Optical Instruments

1
Chapter 25

• 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 nature of
  light must be used

3
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
• Most cameras with variable -numbers adjust them
  automatically

8
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

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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

11
The Eye Operation

• 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

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 cont

• 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

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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

21
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 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

23
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 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

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Angular Magnification

• Angular magnification is defined as
• 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

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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 multiple lenses magnifications of up to
  about 20 can be achieved
• The multiple lenses can correct for aberrations

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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

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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 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
• 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 microscope is
• The angular magnification of the eyepiece of the
  microscope is
• 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)

31
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 distant 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

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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
• Very distant 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

35
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 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

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Resolution

• The ability of an optical system to distinguish
  between closely spaced objects is limited due to
  the wave nature of light
• If two sources of light are close together they
  can be treated as non-coherent sources
• Because of diffraction the images consist of
  bright central regions flanked by weaker bright
  and dark rings

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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 be
  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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Resolving Power of a Diffraction Grating

• If 1 and 2 are 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

45
Michelson Interferometer

• The Michelson Interferometer is an optical
  instrument that has great scientific importance
• 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

46
Michelson Interferometer schematic

• A beam of light provided by a monochromatic
  source is split into two rays by a partially
  silvered 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 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