Dispersion: Index of Refraction
changes with wavelength (color)
Last Time…

Reflection and refraction



n decreases with increasing λ
Violet has largest n
Red has smallest n
Refracted angle changes with
light color ⇒spectrum
n typically varies by ~ 0.02
over visible spectrum
Dispersion
Thurs. Sep. 13, 2007
Quick Quiz
2
Prism
White light is incident on glass,
whose index varies from
1.51 (red) to 1.53 (blue).
n1
n2
A
B
A. A is red, B is blue
δ = angle of deviation
from incident
direction
B. A is blue, B is red


Thurs. Sep. 13, 2007
Physics 208, Lecture 4
3
Rainbows


Thurs. Sep. 13, 2007
Physics 208, Lecture 4
4
Rainbows form when light from the sun is refracted /
reflected reflection inside rain droplets as shown.
Every color you see comes from a different droplet.
Which statement is correct?
n varies from 1.331 @ 700nm to 1.344 @
400nm
A. Ray (1) is Red. Ray (2) is Blue.
1st refraction at front of drop
 Violet light deviates most
 Red light deviates least
Physics 208, Lecture 4
Different colors sent in different
directions by refraction
Deviation angle depends on
index of refraction
Quick Quiz
Water has dispersion:

Thurs. Sep. 13, 2007
Physics 208, Lecture 4
B. Ray (1) is Blue. Ray (2) is Red.
5
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
6
1
Light rays and images
Observing a Rainbow



Thurs. Sep. 13, 2007
Physics 208, Lecture 4
7
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
8
How a lens works
Focusing light

Each point on object
reflects light
Light propagates out,
represented by rays
perpendicular to
wavefront.
Lens in our eye does
some ‘imaging’ so
that we identify origin
of light rays.
Position surfaces to bend light rays in just the right way
Spherical surfaces are very close to the right ones.
Lens: Refracts light so that rays originating from
a point are focused to a point on the other side.
n1
Optical Axis
n1
n2>n1
F
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
9
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
10
Thin-lens approximation:
Ray tracing
Q: where is the image sharp?
q Image distance
p
Object distance
A
B
F
C
Object
Optical
Axis
Image
F
Image
Object
1) Rays parallel to optical axis pass through focal point.
2) Rays through center of lens are not refracted.
f
focal length
Thurs. Sep. 13, 2007
f
Blurry image: rays
originating from from
same point do not end
up at some point on screen
Physics 208, Lecture 4
Blurry image
11
3) Rays through F emerge parallel to optical axis.
Here image is real, inverted, enlarged
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
12
2
Different object positions
Quick Quiz
I project a focused image onto a screen 2
meters away. I now want to make the image
bigger without changing the lens. I should
Image (real, inverted)
Object
A. Move screen farther away only
B. Move screen closer only
Image (real, inverted)
C. Move screen closer and object toward lens
D. Move screen farther and object toward lens
E. Move screen farther and object away from lens
Image
(virtual, upright)
These rays seem to originate
from tip of a ‘virtual’ arrow.
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
13
Thurs. Sep. 13, 2007
Virtual images



These rays seem to originate
from tip of a ‘virtual’ arrow.
can’t be recorded on film,
Can’t be seen on a screen.


Physics 208, Lecture 4
15
Your eye and its lens
Object has been (virtually)
transported to a new
location
Thurs. Sep. 13, 2007
Focal length of diverging
lens is defined to be
negative.
Physics 208, Lecture 4
16
Nearsightedness
Object
Object
I can’t focus on this
Lens
Image
Real (inverted) image is formed on retina by
cornea and crystalline lens.
Image focused by changing lens focal length
 Far point: largest object distance at which image distance
= distance to retina (typically infinity)
 Near point: smallest object distance at which image
distance = distance to retina (typically 25 cm)
Thurs. Sep. 13, 2007
Appear to originate from
point source at focal point.
Result

e.g. lens in your eye (focus on retina)
e.g. lens in a camera (focus on film plane)
Thurs. Sep. 13, 2007


Diverging lens usually
produces a virtual image.
Rays from object at
infinity bent

