Magnification

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Magnification
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Magnification
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• Relationship between object and image height in
  any optical system
• Can be expressed in many different ways

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Relative Magnification
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• Used to compare the sizes of two different
  images
• Relative size magnification
• Relative distance magnification

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Relative Size Magnification
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• Comparing the size of two objects in terms of the
  angle each subtends at (e.g.) the eye

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Relative Size Magnification
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Relative Size Magnification
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• Example find relative size magnification of two
  different print sizes on a near point card at a
  35 cm reading distance

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Appearance of printed matter with different types
of astigmatism depends onAppearance of printed
matter with different types of astigmatism
depends on orientation of principal Appearance of
printed matter with different types of
astigmatism depends on orientation of principal
meridians and on which focal line is closer to
the Appearance of printed matter with different
types of astigmatism depends on orientation of
principal meridians and on which focal line is
closer to the retina. The shape of objects in our
environment consists predominantly of Appearance
of printed matter with different types of
astigmatism depends on orientation of principal
meridians and on which focal line is closer to
the retina The shape of objects in our
environment consists predominantly of horizontal
and vertical lines. This is also the case with
visual acuity chart letters. It follows that
vision, both in everyday tasks and on reading the
visual acuity chart, is worse
36-point
x-height
8-point
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Relative Size Magnification
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• 36-point print (6.75 mm x height) ? lower
  case x subtends 66.3? (1.10O) at the eye (from
  35 cm)
• 8-point print (1.5 mm x height) ? lower case
  x subtends 14.7? (0.246O) at the eye (from 35
  cm)

Relative size magnification of 36-point and
8-point print at 35 cm reading distance
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Relative Distance Magnification
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Relative Distance Magnification
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Relative Distance Magnification
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• The same object viewed at different distances
  subtends a different angle at (e.g.) the eye

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Relative Distance Magnification
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Relative Distance Magnification
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The Simple Magnifier
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Example 1 - Simple Plus Lens Magnifier
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• An emmetropic patient reads the fine print on a
  reading card held 40 cm from the eye
• A 10 D lens is then used to magnify the image.
  The reading card is placed 6 cm from the lens
  and the lens is 4 cm from the (nodal point of
  the) eye
• Find angular magnification with the plus lens

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Example 1 - Simple Plus Lens Magnifier
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Example 1 - Simple Plus Lens Magnifier
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Example 1 - Simple Plus Lens Magnifier
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Example 1 - Simple Plus Lens Magnifier
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Collimating Magnifier (Plus Lens)
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• Place object at Flens ? image at infinity
• ?? ? ? L? 0

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Collimating Magnifier (Plus Lens)
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Image at infinity
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Example 2 - Collimating Magnifier

• An object 10 cm in front of the unaided eye is
  viewed
• A 20 D lens is now placed 3 cm from the eye
  (nodal point) and the object is moved to 4 cm
  from the lens
• Next, the object is moved out to approach Flens
• Calculate total magnification when the object
  reaches Flens ? the lens becomes a collimating
  magnifier

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Example 2 - Collimating Magnifier
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Example 2 - Collimating Magnifier
NOT TO SCALE
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Example 2 - Collimating Magnifier
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• Object approaching Flens

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Example 2 - Collimating Magnifier
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• Object at Flens ? parallel rays emerging from
  magnifier

Nodal ray angle at lens (?2) nodal ray angle at
eye (?2)
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Collimating Magnifier
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Example 2 - Collimating Magnifier

• ? for the collimating magnifier, the
  magnification equation (and ultimately retinal
  image height) is independent of distance between
  lens and eye
• Completing example 2, ?1 -10 cm Flens 20 D

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Collimate
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• To remove the false reading?
• French collimare a false reading
• Extracted from Latin collineare to direct in
  a straight line or make straight

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Increasing Magnification with Accommodation
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Near Magnification Near Point of Accommodation
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• Emmetropic (or distance-corrected) patients need
  not accommodate when looking through a
  collimating magnifier
• But, accommodation usually increases
  magnification
• Maximum magnification should be obtained when
  maximum accommodation is exerted (? amplitude of
  accommodation)

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Example 3 Near Magnification Accommodation
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• Two patients use a 32 D collimating magnifier to
  view a street map.
• Patient 1 has a 1 meter near point of
  accommodation (from Neye)
• Patient 2 has a 6.5 cm near point
• Find the increase in retinal image size for each
  patient when using the magnifier.

