8.5 Focimeter
The focimeter is an instrument for measuring the vertex power of a lens, axis direction of a
cylindrical lens, and any prismatic effect of spectacle lenses.
The focimeter’s optical principle is a linear equation which gives the front and back
vertex of the lens as a function of a target movement along the optical axis of the
system.
The focimeter consists two main parts—the focusing system and the
observation system. The focusing system is composed of an illuminated target which
can be moved relative to a standard collimating lens. A collimating lens is one which
renders light parallel. The lens being tested is placed in a special rack which lies at the
principal focus of the collimating lens.
The target is an opaque plate in which some pattern is drilled, the simplest
pattern probably being a circle of small holes.
In the absence of a spectacle lens at the lens rest, parallel rays will leave the standard lens
when the target is at the standard lens’ first focal point FS. If a plus spectacle lens is now
placed on the lens rest, with its optical center on the focimeter’s principle axis and with its
back vertex at FS, the target will need to be moved a distance x to the right of the first
focal point FS in order to produce parallel rays leaving the spectacle lens. Emergent
parallel rays are necessary at the telescope objective lens. The observer will see a focused
image in the second focal plane of the telescope objective lens.
By applying Newton’s equation to standard lens, we have, xx   f S  .
2
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Since x   fV , we have,
FV  FS2 x
(8.10)
Assuming that the spectacle lens is thin, the equivalent power of the combination of the
standard lens and the spectacle is,
FE  FS  FV  f S FS FV
 FS  FV  FV
(8.11)
 FS  const.
Since parallel rays leave the spectacle lens, the image of the target must be at the first focal
point of the combination of the standard and spectacle lenses. The angular size of the
image is therefore constant all spectacle lens powers,
tan   
h
fS
(8.12)
The image of target gives a
constant value for the angular
size  of the object presented to
the telescope.
If the lens cannot be considered as thin, then the image size will vary slightly with the
spectacle lens power.
The power scale is linear, being calibrated from equation (8.10), and is attached to and
moves with the target. The power scale is viewed through the eyepiece, along with the
target, the axis scale, and the prism tangent scale. The axis scale is a fixed protractor
marked in degree intervals between 0 and 180. A prism tangent scale is used not only to
determine any prismatic effect in a spectacle lens, but it can also be rotated to measure the
cylinder axis setting of an astigmatic spectacle lens.
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The power scale is fixed to and moves with the target.
The view in the eyepiece. The long
line on the prism scale, shown
intersecting the 30 mark on the axis
scale,
is
used
with
astigmatic
spectacle lenses to determine the
cylinder axis.
In the second focal plane of
the
objective
lens,
the
deviation P prism dioptres
produces a displacement ycm
on the tangent scale.
The image of the target is seen as a ring of dots when a spherical lens is tested. However,
in the case of an astigmatic lens the target must be focused separately for the two principal
meridians. The dots of the target are then seen as drawn out lines, the length of the lines
being proportional to the difference between the two principal powers, that is, the
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cylindrical power of the lens under test.
In the case of high minus spectacle lenses, the back vertex will not quite be located at the
second focal point of the standard lens, and this will introduce a slight error.
Position error of the back vertex with a
steeply curved minus lens back surface.
The back vertex focal length of the
plano/concave lens will be measured
from FS, instead of from A2, and will
consequently be measured too long.
Exercises:
8.1
The standard lens of a focimeter is +25.00D. Through what distance does the target
move when the dioptric scale is adjusted from +4.00D to +8.00D?
8.2
A focimeter has a standard lens of power +30.00D. Calculate the distance moved
by the target for each dioptre of back vertex power measured.
8.3
A clear image is formed in the telescope of a focimeter set for parallel light when
the target is 40mm from the standard lens. A lens is now positioned on the lens rest
and the target is moved 12mm away from the standard lens in order to refocus the
telescope image. Find the back vertex power of the lens under test.
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