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Optical Instruments

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Title: Optical Instruments


1
Chapter 25
  • Optical Instruments

2
General Remarks
  • Analysis generally involves the laws of
    reflection and refraction
  • Analysis uses the procedures of geometrical
    optics
  • To explain certain phenomena, the wave nature of
    light must be used

3
25.1 The Camera
  • The single-lens photographic camera is an optical
    instrument
  • Components
  • Light-tight box
  • Converging lens
  • Produces a real image
  • Film behind the lens
  • Receives the image

4
Camera Operation
  • Proper focusing leads to sharp images
  • The lens-to-film 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
  • Most cameras have an aperture of adjustable
    diameter to further control the intensity of the
    light reaching the film
  • With a small-diameter aperture, only light from
    the central portion reaches the film, and
    spherical aberration is minimized

5
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 film
    depends on the light intensity
  • Depends on both the focal length and the diameter
    of the lens

6
Camera, f-numbers
  • The -number of a camera is the ratio of the
    focal length of the lens to its diameter
  • -number f/D
  • The -number is often given as a description of
    the lens speed
  • A lens with a low f-number is a fast lens

7
Camera, f-numbers, cont.
  • Increasing the setting from one -number to the
    next higher value decreases the area of the
    aperture by a factor of 2
  • The lowest -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
    and a fixed aperture size, with an -number of
    about 11 (large depth of field)
  • Most cameras with variable -numbers adjust them
    automatically

8
25.2 The Eye
  • The normal eye focuses light and produces a sharp
    image
  • Essential parts of the eye
  • Cornea light passes through this transparent
    structure
  • Aqueous Humor clear liquid behind the cornea

9
The Eye Parts, cont.
  • The pupil
  • 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

10
The Eyes Parts, final
  • 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
    conditions and contracting the pupil in
    high-light conditions
  • The f-number of the eye is from about 2.8 to 16

11
The Eye How Does It Work?
  • The cornea-lens system focuses light onto the
    back surface of the eye
  • 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

12
The Eye Operation, cont.
  • 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
    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 to the edge of the lens

13
The Eye Focusing
  • The eye can focus on a distant object
  • The ciliary muscle is relaxed
  • The zonules tighten
  • This causes the lens to flatten, increasing its
    focal length
  • 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

14
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
  • The image is focused on the retina

15
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
  • 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 focus light on the retina
  • Normal vision has a far point of infinity

16
Conditions of the Eye
  • Eyes may suffer a mismatch between the focusing
    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

17
Farsightedness
  • Also called hyperopia
  • The image focuses behind the retina
  • Can usually see far away objects clearly, but not
    nearby objects

18
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

19
Nearsightedness
  • Also called myopia
  • In axial myopia the nearsightedness is caused by
    the lens being too far from the retina
  • In refractive myopia, the lens-cornea system is
    too powerful for the normal length of the eye

20
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

21
Presbyopia and Astigmatism
  • Presbyopia (old-age vision) 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 (farsightedness)
  • 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 are not perfectly symmetric

22
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/
  • E.g., a converging lens of focal length 20 cm
    has a power of 5.0 diopters

23
25.3 Simple Magnifier
  • 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

24
The Size of a Magnified Image
  • When an object is placed at the near point, the
    angle subtended is maximum
  • The near point is about 25 cm
  • When the object is placed just inside the focal
    point of a converging lens, the lens forms a
    virtual, upright, and enlarged image

25
Angular Magnification
  • Angular magnification is defined as
  • The angular magnification is a maximum when the
    image formed by the lens is at the near point of
    the eye
  • q - 25 cm
  • Calculated by

26
Magnification by a Lens
  • With a single lens, it is possible to achieve
    angular magnification up to about 4 without
    serious aberrations
  • With one or two additional lenses, which correct
    the aberrations, a magnification of up to about
    20 can be achieved

27
25.4 Compound Microscope
  • A compound microscope consists of two lenses
  • Gives greater magnification than a single lens
  • The objective lens has a short focal length, olt1
    cm
  • The ocular lens (eyepiece) has a focal length, e
    of a few cm

Note q1?L and p1?f0
28
Compound Microscope, cont.
  • The lenses are separated by a distance L
  • L is much greater than either focal length
  • The approach to analyze the image formation 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
  • The image seen by the eye, I2, is virtual,
    inverted and very much enlarged

29
Magnifications of the Compound Microscope
  • The lateral magnification of the objective is
  • The angular magnification of the eyepiece of the
    microscope is

30
Overall magnification
  • The overall magnification of the microscope is
    the product of the individual magnifications

31
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 (? ? 500 nm)

