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OPTIX Camera - Pt. 2 User manual
User manual for OPTIX Camera - Pt. 2. 57 pages in English. Read the original PDF, download or print a copy without registration.
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- Optix
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- OPTIX Camera - Pt. 2
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- User manual
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- English
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- 57
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such a way that a clear image iE obtained. For the
image of a very digtant object, the dietance of the
image is pra-ctically.equal to the, focal dietance of.
The luminous rays of dietant objectr-t:i"'- the camera lene. are esEentially parallel when they leave the objective
lena. Therefore, they merge at the focal point of
that lenE ( aleo see chapter 105) . In this type of ttinfinite adjuetmentrr of the case, we epeak of the
objective. We coneider objecte, separated from the
camera lens by a dietance of at leaet one thoueand
timee the focal distance of that lens, to be an infin'
ite dietance away. We muet still regulate the ad-
justment component ( even if only slightly) , when
we have focueed the objective onto an object 100
meters away.
The image size of objects, at an infinite distance
f rom the lens' can be calculated by the formula pre-
viously learned. However, we replace the image
distance by the focal distance in this formula. Ae
an example let us calculate the diameter of the aerial
image of the moon by using a lens with a focal dis-
tance of 131 millimeters ( the average distance to the
moon is 384r 400 kilometers, and the diameter of the
moon is 3,476 kilometers) . Tbe diameter of the.
aerial irnage of the moon will then be given by the
following calculation:
3 476 000 000 rn x 131 Size of the image. = l. 18 rnm. 384,400,000,000 rnrn
No. 76. LOOKING AT A NEARBY OBJECT
The upper part of the diagram on the left shows
parallel lurninous rays hitting a converging lens
front on. You already know that these lurninous rays
merge at a focal point, which is separated from the
lens by a distance called I the focal distancer.
The angle at which these rays are deviated ( or de-
flected) by this lens is not greatly changed, if these
rays fall slightly obliquely at the same point on the
lens. This explains why rays reaching the lens as
a dispersing cluster, only rnerge behind the focal
point. The lower part of the diagram shows the pheno-
menon of a cluster of rays leaving point A, and which
only concentrates again at the point C after the devia-
tion by the lens.
The srnaller the distance of the object g, the greater
the distance b becornes. This rule holds true when
the distance of the irnage becomes greater than the
focal distance, but srnaUer than twice the focal dis-
tance; and when the object is less than an infinite
distance away, but greater than twice the focal dis-
tanc e.
The distance of the irnage can be calculated precisely
with the following formula:
Distance of irnage:- 4istancedGtatr-ce o{of lhethe oFiec!object x- {oca}focal 4islgncedistance
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According to this formula, for an object that iE at a
dietance of.2,75L meters ( or Z, T5I mm. ) , the distance of the image is 13?.55 mm. if the focal dietance of tho objective lene ie 131 mm.
You now understand (if a clear image of cloee objecte
is deeired) , why the objective musisufficiently p"o- trude.
I
No. 7?. THE OBJECTM AS A TELEMETER
If you direct the.objective at an object (and adjust the
resulting aerial image with precision) , it is possible
for you to calculate the distance from the obiective
t_9 the object (therefore, the d.istance of the object) .
This is possible as long as you know the objectiver's
focal distance, as well as the digtance between the
objective and the aerial irnage ( therefore, the dis-
tan-ce of the image which we have just adjusted) . The following formula is to be used:
Distance of object - Distance of imase x focal distance
Distance of irnage - focal distance.
It is preferable to place a graduated scale in meters
on the objective right away.
This is why you have been provided with a printed
scale e on the cut-out sheet. Stick it onto ihe edee of the universal adjusting component.
I It would be a good idea, first of all, to turn the ob- jective in the universal adjusting component so that
the scaler s lines are to the right and lo the left, for I
the initial and final positions. Having cornpleted this,
focus the lens on an object as far away as possible.
Then, place the scale so that you can read the line above the mark rinfinitel . The other nurnbers 10, 5
www.butkus.us and 3 are meter readings, and you can draw in their exact reference lines.
In order to facilitate the preparation of your tele-
rneter attach it to the back of a chair ( use support #42, as described at the end of chapter 103) . ptace ttre
chair a fair distance frorn a newspaper suspend.ed.
frorn a door. The distances 10, S a.ra 3 rneiers are
useful, in this case, to adjust the distance frorn the
newspaper to the front of the achromatic lens. The
iSage -can be adjusted rrrore precisely if you look through a magnifying glass ( see chapter g5) , holding large obturator I in front of the objective fens ( part' #55 with a 12 rnm. opening)
I No. 78. A LENS WITH VARIABLE FOCAL DISTANCEI
l No lensr maker has ever been able to construct one of these. Stil1, each hurnan being has two such lenses- one in each eye.
To the left of the opposite diagram you see how parallel
luminous r?ISr deviated by the lens of the eye, rneet
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at a certain point behind the eYe.
To the right, you see an eye in which the lens is
thicker and its surface bulge rnore accentuated, than
the one on the left. This is because its focal distance
is so short that rays frorn point A rneet behind the eye
at a precise point, If the lens shown on the right re-
mained as flat as the one in the eye shown on the left,
then the rays could meet behind the eye only if they
were parallel to one another.
The following diagram on the left shows you the ocular
lens L on a larger scale, in its flat resting stage
( to the left) , and in its tense or active state ( to the
right) .
Notice the rnuscles M, which , because of certain
nerves, can produce a tension on the edge of the lene.
This causes an alteration in the lens, shortening its
focal distance. Naturally, these muscles are not
only placed above and below the lens( as shown in our
cross-section diagrarn) They surround the entire
eye lens, forrning a rnuscular ring,
This adjustment of the ocular lens ( professionals call
it accomrnodation to near objects) tires the eye rnore
than the observation of distant objects, since the lensl
rnuscles are used to Droduce tension.
