Overview object at infinity image at infinity
• Last time: – thin lens – object at infinity – image at infinity
• Today: – imaging at finite distances – thick lens – the human eye
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Image formation at finite distances
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object
image
FFP Front Focal Point
Back Focal Point BFP
lens from on-axis object at ∞
to on-axis image at ∞
Lateral magnification Imaging condition
(Newton’s form)
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Real and virtual images
BFP
object
image
FFP BFP
object
image
FFP
+ +
image: real & inverted; MT<0 image: virtual & erect; MT>1
FFPBFP
object
image –
FFPBFP
object image –
image: virtual & erect; 0<MT<1 image: virtual & erect; 0<MT<1
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Example: composite lens \1
L1, f=10 L2, f=10
5 5
original object
image
? 1
(guess)
We seek the image location and lateral magnification for the composite lens imaging system shown above. We will solve the problem by repeated application of the imaging condition and lateral magnification relationships that we derived in Slide #2.
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Begin by considering the first lens in isolation:
L1, f=10L1,
original object
?1
intermediate image formed by L1 (guess)
5
original
f=10
object
12
intermediate image formed by L1 (actual: virtual, erect)
–10
4
L1, f=10 L2, f=10
5 5
originalobject
?1
image (guess)
Example: composite lens \2 5 5
original object
1
30final
image formed by L2 (actual: real, inverted)
L1, f=10 L2, f=10 –4 Next we consider L2 in isolation, with object identical to the image formed by L1 in isolation.
The overall (composite) magnification is
2 ?
final image formed intermediate
image formed by L1 (actual) by L2 (guess)
acting as object for L2
–10 15
L2, f=10MIT 2.71/2.710 02/18/09 wk3-b- 5
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Imaging condition using ray transfer matrices lens
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object
image
FFP Front Focal Point
Back Focal Point BFP
Imaging condition
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Focal Lengths and Principal Planes
BFP Back Focal Point
(or Plane)2nd PP
Back Principal
Plane (or Surface)
EFL
ray from infinity bends at
2nd PP
ray from the FFP
FFP Front Focal Point
(or Plane) 1st PP
Front Principal
Plane (or Surface)
EFL
FFP
1st PP 2nd PP
BFP
FFL BFL
EFL EFL
FFP BFP
bends at then goes 1st PP on to infinity
1st PP 2nd PP MIT 2.71/2.710 02/18/09 wk3-b- 8
then goes through the BFP
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Image formation with composite elements composite element (e.g., thick lens)
object FFP
BFP image
1st PP 2nd PP
To find the imaging condition for the composite element we can use the principal planes as follows: ➡ trace an on-axis ray from infinity through O to the 2nd PP then bend so that it goes through the BFP; ➡ trace a ray from O through the FFP then bend at the 1st PP so that it goes to infinity on-axis; ➡ the intersection of the traced rays is the image point I; ➡ the ray from O through the intersection of the 1st PP with the optical axis should emerge at the
intersection C of the 2nd PP with the optical axis and also go through the image point I; moreover, if the indices of refraction to the left and right of the composite are the same, then OC ||C’I.
➡ It is easy to see that the similar triangle arguments that we used in the case of the single thin lens apply here as well; therefore, the imaging condition and magnification relations remain the same with the notation as shown above.
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Imaging systems in nature: chambered eyes
Image removed due to copyright restrictions. Please see Fig. 1 a,c,d,g in Fernald, Russell D. "Casting a Genetic Light on the Evolution of Eyes." Science 313 (2006): 1914-1918.
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Imaging systems in nature: compound eyes
Image removed due to copyright restrictions. Please see Fig. 1 b, e, f, h in Fernald, Russell D. "Casting a Genetic Light on the Evolution of Eyes." Science 313 (2006): 1914-1918.
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The human eye
Photo from Wikimedia Commons.
Image courtesy of NIH National Eye Institute.
Remote objects: unaccommodated eye (lens muscles relaxed)
Nearby objects: accommodated eye
(lens muscles contracted)
from Fundamentals of OpticsMIT 2.71/2.710 by F. Jenkins & H. White 02/18/09 wk3-b-12
FFP 1.5cm
BFP
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Fig. 10B in Jenkins, Francis A., and Harvey E. White. Fundamentals of Optics.4th ed. New York, NY: McGraw-Hill, 1976. ISBN: 9780070323308. (c) McGraw-Hill. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.
Eye defects and their correction
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from Fundamentals of Optics by F. Jenkins & H. White
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.Fig. 10K,L in Jenkins, Francis A., and Harvey E. White. Fundamentals of Optics. 4th ed.New York, NY: McGraw-Hill, 1976. ISBN: 9780070323308. (c) McGraw-Hill. All rights reserved.This content is excluded from our Creative Commons license.For more information, see http://ocw.mit.edu/fairuse.
The eye’s “digital camera”: retina Macula Optic Nerve head
Image by Danny Hope at Wikimedia Commons.
Image by the NRC Committee on Undersea Warfare.
Retina: Digital camera: ➡ variable sampling rate ➡ fixed sampling rate ➡ “dead pixels” (fovea) ➡ “dead pixels” (fovea) are compensated for are noticeable
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Retina
Retina vs your digital camera
Retinal image CCD image Courtesy of Laurent Itti. Used with permission.
http://www.klab.caltech.edu/~itti/
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Spatial response of the retina – lateral connections
Image from Ramón y Cajal, Santiago. "Structure of the Mammalian Retina." Madrid, 1900.
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Image removed due to copyright restrictions.Please see http://williamcalvin.com/bk4/bk4.htm
What do you see?
http://www.phys.ufl.edu/~avery/
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Temporal response: after-images
Courtesy of David T. Landrigan. Used with permission.
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http://dragon.uml.edu/psych/
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Seeing 3D: binocular vision
Photo by mosso on Flickr.
http://www.ccom.unh.edu/vislab/VisCourse
Courtesy of Colin Ware. Used with permission.
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Photo from Wikimedia Commons.
MIT OpenCourseWarehttp://ocw.mit.edu
2.71 / 2.710 Optics Spring 2009
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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