32
25.5 Telescopes
  • Two fundamental types of telescopes
  • Refracting telescope uses a combination of lenses
    to form an image
  • Reflecting telescope uses a curved mirror and a
    lens to form an image
  • 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

33
Refracting Telescope
  • The two lenses are arranged so 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 o
    e, which corresponds to the length of the tube
  • The eyepiece forms an enlarged, inverted image of
    the first image

Note q?h/fe and q0 ?h/f0
34
Angular Magnification of a Telescope
  • The angular magnification depends on the focal
    lengths of the objective and eyepiece
  • Angular magnification is particularly important
    for observing nearby objects (sun, moon,)
  • Very distance objects still appear as a small
    point of light

35
Disadvantages of Refracting Telescopes
  • Large diameters are needed to study distant
    objects
  • Large lenses are difficult and expensive to
    manufacture
  • The weight of large lenses leads to sagging,
    which produces aberrations

36
Reflecting Telescope
  • Helps overcome some of the disadvantages of
    refracting telescopes
  • Replaces the objective lens with a mirror
  • The mirror is often parabolic to overcome
    spherical aberrations
  • In addition, the light never passes through glass
  • Except the eyepiece
  • Reduced chromatic aberrations

37
Reflecting Telescope, Newtonian Focus
  • The incoming rays are reflected from the mirror
    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 and passes into an eyepiece

38
Examples of Telescopes
  • Reflecting Telescopes
  • Largest in the world are 10 m diameter Keck
    telescopes on Mauna Kea in Hawaii
  • Largest single-mirrored telescope in US is the 5
    m diameter instrument on Mount Palomar in
    California
  • Refracting Telescopes
  • Largest in the world is Yerkes Observatory in
    Wisconsin
  • Has a 1 m diameter

39
25.6 Resolution
  • The ability of an optical system to distinguish
    between closely spaced objects is limited due to
    the wave nature of light
  • Consider two not coherent light sources (like
    stars)
  • Because of diffraction, the images consist of
    bright central regions flanked by weaker bright
    and dark rings

(a) Images are resolved and (b) not resolved
(sources too close)
40
Rayleighs Criterion
  • If the two sources are separated so that their
    central maxima do not overlap, their images are
    said to be resolved
  • The limiting condition for resolution is
    Rayleighs Criterion
  • When the central maximum of one image falls on
    the first minimum of another image, they images
    are said to be just resolved
  • The images are just resolved when their angular
    separation satisfies Rayleighs criterion

41
Just Resolved
  • If viewed through a slit of width a, and applying
    Rayleighs criterion, the limiting angle of
    resolution is
  • For the images to be resolved, the angle
    subtended by the two sources at the slit must
    greater than ?min

42
Barely Resolved (Left) and Not Resolved (Right)
43
Resolution with Circular Apertures
  • The diffraction pattern of a circular aperture
    consists of a central, circular bright region
    surrounded by progressively fainter rings
  • The limiting angle of resolution depends on the
    diameter, D, of the aperture

44
Suppose you are observing a binary star with a
telescope and are having difficulty resolving the
two stars. You decide to use a colored filter to
help you. Should you choose a blue filter or a
red filter?
QUICK QUIZ 25.1
45
Resolving Power of a Diffraction Grating
  • If ?1 and ?2 are two nearly equal wavelengths
    between which the grating spectrometer can just
    barely distinguish, the resolving power, R, of
    the grating is
  • All the wavelengths are nearly the same

46
Resolving Power of a Diffraction Grating, cont
  • A grating with a high resolving power can
    distinguish small differences in wavelength
  • The resolving power increases with order number
  • R Nm
  • N is the number of lines illuminated
  • m is the order number
  • All wavelengths are indistinguishable for the
    zeroth-order maximum
  • m 0 so R 0

47
25.7 Michelson Interferometer
  • The Michelson Interferometer is an optical
    instrument that has great scientific importance,
    but is unfamiliar to most people
  • It splits a beam of light into two parts and then
    recombines them to form an interference pattern
  • It is used to make accurate length measurements

48
Michelson Interferometer, schematic
  • A beam of light provided by a monochromatic
    source is split into two rays by mirror M
  • One ray is reflected to M1 and the other
    transmitted to M2
  • After reflecting, the rays combine to form an
    interference pattern
  • The glass plate ensures that both rays travel the
    same distance through glass

49
Measurements with a Michelson Interferometer
  • The interference pattern for the two rays is
    determined by the difference in their path
    lengths
  • When M1 is moved a distance of ?/4, successive
    light and dark fringes are formed
  • This change in a fringe from light to dark is
    called fringe shift
  • The wavelength can be measured by counting the
    number of fringe shifts for a measured
    displacement of M
  • If the wavelength is accurately known, the mirror
    displacement can be determined to within a
    fraction of the wavelength
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