer, might differ by as much as 0.1 diopters. The optical power of the lens is not merely the sum of the surface powers given by the clock, −10 diopters, because the clock is calibrated for glass with a different index of refraction.
Estimating thickness
A lens clock can also be used to estimate the thickness of thin objects, such as a hard or gas-permeable contact lensContact lens
A contact lens, or simply contact, is a lens placed on the eye. They are considered medical devices and can be worn to correct vision, for cosmetic or therapeutic reasons. In 2004, it was estimated that 125 million people use contact lenses worldwide, including 28 to 38 million in the United...
. Ideally, a contact lens dial thickness gauge would be used for this, but a lens clock can be used if a dial thickness gauge is not available. To do this, the contact lens is placed concave side up on a table or other hard surface. The lens clock is then brought down on it such that the center prong contacts the lens as close to its center as possible, and the outer prongs rest on the table. The thickness of the lens is then the sagitta
in the formula above, and can be calculated from the optical power reading, if the distance between the outer prongs is known.See also
- AstigmatismAstigmatismAn optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances...
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- Corrective lensCorrective lensA corrective lens is a lens worn in front of the eye, mainly used to treat myopia, hyperopia, astigmatism, and presbyopia. Glasses or "spectacles" are worn on the face a short distance in front of the eye. Contact lenses are worn directly on the surface of the eye...
- Galileo
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- OptometryOptometryOptometry is a health care profession concerned with eyes and related structures, as well as vision, visual systems, and vision information processing in humans. Optometrists, or Doctors of Optometry, are state licensed medical professionals trained to prescribe and fit lenses to improve vision,...
- Vertex (optics)
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