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					 PHYSICS 1444-001
  Summer II 2009


     Lecture 17


Optical Instruments
 p
Optical Instruments




                      2
Optical Instruments
   Analysis generally involves the laws of
   reflection and refraction
   Analysis uses the procedures of geometric
   optics
   To explain certain phenomena, the wave
      t     f light    t be
   nature of li ht must b used d


                                           3
The Camera
     single-
The single-lens
photographic camera
p     g p
is an optical
instrument
Components
  Light- g
    g
  Light-tight box
  Shutter
  Converging lens
     Produces a real image
  Film behind the lens or
  electronic sensor
     Receives the image
                             4
           Camera Operation
Proper focusing leads to sharp images
  The lens-to film di t
       l   to-                ill d   d     th bj t
  Th lens-t -fil distance will depend on the object
  distance and on the focal length of the lens
The shutter is a mechanical device that is
opened for selected time intervals
                        p             j
Most cameras have an aperture of adjustable
diameter to further control the intensity of the
light reaching the film
          small-
  With a small-diameter aperture, only light from the
  central portion reaches the film, and spherical aberration
  is minimized

                                                           5
          p       ,         y
  Camera Operation, Intensity
Light intensity is a measure of the rate at
which energy is received by the film per unit
area of the image
  The intensity of the light reaching the film is
  proportional to the area of the lens

The brightness of the image formed on the
fil depends on the light intensity
film d    d      h li h i      i
  Depends on both the focal length and the
  di   t    f the lens
  diameter of th l
                                                    6
               f-
       Camera, f-numbers
     ƒ-
The ƒ-number of a camera is the ratio of
the focal length of the lens to its diameter
  ƒ = f/D
      ƒ-
  The ƒ-number is often given as a
  description of the lens “speed”
                      f-             fast
    A lens with a low f-number is a “fast” lens



                                                  7
                                ƒ-
Increasing the setting from one ƒ-number to the
next higher value decreases the area of the
aperture by a factor of 2
           ƒ-
The lowest ƒ-number setting on a camera
corresponds to the aperture wide open and the
maximum possible lens area in use
Simple cameras usually have a fixed focal length
                                   ƒ-
and a fixed aperture size, with an ƒ-number of
about 11
                             ƒ-
  Most cameras with variable ƒ-numbers adjust them
  automatically

                                                     8
There is a certain range of distances over which
  b        ll b    f       h        ll d h d h f
objects will be in focus; this is called the depth of
field of the lens. Objects closer or farther will be
blurred.
bl     d




                                                        9
               The Human Eye
The normal eye focuses
light and produces a sharp
image (resembles a
camera in its basic
functioning, with an
adjustable lens, the iris,
and the retina)
Essential parts of the eye
    Cornea – light passes
    through this
    transparent structure
    Aqueous Humor – clear
    liquid behind the
    cornea
                               10
            The Eye – Parts
The pupil
       i bl      t
  A variable aperture
  An opening in the iris

The crystalline lens
Most of the refraction takes place at the
outer surface of the eye
  Where the cornea is covered with a film of
  tears

                                               11
                  y
             The Eyes – Parts
The iris is the colored portion of the eye
  It is a muscular diaphragm that controls pupil
  size
  The iris regulates the amount of light entering
  the eye by dilating the pupil in low light
                                           high-
  conditions and contracting the pupil in high-
  light conditions
        f-
  The f-number of the eye is from about 2.8 to
  16
                                              12
         The Eye – Operation
    cornea-
The cornea-lens system focuses light onto the
     s face           eye
back surface of the e e
  This back surface is called the retina
  The retina contains receptors called rods and
  cones
  These structures send impulses via the optic
  nerve to the brain
    The brain converts these impulses into our
    conscious view of the world
                                                  13
           The Eye – Operation
Rods and Cones
  Chemically adjust their sensitivity according to the
  prevailing light conditions
     The adjustment takes about 15 minutes
     This phenomena is “getting used to the dark”
Accommodation
  The eye focuses on an object by varying the shape
            y                  g       p
  of the crystalline lens through this process
  An important component is the ciliary muscle which
  is situated in a circle around the rim of the lens
  Thin filaments, called zonules, run from this muscle
                                                     14
  to the edge of the lens
          The Eye – Focusing
The eye can focus on a distant object
  The ciliary muscle is relaxed
  The zonules tighten
       ca ses              flatten, increasing
  This causes the lens to flatten inc easing its
  focal length
                   infinity,
  For an object at infinity the focal length of the
  eye is equal to the fixed distance between lens
  and retina
    This is about 1.7 cm


