Physics 1161: Lecture 23
Lenses and your EYE
• textbook sections 27-1 – 27-3
Ciliary Muscles
Parts of the Eye
Review of Lenses
Preflight 23.11
Focal point determined by geometry and Snell’s Law:
n1 sin(q1) = n2 sin(q2)
P.A.
n1<n2
F
Fat in middle = Converging
Thin in middle = Diverging
Larger n2/n1 = more bending, shorter focal length.
n1 = n2 => No Bending, f = infinity
Lens in water has _________ focal length!
Review of Lenses
Preflight 23.11
Focal point determined by geometry and
Snell’s Law: n1 sin(q1) = n2 sin(q2)
P.A.
n1<n2
F
Fat in middle = Converging
Thin in middle = Diverging
Larger n2/n1 = more bending, shorter focal length.
n1 = n2 => No Bending, f = infinity
Lens in water has larger focal length!
Preflight 23.7
A converging lens is used to project a real image onto a
screen. A piece of black tape is then placed over the upper
half of the lens.
48% 1. Only the lower half will show on screen
40% 2. Only the upper half will show on screen
12% 3. The whole object will still show on screen
How much of the image appears on the screen?
Preflight 23.7
A converging lens is used to project a real image onto a
screen. A piece of black tape is then placed over the upper
half of the lens.
Preflight 23.7
Still see entire image (but dimmer)!
Two very thin converging lenses each
with a focal length of 20 cm are are
placed in contact. What is the focal
length of this compound lens?
1. 10 cm
2. 20 cm
3. 40 cm
44%
38%
19%
1
2
3
Two very thin converging lenses each
with a focal length of 20 cm are are
placed in contact. What is the focal
length of this compound lens?
1. 10 cm
2. 20 cm
3. 40 cm
94%
6%
1
2
0%
3
Amazing Eye
• One of first organs to develop.
• 100 million Receptors
10 million
– 200,000
– Sensitive to single photons!
/mm2
6,500 /mm2
• http://hyperphysics.phyastr.gsu.edu/hbase/vision/retina.html#c2
Ciliary Muscles
Digital Camera
Which part of the eye does most of the light
bending?
Ciliary Muscles
Cornea
n= 1.38
Lens
n = 1.4
Vitreous n = 1.33
56%
1.
2.
3.
4.
Lens
Cornea
Retina
Cones
31%
6%
1
2
3
6%
4
Which part of the eye does most of the light
bending?
Ciliary Muscles
Cornea
n = 1.38
Lens
n = 1.4
Vitreous n = 1.33
1.
2.
3.
4.
Lens
Cornea
Retina
Cones
63%
Laser eye surgery changes Cornea
Lens and cornea have similar shape, and index of
refraction. Cornea has air/cornea interface 1.38/1, 70%
of bending. Lens has Lens/Vitreous interface 1.4/1.33.
Lens is important because it can change shape.
19%
13%
6%
1
2
3
4
Preflight 23.9
A person with normal vision (near point at 26 cm) is standing in front of a plane
mirror.
What is the closest distance to the mirror where the person can stand and still see
himself in focus?
32%
1) 13 cm
56%
2) 26 cm
12% 3) 52 cm
Preflight 23.9
A person with normal vision (near point at 26 cm) is standing in front of a plane
mirror.
What is the closest distance to the mirror where the person can stand and still see
himself in focus?
26cm
1) 13 cm
2) 26 cm
3) 52 cm
13cm
Image from mirror becomes object for eye!
Multiple Lenses
Image from lens 1 becomes object for lens 2
1
2
f1
Complete the Rays to locate the final image.
f2
Multiple Lenses
Image from lens 1 becomes object for lens 2
1
2
f1
f2
Multiple Lenses: Magnification
1
do = 15 cm
2
L = 42 cm
f1
f2
f1 = 10 cm
di = 30 cm
Net magnification:
m1  
m2  
di
do

8.6 cm
12 cm
30 cm
15 cm
  .7 1 7
di = 8.6 cm
f2 = 5 cm
do=12 cm
mnet = m1 m2
 2
m net  m1 m 2  1.4
Near Point, Far Point
• Eye’s lens changes shape (changes f )
– Object at any do can have image be at retina
(di = approx. 25 mm)
• Can only change shape so much
• “Near Point”
– Closest do where image can be at retina
– Normally, ~25 cm (if far-sighted then further)
• “Far Point”
– Furthest do where image can be at retina
– Normally, infinity (if near-sighted then closer)
Preflight 23.10
Two people who wear glasses are camping.
One of them is nearsighted and the other is
farsighted. Which person’s glasses will be
useful in starting a fire with the sun’s rays?
Farsighted 68%
Nearsighted 32%
Preflight 23.10
Two people who wear glasses are camping.
One of them is nearsighted and the other is
farsighted. Which person’s glasses will be
useful in starting a fire with the sun’s rays?
Farsighted person’s glasses are converging –
like magnifying glass!
Angular Size
Both are same size, but nearer one looks bigger.
q
q
q
q
• Angular size tells you how large the image is
on your retina, and how big it appears to be.
Unaided Eye
How big the object looks with unaided
eye.
object
h0
q
N
Bring object as close as possible (to near point N)
tan( q ) 
ho
N
**If
q 
ho
N
q is small and expressed in radians.
Magnifying Glass
magnifying glass
virtual image
object
hi
q
ho
/
do
di
Magnifying glass produces virtual image behind object, allowing you to bring
object to a closer do: and larger q’
/
q 
Compare to unaided eye:
:
q
h0
N
Ratio of the two angles is the angular magnification M:
M
q
q

ho d o
ho N

N
do
hi
di

ho
do
The focal length of the lens of a simple camera is 40
mm. In what direction must the lens be moved to
“change the focus of the camera” from a person 25 m
away to a person 4.0 m away? i.e. does the image
distance increase or decrease?
1. Away from the film
2. Towards the film
63%
38%
1
2
The focal length of the lens of a simple camera is 40
mm. In what direction must the lens be moved to
change the focus of the camera from a person 25 m
away to a person 4.0 m away? ? i.e. does the image
distance increase or decrease?
1. Away from the film
2. Towards the film
63%
38%
1
2