There is more to see in the diagrarn: Notice that the
lenses are not on the outside surface of the eye, but
rather, behind and towards the rear. There is, first
of all, the outside layer - the transParent cornea
( rnarked H) . Behind the cornea is a transparent
iiquid called the aqueous hurnor ( rnarked K on the
diagrarn) . This liquid bathes the front surface of
the lens L, and its suspension systern. The rear
surface of the lens rests on the ocular globe ( labelled
G) on a concave reinforcernent of the aqueous and
vitreous body, filling the other parts of the eye.
In front of lens L, there is the iris, J. It acts as
a diaphragm ( obturator) with a variable opening.
The pupil ( K) is its opening, allowing the free entry
of iight.
The iris works automatically: the stronger the inci-
dent light, the rnore it closes. The diarneter of the
pupil varies frorn 7 or 8 rnrn. ( when it is dark) , to
1.5 or Z rnrn.(when the light is intense) ..
You can observe the rnobility of the pupil openingl
First, place yourself in a dark corner ( where there i
is only very dirn lighting) , and look at your irnage
in a rnirror. Now, shine a bright light on your face.
Notice that your pupils contract when exposed to { bright light.
You can also test the rraccornrnodationrr of the ocular
lens. HoId a pencil about 25 crn in front of your right eye, and close your left eye. Place yourself in front f
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of a painting, while holding a pencil before your eyes.
Now, focus on the pencil tip - you should see it
clearly. Then, glance at a point on the painting ( right
beside the pencil tip) , without rnoving. If you allow
your eye to shift to the point on the painting, Iou will notice that the pencil tip now appears very hazy.
This is caused by your eye adjusting its focus to the
rnore distant painting.
No. 79. AT NIGHT ALL CATS ARE GREY
The opposite diagrarn shows you a cross-section of
a right eye. You see the well defined line indicating
that the back of the eye is covered by a filrn. This
is the retina ( N) , and has a thicknes s of. l/Z rnrn.
The retina surface is cornposed of nurnerous ultra
light-sensitive cells.
The are.a of the retina, directly before the pupil is
indented. This indentation, called the rcavity of the
retinal is the center of vision. At point B, on the
other hand, light-sensitive vision .Llls are entirely
absent, for it is from here that the optical nerve
Ieaves for the brain. Looking at the diagrarn, you
rnust be asking youself what this cross and this large
circle, both frarned by a rectangle, can pbssibly mean!
You will see its use imrnediately. Close your left
eye, and look at the center of the cross with your
right eye ( from above and at a distance of approxi-
mately 40 cm.) . If you slowly bring your dyb closer
to the cross - while still focusing on it - the black
spot suddenly disappears, but the frarne rernains
visible. How is this possible?o If you refer to the preceding diagrarn, everything
wiII becorne clear. When a cluster of rays hit your
right eye front on, these rays can rrrerge precisely
at that point of the eye where the vision cells are
cornpletely absent. This point is labelled B in the
cross-section diagram of the eye. Consequently,
B represents the blind spot in the eye. Fractions
of irnages touching this spot rernain invisible and
itr s arnazing that the irnage is not jolted or inter-
rupted at this spot. Only the irnage part that happens
to be located over the blind spot smoothly disappears,
If ( instead of a black spot on a white background) ,
there were a white spot on a black background, the
white spot would then disappear and black frarnework
would remain visible,+
Naturally, the left eye also has a blind spot. Test
your left eye by placing this rnanual upside down in
front of you.
On a starry night, it is possible to perform a similar
experiment. If you stare at a certain star that glows
very weakly, you may suddenly see it disappear.
However, this time, the disappearance takes place
at the precise moment that you were gazing very
fixedly at the star. As soon as you glance sideways,
5lView original page 5Page 6 · Read text
the star reaPPears - exactly as though there were
also a blind spot at the center of your line of vision,
er, at the indentation area of the retina. This is
aciually the case! But isnr t there a contradiction in
saying that there is a blind spot in the center of your
line of vision?
No, because there are two types of vision cells in-the
eye - the cone-shaped ones ( cone cells) and the
stick-shaped ones ( rod cells) .
Cones are less sensitive to light rays ernitted by weak
stars. They donlt even register these rays! Further-
rrrore, the cones are particularly dense in the retina
indentation. In fact, there are 41 000 of them in that
area, each with a thickness of only .00I5 mm. ! There-
fore, in this area, there is no space for rod cells
( which are ultra-sensitive to light) . Hence, because
of weak light rays, a second blind spot aPpears in the
retina indentation.
Do you wish to know why the retina indentation is the
cenfe" of our vision? This is simple. The light-
sensitive rod cells are far thicker than the cone cells.
If a section of the retina were cornposed exclusively
of rod cells, images would be very crude and have no
de tail.
If we wish to view objects with precision ( as in the
retina indentation) , then the thin cone cells are rrrore
practical, for they ate far more nurrrerous in that
indentation. Lurninous raysr corning frorn two dis-
tinct points situated very close to one another, can
reach two separate cone cells. The rod cells are so
large, that the rays would reach the sarne cell. Con-
sequently, they would be seen only as one light source.
The cone cells donr t work in a shady arear since we
can only perceive images registered by the thick rod
cells.
The cones ( which need a strong intensity of light in
order to work efficiently) have another advantage.
They make visual perception of colors possible. How
we see colors is one of the rnost fascinating questions
explored by naturalists in the last 150 years. Thanks
to the research work of Professor Dr. George Wald
( who received the Nobel prize in medicine with two
other scientists in 196?) , we now know the answer.
There are three different tyPes of cone cells. One is
sensitive to blue raysr one to green rays and another
to red rays. Therefore, the color image is forrned in
our eye approximately the same way as in a TV.
( You are farniliar with the TV rnechanism from
chapter 40. ) You can now understand what color-
blindness is. A color-blind Person has only two types
of cone cells - or one or two of the cone cell types
may not work properly. ( You know what this rneans
from chapter 39.)
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6ZView original page 6Page 7 · Read text
The rod cells, however, react principally to bluish
light. Since they do not reproduce shades of colors,
we see everything with a bluish-gray tint in dirn
light. The popular expression, rrat night all cats
are greyrr, here is thus scientifically explained.
If you consider that the retina has rnore than one
hundred million rod cells and more than six million
cone cells, you will understand that the TV carnera
(which we consider to be a technological triumph) ,
is actually a very primitive instrument in comparison
with the human eye.
