In my
opinion the problem of the dimension of the figures in a sundial is analogous to
that the optometrists and opticians meet when they measure our visual
acuity.
I
think therefore that the dimensions of the strokes that form the figures or the
letters must have the same characteristics that the ophthalmologists have fixed in a practice of a lot
of years.
Please read the Note below
.
For
this reason I think that, supposing that the observer has a normal visual
acuity, the dimension of the figures must be such as to be seen under an angle at least of 5',
with elements (strokes) at least 1/5th of this quantity.
Since
in a radian there are 3438', the dimension of the figures and letters should be greater of 1/687th
of the distance to which we want
see them.
Rounding off and slightly increasing we may take 1/600th or, to help a lithe the short-sighted persons,
1/500th 1/400th.
So we
obtain Hmm = 1.454*Lmt or
Hmm = 2*Lmt or Hmm = 2.5*Lmt
Where
H is the height of the letters in mm and L the distance in
meters.
Best
Gianni Ferrari
NOTE
Visual acuity is the spatial resolving capacity of the
eye, that is the ability of the eye to see fine detail. It is limited by
diffraction, aberrations, photoreceptor density in the eye , illumination,
contrast.
There are
various categories of acuity but the most important for us is the target
recognition which is most commonly used in clinical visual acuity
measurements and require the recognition or naming of a target, such as with
Snellen letters (optotypes)
Test
objects used here are large enough that detection is not a limiting factor but careful letter choice and chart
design are required to ensure that letter recognition tasks are uniform for
different letter sizes and chart working distances
Snellen letters are constructed so that the size of the
critical detail (for ex. stroke width and gap width in letters F, E, H) subtends
1/5th of the overall height.
To
specify a person's visual acuity in terms of Snellen notation, a determination
is made of the smallest line of letters of the chart that he/she can correctly
identify.
Visual acuity (VA) in Snellen notation is given by the
relation: VA = D/D where D' is the
standard viewing distance (usually 20 foot or 6 metres) and D is the
distance at which each letter of this line subtends 5 minutes of arc (each
stroke of the letter subtending 1 minute).
Therefore, a person is said to have 6/12 vision if at
viewing distance of 6
metres they can just correctly identify an object (eg.
line of Snellen letters) whose critical detail (stroke width) would subtend 1
minute at a distance of 12
metres
In the most familiar acuity test, a Snellen chart is
placed at a standard distance, twenty feet or 6 meters .
At this
distance, the symbols on the line representing "normal" acuity subtend an angle
of five minutes of arc, and the thickness of the lines and of the spaces between
the lines subtends one minute of arc.
This line, designated 20/20, is the smallest line that a
person with normal acuity can read at a distance of twenty feet.
Three lines above, the letters have twice the dimensions
of those on the 20/20 line.
The chart is
at a distance of twenty feet, but a person with normal acuity could be expected
to read these letters at a distance of forty feet. This line is designated by
the ratio 20/40.
If this is the smallest line a person can read, the
person's acuity is "20/40," meaning that this person needs to approach to a
distance of twenty feet to read letters that a person with normal acuity could
read at forty feet. In an even rougher way, this person could be said to have
"half" the normal acuity.
See also
http://www.mdsupport.org/snellen.html