                                                  15
       The Eye - Focusing

The eye can focus on near objects
  The ciliary muscles tenses
  This relaxes the zonules
  The lens bulges a bit and the focal length
  decreases
                foc sed         etina
  The image is focused on the retina


                                               16
The Eye – Near and Far Points
The near point is the closest distance for which
the lens can accommodate to focus light on
the retina
                   10
  Typically at age 10, this is about 18 cm
  It increases with age

The far point of the eye represents the largest
distance for which the lens of the relaxed eye
can f      light    th    ti
     focus li ht on the retina
  Normal vision has a far point of infinity

                                              17
        Conditions of the Eye
Eyes may suffer a mismatch between the focusing
             lens-
power of the lens-cornea system and the length of
the eye

Eyes may be
  Farsighted
    Light rays reach the retina before they converge to form an image
  Nearsighted
    Person can focus on nearby objects but not those far away




                                                                 18
          Farsightedness




             yp p
Also called hyperopia
The image focuses behind the retina
                                 clearly,
Can usually see far away objects clearly but
not nearby objects                             19
   Correcting Farsightedness




A converging lens placed in front of the eye can correct
the condition
The lens refracts the incoming rays more toward the
principle axis before entering the eye
   This allows the rays to converge and focus on the retina
                                                              20
            Nearsightedness




Also called myopia
In axial myopia the nearsightedness is caused by the lens
being too far from the retina
                y p
In refractive myopia, the lens-cornea system is too
                          lens-        y
powerful for the normal length of the eye
                                                        21
 Correcting Nearsightedness




A diverging lens can be used to correct the
condition
The lens refracts the rays away from the
principle axis before they enter the eye
  This allows the rays to focus on the retina   22
Vision is blurry underwater because light rays
are bent much less than they would be if
                             y
entering the eye from air. This can be avoided
by wearing goggles.




                                             23
Presbyopia and Astigmatism
 Presbyopia is due to a reduction in
 accommodation ability
   The cornea and lens do not have sufficient
   focusing power to bring nearby objects into focus
   on the retina
   Condition can be corrected with converging lenses
 In astigmatism, the light from a point
 source produces a line image on the retina
   Produced when either the cornea or the lens or
   both       t    f tl        ti
   b th are not perfectly symmetric
                                                    24
Diopters
   Optometrists and ophthalmologists usually
   prescribe lenses measured in diopters
     The power of a lens in diopters equals the
     inverse of the focal length in meters
       P = 1/ƒ




                                                  25
         Simple Magnifier
      p      g                      g
A simple magnifier consists of a single
converging lens
This device is used to increase the apparent
size of an object
The size of an image formed on the retina
depends on the angle subtended by the eye



                                          26
                g          g
The Size of a Magnified Image
 When an object is
 placed at the near
 point, the angle
 subtended is a
 maximum
   The near point is about
   25 cm
 When the object is
 placed near the focal
 point of a converging
 lens, the lens forms a
 virtual, upright, and
 enlarged image                 27
       Angular Magnification
Angular magnification is defined as
     θ    angle with lens
   m≡ =
     θ o angle without lens