However, it is still true that fro^m the visual angle of
the eye ( which is I40o) , only ?o are useful for ihe
clear observation and deciphering of. a given object.
This is because the density of small cones dwindles
rapidly from the center of the retina towards the
exterior, so that the very edge of the retina consists
only of rod cells.
No. 80. EYESIGHT AND GLASSES
Have you already checked to see if the lenses of a
pair of glasses are converging or divergent? If so,
yourll have noticed that glasses worn only for reading
are usually made with converging lenses, and have a
very small bulge. Usually, elderly people use these
Norrnal vision type of glasses, With age, the strength of the eye
rnuscles dwindle, and the lensr contraction also de--@ creases. The result is that only distant objects are clearly visible. We say then that the eye is pres-
byopic - or that the person is far-sighted.
PresbYoPic@@ For presbyopic eyes, the eye lensr focal length is
longer than its distance from the retina. Naturally,
there are also people born with an ocular globe too
www.butlkus.ussmall for the focal distance of the lens. These poople
therefore suffer from a I congenital presbyoilic
Myopic afflictionr .@1@
Far-sightedness can be corrected by glasses with
converging lenses. Such glasses deviate the incident
luminous rays so that ae soon as rays reach the
glasses they begin to merge. This type of lens, there-
fore, shortens the focal distance of the eye lens.
Instead of t the focal distance of the lener , opticians use a number called a rrdiopterrr. Do you want to know
the.focal distance of the lens of a pair of glasaes? To
do this, divide the number, one, by the diopters given,
and you will thus obtain the focal distance in meters.
Therefore, __l_ . Focal dietance in meters. Diopter
For example, the lens of a pair of glassee of two
diopters, have a focal distance of l/Z m" or 500 mm.
Of couree, there are also glassea with divergent lene.
They are used for rnybpic ( or near-sighted) people.
In this case, the focal distance of the eye length is so
63View original page 7Page 8 · Read text
short, that the incident rays hitting the eye merge
before they reach the retina ( as you can sqe in the
diagram) . Either the ocular globe is too large, or the
lens is too curved. Visual acuitv
when read Divergent lenses used in a pair of glasses, affect the
from a light rays so that they begin to disperse before hitting
distance of the eye. The result is a greater distance between the
- eye lens and the image situated behind the lens. The
divergent lens lengthens the focal distance of the eye --,2m. -. lens. Whether someone needs.to wear glasses or not,
depends on his acuity ( or, sharpness) of vision. L'
We check visual acuity with sheets of paper on which
broken lines of varying length are drawn. We say
that a person has a normal visual acuity of 1.0 if
he can still perceive a .75 rnrn. space between Z broken
see rn. Ifhe a dis- ofZ can only a distance frorn -JI or3 lines, I Z eyesight between his broken rnrn. lines, 1.5 tance of - is only half as good and consequently, he has a visual
acuity of .5. -Z
With the diagram on the left, you will be able to test
your visual acuity. You must check each eye separatel.y
so be sure to close your other eye. W-hen you can per-
ceive the position of the spaces in the circles, Iook to o the right of the page for your visual acuity score. Of
course, you rnust look at the page from a distance of
Z rn. Your visual acuity corresponds to the line in whichoo you can see the separations in the srnall circles perfectly. oco 0.50 The hurnan eye is not, however, the most perfect eye. occ 0.70 Birds have a far greater visual acuity. Therefore, a oooo falcon can very distinctly notice a hole in the ground
t.0 with a 2.5 crn. diarneter frorn a height of 500 rneters. ccoo A hurnan being with normal eyesight, cannot even see ooooo I,L an 8 cm. hole from this height. He can only see a hole
oocco 2.0 distinctly if it has a 15 crn. diameter.
No. 81. USING A MAGNIFYING GLASS
To see a certain object clearer, we place it under a mag-
nifying glass. So, take your converging lens #4 and hold
it 1 or 2 crn, above this page. Part of the print will
appear larger than it actually is: the converging lens
acts as a magnifying g1ass.
If you bring your eye very close to the rnagnifying glass,
the image remains clear as long as you vary the dis-
tance between the magnifying glass and the printed text.
Presbyopic people, not wanting to wear glasses, use a
magniiying glass for reading, not because of the larger
print, but bicause the magnifying glaee provides better
ilarity if it is used in a normal reading position.. Other-
wise, they could not read unless they held tJre printed
page at arml s length.
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r-
If you bring the page too close to the magnifying glass,
you only see a very h.azy picture.
If you need a gmall magnifying glass, but you donr t
have a converging lens, simply place a drop of water
on a clean piece of glass or on the flat surface of a
I transparent ruler. If the drop of water does not
trickle, you will have a small converging lens with
a focal distance of approxirnately 15 rnrn. It can be
used as a rnagnifying glass if you bring your eye
cloee to it. Even though it magnifies print more
than a norrnal reading magnifying glass, it is not
appropriate for reading because of its small diameter.
No. 82. THE ENLARGEMENT CAPACITY OF A
MAGNIFYING GLASS
'When you see an object enlarged 8 tirnes by a rnagni-
fying glass, this means that you see tJre object 8 tirres
larger than it actually is. By I actual sizer , we rrrean
the dimensions which an object usually seems to have
at observation distance of 250 rnm.
Itl s easy to perform an experirnent determining the
degree of enlargement produced by converging lens
#+. HoId screw #72 with a pair of tweezers and look
at it through the lens. While looking with both eyes
open, focus one eye on the part of the wall in front
of you that coincides lengthwise with the enlarged
image of the screw.
Then, hold a ruler at a distance of 250 mm. in front
of your eyes without rnoving. Check the length in-
dicated on the ruler to find the length you had pre-
viously noted on the wall in front of you.
Letl s say you saw an enlarged irnage of the screw
6.7 crn. in length, and the screw itself has a length of
8 mm. You then saw it enlarged 8.3 times, and the
converging lens #4 therefore, has an enlargernent
capacity of 8.3. However, you can also easily cal-
culate the enlargernent of the magnifying glass with
the following formula:
Enlargernent of magnifying glass :___ 359 mm,
Focal distance in rnm.
