Optical instruments

1
Optical instruments

• PHY232
• Remco Zegers
• zegers_at_nscl.msu.edu
• Room W109 cyclotron building
• http//www.nscl.msu.edu/zegers/phy232.html

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optical instruments

• Most optical instruments involve just the laws of
  reflection and refraction microscope, telescope
  etc
• some optical instruments make use of the
  wave-nature of light, such as the interferometer
• In this chapter we consider some optical
  instruments, starting with the eye

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the eye

• the eye essentially consists of a lens that
  focuses light on the retina. The ciliary muscles
  are used to change the curvature of the lens and
  hence the focal length.

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the eye II

• when the ciliary muscles are relaxed, an object
  at infinity is focused onto the retina. The focal
  length is about 1.7 cm.
• optometrists define the power P of a lens in
  terms of diopters
• D1/f (f in m, D in diopters 1/m)
• the typical eye has a power of 1/0.017 m59
  diopters

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the far-point

• The largest distance that can clearly be seen is
  called the far-point FP.
• a good human eye can visualize objects that are
  extremely far away (moon/stars) and the far point
  is then close to infinity.

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nearsightedness (myopia)

• In case of nearsightedness, the far-point is much
  smaller than infinity for example because the
  eyeball is elongated.
• on object placed at infinity is focused in front
  of the retina.
• this can be corrected using a diverging lens

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example

• A person cannot see objects clearly that are more
  than 50 cm away from his eye. An optometrist
  therefore prescribes glasses to solve the
  problem. What should the power of the lens be (in
  diopters) to solve the problem? You can ignore
  the distance between the glasses and the eye lens.

20/20 vision you can see on the chart what
average people can see from 20 feet
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the near point

• The near-point is the closest distance in front
  the eye that a person is capable of focusing
  light on the retina
• the near-point for a normal person is about 25
  cm, making it hard to focus an object closer to
  you eyes than that.

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farsightedness (hyperopia)

• happens when the near-point is much larger than
  25 cm.
• it becomes hard to see objects nearby since the
  eye muscles cannot accommodate it.
• it can be corrected using a converging lens
  (reading glasses)

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example

• a person suffering from hyperopia has a near
  point of 1 m.
• The optometrist has to prescribe a lens of what
  power to put the near point back at 25 cm?

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question

• a person has a far-point of 1 m and a near point
  of 75 cm. In order to help this person see
  objects that are far away and allows him/her to
  read a book
• a) bi-focal glasses are needed, which are partly
  diverging and partly converging
• b) glasses are needed that bring the far-point
  and the near-point together
• c) an operation is needed to solve at least one
  of the problems so that the other can be solved
  with glasses

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lon-capa

• do questions 10,11 from set 9

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simple magnifier

• normal eye cannot focus if the object distance lt
  near point (NP)
• therefore, the maximum subtended angle equals
• ?0h/NPh/(25 cm)
• (assumed that tan?? ? small
• if we put the same object in front of a
  converging lens with pltf, a virtual upright image
  is created
• 1/p1/q1/f with pltf
• qpf/(p-f) with pltf so q negative
• Mhimage/hobject
• -q/p-f/f-p with pltf so Mgt1
• maximum subtended angle now equals ?Ih/qh/p
• angular magnification m?I/?0
• m?I/?0(h/p)/(h/NP)NP/p

eye
?0
h
NP
h
h
p
f
q
the best result is obtained if the image is at
infinity (eye relaxed). to do so pf and mNP/f
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example

• A lens with f10 cm is used as a magnifier. What
  is the angular magnification if the image if
  formed at the near point?
• What is the angular magnification if the eye is
  relaxed (image at infinity?)

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the microscope
L
uses two converging lenses with focal lengths f1
and f2 with f2gtf1 moreover, Lgtgtf2 For lens 1 p1
is chosen such that q1L (image 1 will appear
just within F2) This happens when p1f1 so
M1-q1/p1-L/f1 Lens two then acts as a
magnifying glass with m2NP/f225/f2 The
magnifying power is defined as mM1m2(-L/f1)(25/f
2)-25L/(f1f2) (all units in cm), usually
written as m-25L/(fOfe) (inverted!) with O for
objective and e for eyepiece
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example
A red blood cell has a size of about 7x10-6 m. A
microscope is used to visualize it. The
microscope has L30cm, f01 cm, fe0.5 cm. How
large is the cell when seen through the
microscope?
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a telescope
L
size of image of objective lens hi
?e
?o

• a telescope is very similar to a microscope
  except that the lenses are slightly differently
  configured
• light comes in (from a star) almost parallel. It
  is focused at the focus point fo of the first
  converging (objective) lens.
• this image becomes the object for the second
  converging (eyepiece) lens and is place just at
  the focal length fe of that lens.
• tan(?o)??ohi/fo
• tan(?e)??ehi/fe
• magnifying power m ?e/?ofo/fe note Lf0fe

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example

• A telescope has two lenses which are 92 cm apart
  from eachother. The angular magnification of the
  telescope is 45. What are the focal lengths of
  the objective and eye-piece lens?

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loncapa

• do problem 12 from lon-capa 9

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resolution

• resolution the ability of an optical system to
  distinguish between two closely spaced objects
• resolution is limited by the wave nature of
  light when light passes through a slit, it is
  diffracted and thus smeared out.
• if the angular separation becomes two small,
  objects become hard to distinguish

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rayleighs criterion

• two images are just resolved if rayleighs
  criterion is fulfilled.
• Rayleighs criterion the central maximum of
  image A false into the first minimum of image B
• first diffraction minimum sin????/a with A the
  slitwidth
• images separated by a minimum angle ?min?/a can
  just be resolved
• if the aperture is circular with diameter D
  ?min1.22?/D

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question

• ?min1.22?/D

• a binary star system consists of two stars that
  are rotating around each other. Because of there
  closeness they are hard to separate. A color
  filter can be used to improve the separation. Is
  it better to use blue or red to make a picture
  that best separates the stars?

• Blue
• Red
• doesnt matter

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lon-capa

• do problem 13 from lon-capa 9
• use ?min1.22?/D
• distance earth moon is 3.84E8 m
• how to calculate ?min? you can use tan??
  (radians)
• use a wavelength of 550 nm

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The Michelson Interferometer

• monochromatic light is incident on mirror
• light travels to moveable mirror and is
• reflected
• some light is also passed through and is
• reflected
• beam 3) and 5) interfere and make an interference
  pattern
• by moving the moveable mirror, the path length
  difference can be varied

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Michelson interferometer

• the compensator servers to make sure that the
  light going to either branch travels the same
  distance through the glass.
• The path length difference D2d23-2d45
• If the movable mirror moves by ?/2, D changes by
  ? and the interference pattern is shifted by 1
  fringe.
• Insertion of a material with index of refraction
  n in path 2-3 will also make a path length
  difference, and by observing the change in the
  interference pattern, one could determine n
• more about this in the last weeks lecture on
  relativity