Optics I

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Light Control through Optical System
Our major concerns field of view and image
brightness We will learn aperture, stop,
aperture stop, field stop, pupil and window. The
element in an optical system that determines the
maximum cone of light passing through the system
is called the aperture stop (AS). The limiting
cone angle ?1 is easy to obtain but ?2 is not.
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Light Control through Optical System
A front stop serves as an aperture stop.
Entrance pupil (EnP) the image of AS seen
through the optical elements in front of it. Exit
pupil (ExP) the image of AS formed by all
imaging elements following it. EnP is conjugate
with ExP.
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Light Control through Optical System
A rear stop behind the lens serves as the
aperture stop (AS) and the exit pupil (ExP).
A front stop serves as the aperture stop (AS) and
the entrance pupil (EnP).
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Light Control through Optical System
Chief ray a ray from object that passes through
the axial point in EnP. The ray must also passes
through the axial point of both the AS and ExP.
Entrance and exit pupils are related to AS and
govern the brightness of the image.
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Light Control through Optical System
The field of view describes the range of the
object that can be viewed. The partial shielding
of the outer portion of the image by stop S for
off-axis object points is called vignetting.
Excessive vignetting may make the image of a
point object appear astigmatic. The field of
view (object plane) is often defined as the
circle (OU) that consisting of all object points
having at least half the maximum irradiance found
at the center of the image. Field stop (FS)
limits the size or angular width of the object
that can be imaged. Entrance window (EnW) the
image of FS formed by all optical elements
preceding it.
Exit window (ExW) the image of FS formed by all
optical elements following it.
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Light Control through Optical System
Example Consider an optical system made up of
two positive thin lenses with a stop S located
between them as shown in the figure. (a) Locate
the position and size of the final image. (b)
Locate the AS, EnP, and ExP for the system. (c)
Locate the FS, EnW, and ExW for the system.
Solution s1?40 cm f140/3 cm
s1?20 cm s2?10 cm
f220/3 cm
s2?20 cm
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Light Control through Optical System
(b) Lens L1 is AS and EnP. Using thin lens
equation, ExP is located 8.57 cm to the right of
lens L2 with an diameter of 4/7 cm. (c) To find
FS, we must determine the angles subtended at the
center of the entrance pupil.
The stop S is FS. EnW is located in the object
plane with a diameter of 2 cm. ExW is located at
the image plane with a diameter of 2 cm.
A schematic eye
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Light Control through Optical System

• Homework
• Two positive lenses, each of diameter 5 cm and
  focal length 15 cm, are separated by a distance
  of 10 cm. For what range of object positions
  along the optical axis will (a) the first lens
  and (b) the second lens control the amount of
  light passing through the system?
• An aperture of opening 5 cm in diameter is
  positioned 15 cm to the left of a positive lens
  of rim diameter 10 cm and focal length 12 cm.
  Each element is centered on the optical axis.
  (a) For an object located 6 cm to the left of the
  aperture, which element serves as AS? (b) Where
  are the entrance and exit pupils located?
• An aperture of 5-cm opening is located 8 cm to
  the right of a positive lens of diameter 10 cm
  and focal length 12 cm. (a) For an object
  located 6 cm to the left of the lens, which
  element is AS? (b) Where is EnP? What is its
  size? (c) Where is ExP? What is its size?
• An object measures 2 cm high above the axis of an
  optical system of a 2-cm AS and a thin convex
  lens of 5-cm focal length and 5-cm aperture. The
  object is 10 cm and the AS is 2 cm in front of
  the lens. Determine the position and size of the
  entrance and exit pupils, as well as the image.
• An optical system, centered on an optical axis,
  consists of (left to right) object plane, thin
  lens L1 30 cm from the object plane, aperture A
  15 cm farther from L1, thin lens L2 10 cm farther
  from A, and image plane. Lens L1 has a focal
  length of 10 cm and a diameter 6 cm L2 has a
  focal length of 5 cm and a diameter of 6 cm
  aperture A has a centered, circular opening of
  2.0 cm in diameter. Locate (a) image plane, (b)
  AS and EnP, (c) ExP and (d) FS, EnW and ExW.

9
Optical Instrumentation
Prisms generally not used alone Angular
deviation Minimum deviation occurs when the
ray of light passes through the prism
symmetrically.
For small prism angle Or
Ophthalmic Prisms Small angle prisms are used in
ophthalmology to correct double vision. When two
eyes do not aim simultaneously at an object
correctly, tow nonoverlapping images are
perceived.
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Optical Instrumentation
Bending power of prism (prism diopter pd)
measured in terms of the displacement y caused
by the prism on a screen 1 m from the prism.
For two thin prisms
Example An ophthalmic prism of prism power
Pprism2.5 is desired. If the prism material is
of index n1.56, what should be its apex angle?
How should it be oriented to bend the ray
downward from the horizontal? Solution
The apex angle should be about 2.6? with base
downward.
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Optical Instrumentation
Example A prism material has an index of 1.50
and apex angle of 5?. (a) What is the power of
the prism? (b) By how much does it displace an
incident ray at 60 cm? Solution The
ray is displaced 4.36 cm at a distance of 100cm.
So it is displaced 2.6 cm at 60 cm. Example Two
small angle prisms, both base down, are used in
combination. One has a power of 2.5 pd, the
other of 4.4 pd. (a) What is the deviation angle
of the pair? (b) What is the displacement at 100
cm from the pair? Solution The
displacement is 6.9 cm at 100 cm and is downward
toward the base of the prism. Dispersion angular
spread Cauchy equation
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Optical Instrumentation
Three specified colors are used     C line
(656.3 nm) from a hydrogen vapor lamp.     d
line (587.2 nm) from a sodium lamp.     F line
(486.1 nm) from a hydrogen vapor lamp. The
refractive indices of substances for these three
precise colors are denoted by nC, nd, and nF,
respectively. Dispersive power An
instrument using a prism as a dispersive element,
which is able to measure the angles of deviation
of various wavelength, is called a prism
spectrometer.
D
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Optical Instrumentation
Prisms may be combined to produce achromatic
overall behavior, that is, the net dispersion D
for two given wavelength may be made zero, even
though the deviation is not zero. The direct
vision prism accomplishes zero deviation for a
particular wavelength while at the same time
providing some dispersion.
achromatic prism
For particular wavelength
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Optical Instrumentation
Camera It forms a real, inverted image on a
light sensitive surface by a converging lens.
Below is a Zeiss Tessar system produces a flat,
well-focused image over a large angular field.
f-number (relative aperture), exposure E
exposure time ?t and intensity I. If the
f-number is 8, it is usually referred to f/8 by
photographers.
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Optical Instrumentation
Depth of Focus
The blur disc diameters PQ and RS are their
maximum, above which blur would be noticed in an
image in the planes PQ or RS. The distance
between the blur discs is known as the depth of
focus for the image B. It is increased with a
smaller aperture.
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Optical Instrumentation
Depth of Field
l1
l'2
l'
l
l2
l'1