But rays can be focused by another lens



Virtual image

14
Virtual image and diverging lens
objects closer to a converging lens than
the focal length form a virtual image
Image
(virtual,
upright)
Physics 208, Lecture 4
Physics 208, Lecture 4
17
This, I can see
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
18
3
Fixing nearsightedness
Making an image
Object distance
Object
Image distance
s
s’
Object
Image
How are all these related?
f
f
1 1 1
+ =
s s" f
focal length
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
19
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
20
!
Magnification
Image distance
Object distance
Image and object
different sizes
Image distance
s
s’
Object
Image
1 1 1
+ =
s s" f
Image (real, inverted)
p
f
focal
length
f
q
Check:
Object at infinity:!
1 1 1
1 1
+ = $ = $ s# = f
" s# f
s# f
Image at focal point
Object moves
! in:
1 1 1
= #
s" f s
Image farther away
Thurs. Sep. 13, 2007
Physics 208, Lecture 4

Magnification = M =
object height s object distance
= =
image height s" image distance
!
21
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
22
!
Question

Camera

At what object distance does image size
equal object size (magnification=1)?


A. Object distance = f
Create real (inverted) image on ‘film’
Object distance-distance from camera lens to object.
Image distance = distance from camera lens to ‘film’.
1 1 1
+ =
s s" f
1 1 1
+ =
p q f
B. Object distance = 2f
• focal length f fixed.
C. Object distance = f/2
!
!
• Image distance must change
when object distance changes
• Lens must move in order to
focus image on film
• Limited lens motion
-> limited focusing range.
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
23
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
24
4
Changing focal length: zoom lens
Increasing the image size



Focal length=focus point
for object at infinity
To get a bigger image on the film,
move closer to the object.
Image
(real, inverted)
Object
This also requires changing the image distance
(distance from lens to film).
This is what you do when you ‘focus’ the lens.
Object

Could also increase the image size by changing
the focal length (zoom lens).



Thurs. Sep. 13, 2007
Physics 208, Lecture 4
25
Image size increases as focal length increases.
e.g. zoom lens on camera.
Spreads light over bigger area, dimmer image.
Thurs. Sep. 13, 2007
Your eye can change focal length
Physics 208, Lecture 4
26
Question
Object
1 1 1
+ =
s s" f

!
Lens
Image
A) Only lower half of object will show on screen
What is range of focal lengths if it can focus from
near point (25 cm) to inf. onto retina 1.7 cm away?
B) Only upper half of object will show on screen
1
1
1
+
= # f = 1.7cm
Object at infinity:
" 1.7cm f
1
1
1
+
= " f = 1.59cm
Object at near point:
25cm 1.7cm f
C) The whole object will still show on the screen.
Very limited range
!
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
27
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
28
!
Bigger lens, brighter image
Lens combinations

Image at film plane
(real, inverted)
Object


Some light rays miss the lens
Larger lens focuses more rays, brighter image
2
 Intensity increases as area, prop. to (diameter)
Image of one lens acts as object for next.
Telescope:



Used to look at images far away
Image usually at ~infinity
First lens forms image very close to focal point
Image at film plane
(real, inverted)
Object
Thurs. Sep. 13, 2007

Physics 208, Lecture 4
29
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
30
5
Telescope: object far away
Object ~
at infinity
p
Two lenses:
microscope
q
Real image
formed by
objective

Eyepiece Lens

Image formed by
objective becomes
object for the eyepiece
Virtual image
formed by
eyepiece


Objective Lens




Thurs. Sep. 13, 2007
Physics 208, Lecture 4
p
q
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
32
Real, inverted, image
Object
=-q/p~L/f objective
31
Compound
Microscope
Objective
Objective lateral mag.
L~fo+f e
Short focal length

Object distance slightly > focal length
So real image formed far from objective.
Image formed by objective is quite large,
much larger than object
(Lateral mag M=s’/s ~ L/fo).
Also short focal length
Use image formed by
objective as object
Virtual image is formed, rays
to be focused by eye, or
camera.
Virtual
image
‘Object’
Eyepiece: simple magnifier.
Angular Mag.=25cm/p
Eyepiece
~25cm/feyepiece
Thurs. Sep. 13, 2007
Physics 208, Lecture 4
33
6