To the left of the diagram, you see how screw AB is
reproduced as CD on the eye retina, when it is at a
point 250 mm. from the eye. The center drawing
shows that the larger irnage FE would be situated
far behind the retina, if the distance between the eye
and the screw was diminished to length b. On the retina
itself , only a vety hazy picture of the screw would
appear. The right-hand side of the diagram shows
you that by placing a magnifying glass between the
screw and the eye, the irnage CD is reproduced with
clarity on the retina, you can also see at what size
GH is, seen 250 mrn. from the eye.
From what has preceded, you will understand that
image GH is a virtual image, gince it is seen in the
65View original page 9Page 10 · Read text
direction of the extensio4 of the deviated rays ( see
chapter 38 and the end of chapter 73) .
If you hold the scale from rnicrorneter #l3a under
converging lens #4 instead of screw AB in the right-
hand side of the diagram and place the millimeter
scale from the front of the book on a table 250 mm.
below your eyer )rou will see both scales super-
imposed. The rnicrometer divisions consist of 60
sub-divisions. Each group of 10 sub-divisions
equals 1 mm.; therefore, the rnicrometer divisions
measure 6 mrn. 'W'ith an 8. 3 enlargement this divi-
sion ( seen enlarged through converging lens #4) ,
covers 50 mrn. of the millirneter scale. This is
seen gimultaneously with your free eye, at a dis-
tance of 250 mm.
No. 83. DISTAI\CE OF THE EYE FROM THE
MAGNTFYING GLASS
250nn Observe the screw through the magnifying glass held
close to your eye ( Ieft side of diagram) , and then
bring your eye slowly away frorn the magnifying glass
( right side of diagram) The enlarged part GH be-
corrres smaller and smaller. The points A and B
( from which the lurninous rays hitting the eye are
emitted) , come closer and closer together as the
eye is brought further away from the rnagnifying
glass. When the eye is far enough frorn the magni-
fying glass, the rays are nearly parallel between
the rnagnifying glass and the eye. In this case,
points A and B rneet at the focal point of the magni-
fying glaes ( if the magnifying glass is rnaintained
above the observed area at a distance equal to its
focal distance) .
The largest visual field is obtained when your eye
-A A is as close as possible to the rnagnifying glass. You
..1-\ .:IN will see that the image is too distinct if you look into the planar surface of the lens rather than the bulging
one.
No. 84. SMALL LENSES WHICH ARE STRONGER THAN
LARGER ONES
Now, use srnall converging lens #6 as a rnagnifying
glass rather than converging lens #4. You can see
that it enlarges rrrore strongly. This is not sur-
prising, since it has a smaller focal distance and
therefore gives a greater enlargement. ( It enlarges
by 16. 7 tirnes - see chapter 82. ) {
The srnaller the focal distance of a lens, the greater is
the bulging of its gurface. The sphere ( of which the
lens is a part) therefore has a smaller diarneter when
the focal distance of the lens is srnaller. That is why
the diarneter of a lens which greatly enlarges, cannot
be as long as that of a lens which enlarges only slightly
and which has a nearly flat surface.
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For easier handling in tests corning up, srnall converging
lens #6 will be placed in support #17. If lens #5 is still in
part # 17, rernove it. On the KOSMOS side of support #I?,
are six ribs at the center holers edge: three are tall and
thin; three are thicker but shorter. Lens #6r s edge should
rest on these latter ribs. Part #I7 is injection-moulded
frorn plastic and srnall bits rnay rernain on these ribs when @-'s the rnould is lifted. Scrape this off with a pen-knife. IfrI lens #6 is not in position, it distorts the picture. Place *gr;fl Iens #6t s flat side on wheel #Z9r s hub. Bring the hubhole -' to exactly the lensr center. Before placing part #l? over
the wheel, check that the lens is in the center under the
upside-down support - otherwise the lens could be lopsided
and the support darnaged.
No. 85. THE IMAGE ON THE SMALL MAT DISK SEEN
THROUGH A MAGNIFYING GLASS
Using the magnifying glass ( forrned. by lens support f 17
and srnall converging lens #6) , you can observe the image
on the rnat side of the disk ( cut frorn rnat screen #371 in
the telerneter frorn chapter 77. When you hold the eye lens
support by its open side (on the extrernity of the telemeter
tube) , you have the correct distance with which to pre-
cisely observe the image. Naturally, the exterior side of
the eye lens support is turned towards the eye.
You now see the irnage on the mat disk enlarged by 16.7
times. If you point the telemeter towards the rnoon, you
then see it with a.diameter of approximately 19.7 rnm.
( see chapter ?5) .
If, on the other hand, you hold a ruler 250 mrn. in front
of your eye, and deterrnine the diarneter of the rnoon
when measured in this way, you discover that it is 2.26
rrrm. If you cornpare the diarneter of the moon as seen
in the rnat disk, with the diarneter seen with the naked eye,
you will realize that you see it 8.? times larger through
the telemeter.
To calculate this you must only check how rnany tirnes
2.25 is contained in I9. ?. Therefore, divide Ip.7 by
z.26.
No. 86. KEPLERT S TELESCOPE SIMPLIFIED
As you rernernber, we used the rnat surface of the disk
in order to see the aerial irnages projected by the ob-
jective lens ( see chapter 74) . We should be able to
observe the aerial image just as well by using the rnag-
nifying glass directly. To try this, remove the rnat
disk with its moveable support from the sliding tube,
but leave the telerneter as it is. So that the support of
the eye lens is rnaintained at the correct distance from
introduce the eye lens support ( with its srn311 .47 theFirst,aerial image, use field lens support #18. converging lens) into lens support #18 as indicated in -t, the diagrarn. You will notice a reference line between
67View original page 11Page 12 · Read text
the eye lens support and support #18. Introduce lens
support #18 into the sliding tube of the telemeter until
you have reached this reference line. Make sure that
the eye lens support still protrudes.