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Optical Instrumentation
Example A camera with a 5-cm focal length lens
and f/16 aperture is focused on an object 274.3
cm away. Allowing satisfactory quality of the
image when d is 0.04 mm, what are the near and
far distances and the depth of field?
Solution d0.04 mm, f/D16, f5 cm, D5/16
cm, l?274.3 cm, near point far
point The depth of field is 721 cm.
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Optical Instrumentation
Angular Magnification
The visual angle ? is aided with the lens and ?
is the unaided angle.
The angular magnification is dependent on the
position of the observers eye (distance d).
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Optical Instrumentation
Nominal Magnification
When the image is formed at infinity, M is
referred to as the nominal magnification Mnom.
And is equal of one-quarter of the lens power.
Eyepieces The eyepieces, or ocular, of an
instrument is fundamentally a magnifier. Its
function is to view the image (called objective)
formed by a lens or lens system preceding it in
an optical instrument. Most types of eyepieces
consist essentially of two lenses referred to
respectively as the field lens (it increases the
field of view) and the eye lens (is placed next
to the observers eye).
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Optical Instrumentation
Huygens Eyepiece
The two lenses are separated by a distance equal
to the average of their focal lengths. The
function of the field lens is to deviate inward
those rays which would otherwise have missed the
eye lens, thus increasing the field of view.
Huygens eyepiece reduces longitudinal chromatic
aberration.
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Optical Instrumentation
Ramsden Eyepiece
Ramsden eyepiece consists of two same
plano-convex lenses, separated by about 2/3f?.
The final image is formed at infinity. The
function of the field lens is to deviate towards
the axis those rays which would otherwise miss
the eye lens. This increases the field of view.
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Optical Instrumentation
Microscope
The simplest form of microscope consists of two
positive powered lenses the objective (O-lens)
which has a shorter focal length and the eyepiece
(?-lens) which has a longer focal length. In
normal use the final image is at the standard
near point distance of 25cm from the ?-lens.
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Optical Instrumentation
Microscope
If the observers eye is emmetropic and
unaccommodated, the final image must be formed at
infinity instead of at the standard near point.
This is achieved by withdrawing the ?-lens
slightly such that the primary image falls on the
first focal plane of this lens. More prolonged
viewing of the image is possible with less eye
strain.
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Optical Instrumentation
Telescope
The telescope is used to enlarge the image of a
distant object. The figure shows the image
formation by a Keplerian Astronomical Telescope.
In normal usage the primary image also coincides
with the first focal plane of the eyepiece. The
equivalent power of the afocal configuration
telescope is zero. The instrument enlarges the
visual angle.
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Optical Instrumentation
Telescope
The terrestrial telescope with an erector lens.
With the erector lens, the telescope is longer
but the image viewed is upright. The Galilean
telescope with a diverging eyepiece. The final
image is upright.
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Optical Instrumentation

• Homework
• A parallel beam of white light is refracted by a
  60? glass prism in a position of minimum
  deviation. What is the angular separation of
  emerging red (n1.525) and blue (n1.535) light?
• Ophthalmic prisms of 2.0 and 3.0 pd are to be
  designed for the left and right lenses,
  respectively, of a pair of eyeglasses, in order
  to correct for a 5.0 pd misalignment in the
  vertical vision of a patient. The prism in the
  left lens is to produce a downward displacement
  of the light passing through it, while the prism
  in the right lens is to produce an upward
  displacement. The glass used for each lens has a
  refractive index of 1.523. (a) What is the prism
  apex angle for each ophthalmic prism? (b) What
  is the orientation of the prism base in each
  lens?
• A prism of 60? refracting angle gives the
  following angles of minimum deviation when
  measured on a spectrometer C line, 38?20? D
  line, 38?33? F line, 39?12?. Determine the
  dispersive power of the prism.
• A camera is used to photograph three rows of
  students at a distance 6 m away, focusing on the
  middle row. Suppose that the image defocusing or
  blur circles due to object points in the first
  and third rows is to be kept smaller than a
  typical silver grain of the emulsion, say 1 ?m.
  At what object distance nearer and farther than
  the middle row does an unacceptable blur occur if
  the camera has a focal length of 50 mm and a
  f?number of f/4?