The angular magnification is at a maximum
when the image formed by the lens is at the
near point of the eye
  q = - 25 cm
  Calculated by
                    25cm
       mmax = 1 +
                      q                  28
     Magnification by a Lens
With a single lens, it is possible to achieve
angular magnification up to about 4

With multiple lens, magnifications of up to
about 20 can be achieved
  The multiple lens can correct for aberrations



                                                  29
   p             p
Compound Microscope
 A compound
 microscope consists
 of two lenses
   Gives greater
   magnification than a
      g
   single lens
   The objective lens has a
   short focal length, ƒo<1
   cm
   The ocular lens
   (eyep ece) as oca
   (eyepiece) has a focal
   length, ƒe of a few cm
                              30
        p             p
     Compound Microscope
The lens are separated by a distance L
   L is much greater than either focal length
The approach to analysis is the same as for any
two lenses in a row
   The image formed by the first lens becomes
   the object for the second lens
                         eye,      virtual
The image seen by the eye I2, is virtual,
inverted and very much enlarged

                                             31
  Magnifications of the Compound
             Microscope
The lateral magnification of the microscope is
                     q
              M = − pl ≈ − L
                l      l   ƒo
The angular magnification of the eyepiece of the
microscope is
                      me = 25 cm
                             ƒe
          ll      ifi ti
Th overall magnification of th microscope i the
The                         f the i       is th
product of the individual magnifications
                          L ⎛ 25 cm ⎞
             m = M me = − ⎜         ⎟
                  l      ƒo ⎜ ƒe ⎟
                            ⎜
                            ⎝
                                    ⎟
                                    ⎠
                                                   32
Other Considerations with a
        Microscope
The ability of an optical microscope to view
an object depends on the size of the object
relative to the wavelength of the light used
to observe it
  For example, you could not observe an atom
  (d ≈ 0.1 nm) with visible light (λ≈ 500 nm)
                                  (λ



                                                33
Telescopes
 Two fundamental types of telescopes
   Refracting telescope uses a combination of lens to
   form an image
   R fl ti telescope uses a curved mirror and a
   Reflecting t l                  d i         d
   lens to form an image
   l            b      l db          d
 Telescopes can be analyzed by considering
 them to be two optical elements in a row
   The image of the first element becomes the object
   of the second element
                                               34
Refracting Telescope
 The two lenses are arranged so
                            real,
 that the objective forms a real
 inverted image of a distance
 object
 The image is near the focal
 point of the eyepiece
 The two lenses are separated
 by the distance ƒo + ƒe which
 corresponds to the length of
 the tube
 th t b
 The eyepiece forms an
 enlarged, inverted image of the
 first image
                                    35
Angular Magnification of a
Telescope
   The angular magnification depends on the
   focal lengths of the objective and eyepiece
        θ ƒo
      m= =
        θo ƒe
   Angular magnification is particularly important
   for observing nearby objects
     Very distance objects still appear as a small point of
     light
                                                              36
Reflecting Telescope
   Helps overcome some of the disadvantages of
            g        p
   refracting telescopes
     Replaces the objective lens with a mirror
     The mirror is often parabolic to overcome spherical
      b    ti
     aberrations
   In addition, the light never passes through
    l
   glass
     Except the eyepiece
     Reduced chromatic aberrations
                                                           37
Reflecting Telescope, Newtonian
Focus
 The incoming rays are
 reflected from the mirror
             g
 and converge toward
 point A
   At A, a photographic plate or
   other detector could be
   placed
                     , ,
 A small flat mirror, M,
 reflects the light toward
 an opening in the side
  nd p e
 and passes into an  n
 eyepiece                          38
Examples of Telescopes
   Reflecting Telescopes
        g
     Largest in the world are 10 m diameter
     Keck telescopes on Mauna Kea in Hawaii
     Largest single mirror in US is 5 m diameter
     on Mount Palomar in California
   Refracting Telescopes
     Largest in the world is Yerkes Observatory
     in Wisconsin
       Has a 1 m diameter
                                                   39

				
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