At this point, you are ready to observe the aerial image
through the small converging lens #6 which is now acting
as a magnifying glass, and which we shall now call the
eye lens. The irnage seen through the eye lens appears
8.7 tirnes larger than in reality. The instrurnent which
has been built from the objective lens and the eye lens
is therefore a magnifying glass which enlarges 8.7 times.
This telescope is different from Keplerr s telescope since
its eye lens is a converging lens, and it produces rever-
sed irnages. Instrurnents of this nature are called
rrKeplerl s telescopesrr, because the discovery of a tele-
scope in which the objective lens and the eye lens were
converging lenses, is attributed to the famous Gerrnan
naturalist Johannes Kepler.
Kepler is especially famous as an astronorner, and ob-
served the heavens with his telescopes. He did not
consider the problem of the reversed irnages irnportant
because when observing celestial bodies, it does not
matter if the images are reversed. Moreover, he
wanted to avoid any loss of lurninosity and tJre danger of
errors in representation that rrstraightened outrr reversed
irnage s .
The Kepler telescopea are still used today. Naturally,
Kepler had corrective instruments added to sorne of his
telescopes. These telescopes are called rterrestrial
telescopesl , for they are different than I astronornical
www.butkus.us telescopesl.
Unlike your simplified Keplerr s telescope ( the cross
section of which is represented by the diagram) , Keplerr s
telescopes did not have an achrornatic lens, but had only
a simple converging lens at the objective.
When you focus the telescope on a certain object, you
will certainly notice how the adjustment can be modified
within certain limits ( without thg clarity of the irnage
being diminished) . How can this be done ?
It is actually very easy! When the magnifying glass,
through which you observe the aerial irrnge ( in this
example the srnall converging lens #6) , is separated
frorn this aerial image by a distance equal to its focal
distance, the rays corning frorn a point in the aerial
irnage are parallel to one another. This image is then
seen clearly ( to the eye) if we adjust the lens to infin-
ity. The nearer the magnifying glass is to the aerial
image, the rnore the luminous rays (while coming frorn
the aerial image) diverge. Despite this divergence,
they always rnerge on sorne part of the retina when the
eye adjusts to vieyv a close object.
Consequently, the eye compensates for certain differ-
ences in telescope adjustment. The eye muscles are
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very much in use when the telescope is not properly
adjusted.
In order to observe for a long time without tiring the
eyes, when viewing a very clear image, the telescope
must be adjusted so that the distance between the ob-
jective lens and the eye lens is as great as possible.
This is valid for all telescopes, theatre binoculars,
and ordinary binoculars. You will be able to adjust your
telescope more easily if you turn the objective tighter
and then try to obtain a clear irnage by unscrewing it.
In this way your eyes will be relaxed after the initial
blurred image.
People who wea! glasses can use binocularg without
wearing their own glasses since they can adjust the
binoculars.
No. 87. THE PRECISE ADJUSTMENT OF KEPLERT S
TELESCOPE
As you have learned in chapter 68, we cannot obtain
a clear image with the telescopes unless the parallel
lurninous rays, reaching the objective lens, are still
parallel when they leave the eye lens. These rays are
only inclined relative to one another between the camera
lens and the eye lens.
In Keplerl s telescope, this condition is always fulfilled
when the rear focus of the objective lens LI coincides
with the front focus of the eye lens L2. On the diagrarn,
this common focus point is shown as Fg. By adjusting
Keplerl s telescope to infinity, we obtain the necessary
distance to do this. Add the focal distance of eye lens
FZ to the focal distance of the carrrera lens Fl between
the objective lens and the eye lens. For your sirnplified
Keplerl s telescope, the totat distance is therefore,
l3l mm. t 15 mm. 146 rnrn. You already know (from
chapter 76) that the =length of the telescope increases if
we focus it on nearby objects, due to the fact that the
distance between the objective Iens and the image pro-
jected by it, becomes greater.
No. 88. HOW THE ENLARGEMENT IS PRODUCED IN
KEPLERIS TELESCOPE
You already know ( frorn chapter 69, which dealt with
the adjustrnent of the telescope to infinity) that parallel
lurninous rays, leaving the eye piece, parallel to one
another, have nothing to do with the enlargernent of the
telescope. The enlargement depends on the cluster of
parallel rays hitting the objective at a small angle and
Ieaving the eye lens at an even more oblique angle.
However, it does not deterrnine the enlarging properties
of the telescope if the cluster of parallel lurninous rays,
exiting frorn the eye lens, has a srnaller diarneter than
of the incident ( or entering) cluster.'iiir"" that
On the oppoeite diagram we have drawn only one tay of
69
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the cluster, becauae we are dealing with the angle at
which the lurninous rays reach the objective lens, and
the angle at which they leave the eye lens.
Notice how the lurninous incident ray ( or entering ray)
forms a small angle with the axis of the telescope at Fl.
Since we have chosen a ray which crosses the front focus
FI of lens L1, it is clear that, the ray travels parallel
to the axis of the telescope between lens Ll and L2.
However, this ray is then refracted ( or broken) by
eye lens L2 so that it crosses the rear focus FZ. If the
focal distance of. LZ is shorter than that of Ll, then the
optical angle at FZ is greater than the one at Fl. If
tiee A catt be seen through the telescope with a larger
optical angle ( C) than with the naked eye,-it is.because
tie telescope enlarges objects on which it has been focused.
The enlargement occurs when the focal distance of lens
Ll is g".Jte" than that of lens L2. So, we can say ( as
we did for the GaLilean telescope) : Enlargernent of the
telescope = Focal distance !f the objgctivq lene Focal distance of the eYe lens.
'ffith this forrnula you can check if the enlargement ( which had been previousiy calculated) for your Kepler tele-
scope is the sarne. Enlargernerrt of the telescoPe':
131 rnm. 3 8. ?3 times, or ( in round numbers) 8.7- '
15 rnm.
When comparing the trajectory of the rays in Kepler.r s
telescope *itn tft" diagrarn of the trajectory of rays in
the Galilean telescope, your11 understand why the images
in the Kepler telescope are upside down. The irnage seen
through the Kepler telescope is of course, a virtual one.
No. 89. IMPROVING THE EYE LENS
The Kep1er telescope described in chapter 86 obviously
doesnr f produce very clear images. This is why wel ll
irnprove this telescope step by step, until ( by chapter
94) , we finally obtain absolutely perfect images.
