Overview object at infinity
•
Last time:
– thin lens – object at infinity – image at infinity
•
Today:
– imaging at finite distances
– thick lens
– the human eye
image at infinity
MIT 2.71/2.710
02/18/09 wk3-b- 1
1
Image formation at finite distances lens
from on-axis
object at ∞
Back
Focal
Point
BFP
object
image
FFP
Front
Focal
Point
to on-axis
image at ∞
(Newton’s
form)
Lateral
magnification
Imaging condition
MIT 2.71/2.710
02/18/09 wk3-b- 2
2
Real and virtual images object
+
image
+
object
image
BFP
FFP
image: real & inverted; MT<0
image
image: virtual & erect; MT>1 image
–
BFP
FFP
object
–
object
BFP
FFP
image: virtual & erect; 0<MT<1
BFP
FFP
image: virtual & erect; 0<MT<1 MIT 2.71/2.710
02/18/09 wk3-b- 3
3
Example: composite lens \1 5
5
?
1
image
(guess)
original
object
L1, f=10
L2, f=10
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.
Begin by considering the first lens in isolation:
–10
2
5
?
1
intermediate
image formed
by L1 (actual:
virtual, erect)
MIT 2.71/2.710
02/18/09 wk3-b- 4
intermediate
image formed
by L1 (guess)
original
object
L1, f=10
4
Example: composite lens \2 5
5
30
final
? image formed
1
by L2 (actual:
real, inverted)
image
(guess)
original
object
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 –10
2
intermediate
image formed
by L1 (actual)
acting as object
for L2
MIT 2.71/2.710
02/18/09 wk3-b- 5
15
?
final
image formed
by L2 (guess)
L2, f=10
5
Imaging condition using ray transfer matrices
lens
Back
Focal
Point
BFP
object
image
FFP
Front
Focal
Point
Imaging
condition
MIT 2.71/2.710
02/18/09 wk3-b- 6
6
Thick lens BFP
Back
Focal
Point
FFP
Front
Focal
Point
MIT 2.71/2.710
02/18/09 wk3-b- 7
7
Focal Lengths and Principal Planes 2nd PP
Back
Principal
Plane
(or Surface)
BFP
FFP
Back
Focal
Point
(or Plane)
Front
Focal
Point
(or Plane)
EFL
1st PP
Front
Principal
Plane
(or Surface)
EFL
ray from
infinity
FFP
BFP
FFL
EFL
BFL
EFL
ray from
the FFP
1st PP
then goes
through the BFP
FFP
BFP
bends at
1st PP
1st PP
MIT 2.71/2.710
02/18/09 wk3-b- 8
bends at
2nd PP
then goes
on to infinity
2nd PP
2nd PP
8
Image formation with composite elements composite element (e.g., thick lens) 1st PP
2nd PP
BFP
object
image
FFP
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.
➡
MIT 2.71/2.710
02/18/09 wk3-b- 9
9
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.
MIT 2.71/2.710
02/18/09 wk3-b-10
10
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.
MIT 2.71/2.710
02/18/09 wk3-b- 11
11
The human eye Image courtesy of NIH National Eye Institute.
FFP
BFP
Photo from Wikimedia Commons.
1.5cm
Remote objects:
unaccommodated eye
(lens muscles relaxed)
Nearby objects: accommodated eye (lens muscles contracted) 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.
from
For more information, see http://ocw.mit.edu/fairuse.
MIT 2.71/2.710
02/18/09 wk3-b-12
Fundamentals of Optics
by F. Jenkins & H. White
12
Eye defects and their correction from Fundamentals of Optics
by F. Jenkins & H. White
MIT 2.71/2.710
02/18/09 wk3-b-13
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.
13
The eye’s “digital camera”: retina Macula Optic Nerve head
Retina
Image by Danny Hope at Wikimedia Commons.
Image by the NRC Committee on Undersea Warfare.
Retina:
➡ variable sampling rate
➡ “dead pixels” (fovea)
are compensated for
Digital camera:
➡ fixed sampling rate
➡ “dead pixels” (fovea)
are noticeable
MIT 2.71/2.710
02/18/09 wk3-b-14
14
Retina vs your digital camera Retinal image
CCD image
Courtesy of Laurent Itti. Used with permission.
http://www.klab.caltech.edu/~itti/
MIT 2.71/2.710
02/18/09 wk3-b-16
16
Spatial response of the retina – lateral connections Image removed due to copyright restrictions.
Please see http://williamcalvin.com/bk4/bk4.htm
Image from Ramón y Cajal, Santiago. "Structure of the Mammalian Retina." Madrid, 1900.
MIT 2.71/2.710
02/18/09 wk3-b-17
17
What do you see? http://www.phys.ufl.edu/~avery/
MIT 2.71/2.710
02/18/09 wk3-b-18
18
Temporal response: after-images Courtesy of David T. Landrigan. Used with permission.
http://dragon.uml.edu/psych/
MIT 2.71/2.710
02/18/09 wk3-b-19
19
Seeing 3D: binocular vision Photo by mosso on Flickr.
http://www.ccom.unh.edu/vislab/VisCourse
Courtesy of Colin Ware. Used with permission.
Photo from Wikimedia Commons.
MIT 2.71/2.710
02/18/09 wk3-b-20
20
MIT OpenCourseWare
http://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.