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The Single-Lens Magnifier:
Eye
Fig 1
What is the effective magnification?
Let, Object height = h, and assume the user places his/her eye as close to the lens as
feasible. We will consider that the angle the central ray makes is representative of the
image angle (paraxial approximation).
h
. We need to compare this to the
S1
largest angle that the object can be viewed at without a lens. This is obviously dependent
on how close someone can focus their eyes, so is not a universal constant. For the
purpose of these kinds of calculations, however, it is usual to use 250 mm as the average
close viewing distance achievable for most of the population (the older population may
have to use reading glasses!). Hence the maximum angle the object can subtend to the
h
unaided eye is:  E 
250
The angle the virtual image subtends is  M 
We will further assume that the distance, S2, of the virtual image is made to also equal
250 mm. This will give us slightly more magnification, since the object can be closer to
the lens than for an object at infinity.
The thin lens equation then gives us:
1
1
1


(since S2 is negative).
f
S1 S 2
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S2 f
250 f
h
h 250  f
. The effective

, and  M 
 
S 2  f 250  f
S1 f
250

250  f
magnification, therefore, is M  M 
.
E
f
Hence: S1 
What is a good magnifier capable of? The average Human eye can resolve objects that
subtend about 1 min of arc (3x10-4 rad). (This is ~ 1 in at 100 yards, or a telephone pole
at a mile.) Thus, the smallest object detectable by the (average) Human eye is 250 x
3x10-4 = 0.075 mm or 75 microns.
Handheld magnifiers (Hastings triplets) are available with focal lengths down to 12.5mm,
corresponding to M=21, and the smallest object visible = 3.6 microns.
Doublets are available with focal lengths of 4.5 mm (diameter = 3mm), corresponding to
M=56, smallest object = 1.3 microns (about 2.5 wavelengths of green light).
(What about diffraction effects? The Rayleigh criterion for angular resolution is
1.22
 min 
, where  is the wavelength of light and D is the diameter of the circular
D
aperture. According to this, the minimum aperture for 1 min resolution is 2mm, easily
achieved by the eye and magnifier.)
Telescopes:
Telescopes can be considered as an Objective lens creating a real image of distant objects
and an eyepiece working as a magnifier to allow the eye to observe the real image:
Newtonian Telescope
Image of Distant Object
Image of Objective Lens
One of the tasks of the eyepiece in a good telescope is to re-image the Objective Lens
into the space behind the eyepiece. Since the Objective Lens is the stop (limits the
amount of light from the object), it’s image is the exit pupil of the system. The distance
that this image is behind the eyepiece is known as the eye relief, and the user should try
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to match this image with their eye’s pupil. This allows all of the light that enters the
Objective Lens to pass into the eye, producing the greatest brightness and field of view.
Since the exit pupil is a diminished image (by the ratio of the focal lengths of the
Objective and Eyepiece), a telescope can be also used as a magnifying device: Put the
object to be observed near the exit pupil and look at the magnified image in the
Objective.
The Galilean telescope, with it’s negative eyepiece, does not make a good telescope
despite the upright image and compact length – there is no real image of the Objective
Lens to place the eye near and hence the user can only see a small portion of the light
entering the telescope at any one time. This design is only used in cheap, low power toys
and opera glasses.
Galilean Telescope
Layout
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Total Axial Length:
90.00000 mm
ParaxialTele_Galilean.zmx
Configuration 1 of 1
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