Letl s start with the eye lens. Undoubtedly, you have
noticed that the field of vision is foggy if you even glance
obliquely into the eye lens. This problem really bother-
ea the firnous Dutch physicist Christian Huygens, who
woiked at improving the Kepler telescope.
Huygens perfected the eye glass of Keplerl s telescope
Uyloining it to a second lens. This lens is called the
ttii;Id lens", and its focal distance, and distance from
the eye lens, are synchronized. You can improve the
eye lLns of your own Kepler telescoPe by placing this
field lens into it.@o First of all, remove the eye lens. At this point, it is
cornposed of an ernpty field lens support in which we g_,.ffi havJintroduced the eye lens support containing the eye
lens from the Kep1er telescope. Rernove the field lens
support, the eye lens support, and its eye lens, and@-,M put thern aside.
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'To incorporate the field lens into the field lens support,
it is preferable to use picture-counting dial suppori
#30. Place converging lens #4, with its bulged surface,
on the upper edge of the round hole of part #30 ( as shown
ffi-,r-, in the diagram) . Then, hold field lens support #18 r{Fr ffi andexactlylookoverinto thesethe obturation(its largestholeend( whichtowardsis onthethebottom)field , Iens support) , to check that the lens is situated exactly
at the center of the support. If this is so, place the fieldkJ-''-ElL, lens support exactly on the planar surface of the lens and
press firmly until the lens is well fixed onto the 3 grooves
of this support.
To ensure that the field lens is not lopsided, the planar
surface of this lens must rest all around on the slightly
grooved interior surface of the field lens support.
Finally, replace eye lens support #1? with eye lens #6
onto the field lens support. 'We have thus improved
Keplerr s telescope according to Huygensl ideas.
No. 90. MODIFYING KEPLERT S TELESCOPE
Now, place Huygenst eye piece into the sliding tube of
Keplerr s telescope until the separation between the field
lens support and the eye lens support is ( as before) ,
barely visible. The adjustrnent cornpleted, you will
notice that the iheage appears very stable. Moreover, if
you look into the eye lens obliquely, you will see that
the field of vision has been widened. This, however,
is produced at the cost of sorne properties of enlarge- ment.
The image is now much clearer than it waEwithdut the
field lens. Unlike the single lens, this new eye piece
even corrects colors ( as you will see later on) , al- though it is not achromatic ( and is cornposed of-two
lenses made of the same material) .
No. 91. THE FIELD LENS IMPROVES THE IMAGE
If you would like to know what opinion Christian Huygens
had of the eye piece he had just invented., look at thele
two diagrarns. The upper one shows a very simple
Ke-pler telescope with 3 parallel lurninous rays tatting
sideways on its objective lens. Having been deviateiUy
objective lens Ll, these rays cross ejch other at one
point in the interrnediary irnage Zw ( tihe aerial image
between the 2 lenses of the telescope) . The center-of
this interrnediary image is focal point fg. AJter having
crossed one another at this point, the rays disperse once
again.
Using eye lens LZ as a magnifying glass, it is possible
to observe this interrnediary image. However, we can
only see rays which have been deviated from LZ towards r
the eye ( for example ray 3) . Rays Z and I pass beside LZ and disappear.
?l
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If we place field leng L3 in front of' LZ in the trajectory
L: Lz Ja of the rays ( see the diagram) , then the rays are deviated
'l sooner than before slightly towards the center, and before
F2 the intermediary itnage Zw. Rays 2 and I also reach the
7w Ft eye by way of L2. With a field lens, more rnarginal rays
are deviated towards the eye, so you can now look rnore
obliquely than before at the eye lens-
Moreover, tJre image is clear, since therrspherical
defectrr ( see chapter 95) is largely compensated for by
the {act that the rays cross between the two lenges.
The marginal rays, that cross field lens L3, pass through
LZ as mediatt rays. The rays that cross L3 as median
rays, pass through LZ as marginal rays.
Finalty, the chrornatic aberration caused by field lens L3
is compensated for by L2, so that the ocular globe is
chrornitically corrected. This was not the case when we
had lens LZ alone! This chromatic correction ( color
correction) is always produced when two converging
Ienses rnade from ideniical substances, are placed beside
each other at a deterrnined distance from one another'
From this we get the formula:
Distance between lenses I .
Focal distance ( f) gf lst lens * f of ZESI lens
z
In the case of Huygensl eyepiece, this chromatic
correction can be explained as follows:
Red rays are more weakly deviated than blue tays by
the field lens ( which acts as the first lens of the eyepiece)
The red and blue rays ( into which the incident white ray
has been decornposed) , consequently disperse between
the field lens and the eye lens of the eye piece. The
eye lens of the eye piece which acts as a second lens
behind the field lens is therefore, hit rnore frequently
by the red rays than by the blue ones. However, each
lens deviates more rays touching it on the edge than
those touching it as medians. Thus, in the second lens,
the red rays are more strongly deviated than the blue
ones, and they leave the second lens parallel to the blue
ones.
This is why the chromatic correction is first effected in
the eye. The lurninous rays entering the eye parallel
to one another, are concentrated by the lens of the eye
at a focal point situated precisely on the retina. Thus'
red rays and blue rays rneet on the retina at a single
point of a given image, whereupon they again-merge as
white light.
There is only one disadvantage with Huygensr eye piece.
Enlargement by the sirnple magnifying glass cannot be
attained, since the field lens deviates the rays a little
towards the center, and in front of the intermediary
image, so that the intermediary image contracts' When
we jdd the field lens, the enlargement which we had pre-
viously attained with the magnifying glass, becornes lZ. 5
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7ZView original page 16Page 17 · Read text
times rather than 16.7 times ( approximately 3/4 of its
previous value) . The Kepler telescope, when used
with the Huygensr eye piece, enlarges objects only by
approximately 6. 5 times.