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Example 3 Near Magnification Accommodation
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Patient 1
Patient 2
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Example 3 Near Magnification Accommodation
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• With the same 32 D magnifier
• Patient 1 M 32 ?
• Patient 2 M 2.08 ?
• Here magnification represents the change obtained
  by each patient we are not comparing the two
  patients
• Patient 1 obtains much greater magnification with
  the same (32 D) lens because of the greater
  change between unaided and aided viewing distance
  ? greater change between unaided and aided
  retinal image height

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Near Magnifiers - Standard Reference Distance
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• The nominal magnification (NM) value for near
  magnifiers is standardized on a 25 cm unaided
  viewing distance (?1 ?25 cm) considered the
  least distance of distinct vision. Problem is,
  LDDV varies with age.
• Nominal magnification values underestimate the
  actual magnification (change) obtained by older
  patients, whose LDDV is beyond 25 cm, due to lt 4
  D amplitude of accommodation.
• Likewise, patients with (unaided) near points
  inside25 cm will obtain lower magnification than
  the standardized NM value

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Near Magnifiers - Standard Reference Distance
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• The angular magnification for a collimating
  magnifier based on the standardized 25 cm unaided
  viewing distance (?1 -25 cm) is

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Example 4 Standardized vs. Actual Magnification
An emmetrope with 5 D amplitude of accommodation
buys a 6? (NM) magnifier to read the phone book.
What actual angular magnification will she obtain
with the magnifier relative to her near point?

• Power of the magnifying lens 24 D
• Assume the lens is used as a collimating
  magnifier
• Near point 20 cm in front of eye (1/-5 D)

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Example 4 Standardized vs. Actual Magnification

• The magnifier is rated at 6? (NM) for the
  standard 25 cm unaided distance
• If the unaided distance is closer than 25 cm, the
  patient obtains lower magnification (4.8 ? in
  this case)

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Example 5 Standardized vs. Actual Magnification

• A patient with 40 cm near point uses a
  collimating magnifier to read the newspaper
• Actual magnification obtained with the magnifier
  is 9?
• What is the standard magnification (NM) of the
  lens?

Start by finding the actual power of the magnifier
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Collimating Magnifiers (Special Cases)

• Object at same distance from eye with and without
  magnifier
• Isoaccommodative Magnifier and Maximum
  Accommodation

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Collimating Magnifiers (Special Cases)

• Object at same distance from eye with and without
  magnifier

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Collimating Magnifier - Special Case (Object to
Eye Distance unchanged)
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Image at infinity
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Collimating Magnifier - Special Case (Object to
Eye Distance unchanged)
Image at infinity
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Collimating Magnifiers (Special Cases)
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• Object at same distance from eye with and without
  magnifier
• Isoaccommodative Magnifier and Maximum
  Accommodation
• isoaccommodative magnification means that the
  same amount of accommodation will be required
  with and without the magnifier
• this means that the virtual image produced by the
  magnifier must be in the same plane as the
  original object that was viewed unmagnified

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Isoaccommodative Magnifiers (Maximum
Accommodation)
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Isoaccommodative Magnifiers (Maximum
Accommodation)
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Isoaccommodative Magnifiers (Maximum
Accommodation)
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Isoaccommodative Magnifiers (Maximum
Accommodation)
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Magnification Image at ? vs. Maximum
Accommodation)
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