Optical Instruments

1
Chapter 25

• Optical Instruments

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Farsightedness

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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
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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

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Magnifications of the Compound Microscope

• The lateral magnification of the objective is
• The angular magnification of the eyepiece of the
  microscope is

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Overall magnification

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

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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)

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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

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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
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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

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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

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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

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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

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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

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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)
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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

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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

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Barely Resolved (Left) and Not Resolved (Right)
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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

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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
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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

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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

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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

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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

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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