No. 92. THE AERIAL IMAGE BEHIND THE TELESCOPE
It seems peculiar, but the eye piece can function as an
objective. W'e are not referring here to the case in
which you look into the wrong side of your telescope and
thus see shrunken images. 'W'e are thinking now of an
aerial irnage occurrence ( of the opening of the objective) ,
which is produced outside the telescope by the eye piece.
This image is seen from the interior, and appears to
you in the forrn of a clear floating disk, a few 4m. in
front of the eye lens. You may calculate the diarneter
of this small disk, which we call therrexit pupilrr ( or
ocular circle) with the following formula:
Diameter of the e*it pupil=liemeter of th.-ca*e
Enlargement of the telescope.
The diameter of the exit pupil is equal to the diarneter of
the cluster of rays which have passed through the eye.
The dimension of the exit pupil thus indicates the lurnin-
osity of the irnage seen. For observations during the
day or observations of a clear object ( for exarnple, the
lunar surface) , the exit pupil must have a diarneter of
3/4 rnrn. r- otherwise the irnage is too dark. For
Huntersr binoculars ( used after nightfall) , or astrono-
rnersl telescopes, the exit pupil must obviously be rnuch
larger. However, it is useless to make it larger than
the diarneter of the eye pupil when it is cornpletely open
in the dark ( approximateLy 7 rnrn. ) .
No. 93. PLACING THE DIAPHRAGMS
Notice that the exit pupil of your Kepler telescope is
surrounded by a clear border. Looking at it more
closely, you realize that this is caused by light reflected
into the telescope by the interior walls of the objectiver s
half shells. We rnust rernove this secondary light for it
causes the dark points of the image to turn pale. The
good quality of the telescope image is darnaged by light
emitted.frorn a point laterally outside itre field of vision.
This secondary oblique light can easily be elirninated
when the diarneter of the tube is greater than that of
the cluster of luminous rays, contributing to the forma-
tion of the image. If we only need an exit pupil diameter
of 1.8 rnrn., the diameter given by the eye piece does
not need to be over 12 rnrn. An obturator ( diaphragm)
with a hole of 12 mm. (part #561 , gives quite a bit of
shadow, so we place it just behind the objective lens.
We then place a second obturator further behind ( part
#57, with a hole of diametet 16.4 mm.) , and this is
our interrnediary obturator. In this way, the narrower
sliding tube is also darkened on the interior.
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For the placement of the obturators, we must take the
objective apart. First, remove universal adjusting
corrlponent #I2 frorn the objective. This is easy if
you simply turn the objective cornpletely.but slowly to
the right, as if it had to be unscrewed in the wrong
direction. Place the tip of a small screwdriver into
one of the notches at the separation crack between
obturator #32 and the half shells of the camera piece
#48. Then, turn the screwdriver clockwise until the
obturator can be removed.
You must now place large obtuartor II ( exterior dia-
meter 38 rnrn., hole diarneter 16.4 mm. , part #57
with its mat surface forward) into the opening of tele-
scopic tube #24. After we have finished the asse:nbly,
this obturator will be secured by the tube of adjusting
cornponent #lZ.
Now, place large obturator I ( exterior diarneter 38 rnrn.
diameter of hole 12 mm. , part #56) into half shell #48,
behind the achromatic lens, It is situated inside the
telescope directly beside large converging lens #7 of
the achromatic lens. The mat surface of the obturator
rnust be turned towards the achrornatic lens. When you
have made sure that the srnall protrusion, rnarked y,
of telescopic tube #24 is well placed into the spiral groove
of the objectivel s lower half shell, you will be able to
place the upper half shell of the objective. Refer to
chapter 64 to rernind you how to close the objective
containing the obturator.
FinaIIy, introduce the telescopic tube and check that
the large obturator II ( part #57) is still well placed.
Then place the universal adjusting cornponent by turning
it to the right as if it had to be screwed on. Make sure
that the universal adjusting component is secure and in
the correct position ( observe the reference rnark z,
see diagrarn in chapter 641 .
No. 94. A VERY CLEAR IMAGE IN KEPLERT S
TELESCOPE
AJter having incorporated both obturators into the ob-
jective, introduce once again sliding tube #53, with its
thicker end in the hole of universal adjusting component
#tZ. Then, push the Huygenst .yu piece ( described in
chapter 8$) into the groove between the eye lens support
and the field lens support, at the free end of sliding
tube #53.
Thus, the Kepler telescope, with its Huygens' .y" piece
is completed. Itgives a clearpicture. Its enlargernent
is 6. 5 tirnes and its opening is 12 mrn, Specialists
refer to it as a 6.5 x 1Z rnrn. telescope. The first
nurnber denotes the enlargernent while the second number
in mrn. refers to the camera lensl diarneter.
No. 95. OBTURATORS A.FFECT THE IMAGE
The quality of image in yourwww.butkus.usKepler telescope is con-
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siderably improved by the incorporation of the two ob-
turators. This is essentially due to the fact that no
secondary light can penetrate the telescope. The irn-
provernent is effected with the obturator of the objective
lens, since it repels rnarginal rays from the objective
lens. On the opposite diagram, observe that the only
rays, which cross the converging lens, rneet at focal
point F; near the center. On the other hand, the rnar-
ginal rays meet before, as if the edge of the lens be-
longed to a lens with a smaller focal distance. More
precisely it seerns that the marginal zones of the lens
have a focal distance which becornes shorter and shorter
as they are placed farther towards the exterior of the lens.
Frorn your study of the concave mirror, you already know
that the rnarginal rays concentrate at different points
than those closer to the center, However, this phenorrrenor
cannot be produced with concave parabolical mirrors.
This effect does appear with converging lenses though:
the marginal rays rnerge before they focus, because the
lenses are parts of spheres. We therefore speak of
llspherical defectslr when referring to the divergence
of focal distances of marginal rays.
On the right of the diagrarn, the rnarginal rays are re-
pelled by the obturator of the lens. If the obturation does
not take place, the rays do not strike the points of the
irnage as a function of their departure points, but rather,
touch the neighboring parts of the irnages ( since the rays
cross each other before the interrnediary image) ,.and
disperse at a fair distance from the interrnediary image.
The image consequently, is sornewhat hazy and cannot be
regulated with precision. You know ( from chapter pI)
that the ttspherical defectrr is not compensated for
only by the obturation of the marginal rays.
