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Vision: Focusing
W. Rose
See Martini & Ober (VA&P), chapter 15.
See Marieb & Hoehn (9th ed.), chapter 15.
Useful source of information:
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/visioncon.html
Department of Kinesiology and Applied Physiology
Object distance
o
Image distance
i
Figures from Visual
Anatomy and
Physiology, © 2011.
Image distance* (i) is determined by lens shape
(curvature, C) and distance to object being
viewed (o).
* VA&P calls the image distance "focal distance".
Department of Kinesiology and Applied Physiology
i 1 
1

C  o 




Equation for a lens
made of glass, in air.
Object distance
o
Image distance
i
Figures from Visual
Anatomy and
Physiology, © 2011.
i 1 
1

C  o 


When an object is far away, the object
distance o is large. When o gets large, i
gets small (if curvature is constant).


When o=infinity, i=1/3C.
Department of Kinesiology and Applied Physiology
Object distance
o
Image distance
i
When lens curvature C increases
(rounder lens), image distance i
gets smaller (if o is constant).
i 1 
1

C  o 


Department of Kinesiology and Applied Physiology


Summary
1. When object distance o gets smaller, image distance i gets
larger (if curvature is constant).
2. When curvature C increases, i gets smaller (if o is
constant).
3. Therefore, if C increases while o decreases (lens gets
rounder as object gets closer), it is possible to keep i
constant. In other words, the image will stay in focus at a
constant distance from the lens. This is what we want for
vision, since the distance from lens to retina is constant.
i 1 
1

C  o 




Department of Kinesiology and Applied Physiology
Background page showing the derivation of the equation for i.
Thin lens
equation
1 1 1
 
o i f
1 1 1
 
i f o
1
i
 1 1
  
 f o
Top equation above is
offered without proof.
For a glass lens
in air:
1
C
f
where C = lens
curvature: a
flat lens has
low curvature,
a round lens
has high
curvature.
C=1/R, R=radius of curvature, presumed
same on front & back of lens.
Image distance i
i 1 
1

C  o 




Image distance (i, distance to
focal point) depends on object
distance (o) and lens shape
(curvature C).
Equation above follows from the
equations in the previous boxes.
Department of Kinesiology and Applied Physiology
More background: glass lens in air versus human lens in ocular humors.
Thin lens immersed in a medium with index n0:


n

n


1  lens o  1  1 
no  R R 
f
 1
2






Glass in air, double convex
R1=1/C, R2= -1/C:
Human lens, aqueous &
vitreous humor:
1  1.512C   C
f  1  
1  1.411.34 2C   0.1C
f  1.34  
i
Top equation above is
offered without proof.
1
C 1 o
Image distance i
C=1/R, R=radius of curvature, presumed
same on front & back of lens.
i
1
0.1C 1 o
Lower equations follow from top
equation and from 1/f=1/i+1/o.
Department of Kinesiology and Applied Physiology
How is the non-uniform
refractiveindex of the lens
handled in the model? To
answer , compare results on
slide to calculations of powers:
P = (n2-n1) / R
From aqueous humor into lens,
using central n2:
n1=1.336, n2=1.406, R=.008672
P=0.070/.008672=8.07m-1
This calculated power matches
the result on the diagram.
Evidently the model uses the
central lens index for
calculations.
Eye model by Carl Rod Nave. Retreived 2012-05-09.
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/eyescal.html
Model check: Sum of powers = 63.7 m-1, which corresponds to focal length 15.7 mm,
which equals model distance from back of lens to retina (estimated by measurements on
diagram above and by subtracting sum of distances listed from 24 mm).
Note: Real lens has greater index of refraction (n) at center than at periphery. A check
shows that the model uses the central n to compute focusing power.
Department of Kinesiology and Applied Physiology