On the opposite diagram, you see that an obturator which
must retain the marginal rays, has to be placed near the
objective lens. If you place it too far behind, it obturates
the obliquely arriving incident rays
Certainly, youl ve already noticed that the image size'in
your Kepler telescope has not been modified by the in-
corporation of the objectivers obturator. This did occur
with the Galilean telescope ( chapter 70) , when you held
the objectiver s obturator in front of the telescope. The
explanation is very simple. In your Kepler telescope,
the interrnediary irnage totally appears, whether you have
an obturator or not. An obturator in the objective only
prevents the rays frorn becorning too numerous at different
points on the irnager The luminosity of the image is con-
sequently, decreased. On the other hand, the size of the
image is not reduced. This would only occur if an inter-
rnediary obturator were placed at a greater distance be-
hind the objective lens.
The reason why an obturator in the objective ghrinke the
irnage of the Galilean telescope can be seen quite clearly
in the diagrarn. You will find the explanation fairly simple,
There is no intermediary image in the Galilean telescope
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becauee, with tJ,.e eye lens the eye ia eituated before the
interrnediary image. Observe point A in our diagram.
Without an obturator ( and starting frorn point A) , we can
see obliquely towards the top, through-the o-bjective.Iens.
However-rhavingplacedtheobturatorintotheobjective,
this direction is now blocked. Starting from A, we can
only see through the objective-I-ens if we look through
the obturdtor, opening at an oblique angle' In-the
Galilean telescope, the objectivel s obturator therefore
rnasks part of the PersPective.
No. 96. TwO LENSES INSTEAD OF ONE
Previousllr, .the enlargernent capacity of an eye piece magnifying glass was Iessened when a second lens was
intioduced ( see the end of chapter !1) . This drop frorn
16.? times to lZ.5 tirnes ( in the enlargement of the
magnifying glass) , is shown as being the extension from
15 to 20 rnm. of the eye piecer s focal distance. You can
verify this by using the forrnula in chaptet 82. Therefore,
two individual lenses can be assernbled into one systern
which acts as a single lens. The focal distance of a lens
systern cornposed of two individual lenses can be calcu-
lated if we multiply the focal distances of both lenses
together, and then divide the result by the sum of the two
foial distances diminished by the distance between the
lens es :
Focal distance ; focal distance fI x f2, ,
(focal distance f.I + f'Zl - distance between
the lense s.
As youl ve seen ( in the example of the achrornatic lens
and Huygensr eye piece) , instead of a single lens, we
frequently use lens systems composed of rnany lenses,
having the same focal distance. In this way, we cornPen:
sate for chrorratic aberration defects, rtspherical
defectstr, and other lensl defects of which you are
not yet aware; all you need to do is appropriately
adjust the lens system with the single lens.
No. 9?. A DOUBLE LENS! MAGNIFYING GLASS
A magnifying glass always has two disadvantages: It
rnust be held close to the object observed, and this object
then appears dark and the visual field is relatively srnall.
The rnagnifying glass you are about to build consists of
two lenses. The bottom lens rests on a transparent
pedestal, so that light can easily reach the object to be
observed.
Place square converging lens #47 ( with its bulging sur-
face upriard) , in transparent pedestal #46. This pedestal
rnust rest on its smaller surface. Place vision f'tarne #45
lr7 over the magnifying glass and insert converging lens #4 this into downward) facing surface bulging its ( withtr ' The loosening. prevent will part. Support ring #6I new @y*lr----1| the on is assembled glass part of the magnifying uppet@ tiinsparent pedestal ( upon which we have fixed the square
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@-or converging lens) . The double lens magnifying glass is
now completed. 9--'
This magnifying glass shows distance that the focal of a
need I.-F--Hil-*-'S-:N <Ltwww.butkus.us lens not be longer when assembled with a second
lens ( and thus forrns a lens systern) . This rnagnifying LN/\:o, glass ( in which the individual lenses have focal dis- NN tances of 30.0 mm. and 73.6 rnrn. ) , has - in effect - a
tota1focaIdistanceofonlyZ5.0rnm.Verifythisby
inserting the individual focal distances into the formula
frorn the preceding chapter, and take 15.3 mm. as the@6! distance between lenses ( see the cross-section diagram) .
According to the forrnula frorn chapter 82, an enlargernent
of l0 tirnes is produced. 'ffi*
No. 98. OPTIC BENCH
'We give this narne to an instrurnent in which rnany lenses
are placed one behind the other, so that their order, and
distances between them, can be modified. You will find
all the necessary pieces in your kit to build this I optic
benchr. The lenses must be placed in sliding supports
and introuced into a tube rnade by assernbling the sliding
tube s.
The diagrams show you the assembling procedure and how
to go about introducing the lenses and obturators into the
sliding supports formed by two haE shells #3I. In groove
s ( which is located on the side of reference hole x) , there
is space for divergent lens #5, and a srnall obturator, or
for converging lens #4 with holding ring #61 , and a small obturator.
In grooves t andw, there is also space for smaIl divergent
lens #5 or converging lens #4 witln a holding ring #61.
Small obturators or color filters can be placed in grooves
I rl l=lE!-il u and v.
S'trGzry,v The diagrarn shows (as an exarnple) , a double lensr rnagni- ( fying glass composed of two converging lenses #4 ( whose
bulging surfaces face each other) , with a7.5 mrn. ob-
turator placed between them. The distance between the
lenses is 4. I mm. Therefore, tJre total focal distance is
16.6 mm. and the enlargement is l5 times.
No. 99. CALCULATING THE FOCAL DISTANCE
To calculate the distance between lensesr fou must know frorn which point of the lens to measure this distance. you
need only realize that there can be planar convex lenses of
different thicknesses ( with the same focal distances) , in
order to understand that the center between the two surfaceg
of a lens is not used as a starting point for our measurernent. -ffi In a very thin planar convex lens, the focal distance is
naturally calculated from the highest point on the bulging
surface. This is also true for thick planar-convex lenses,
where the focal distance must be rneasured to the focus
towards the direction of the bulging surface. #;r
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