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```									          Property 5: Refraction
experiment ?
particle (photon)?
wave (E&M) ?
Property 5: Refraction
• experiment: objects in water seem closer
than they really are when viewed from air

eye
air

water
apparent
location

real object
Property 5: Refraction
• particle (photon) ?
incident ray

air

surface
water

refracted ray
Property 5: Refraction
• particle (photon) ?
incident ray                      vxair = vxwater
vxair
air                vyair                  vyair < vywater

surface
therefore
water
vxwater       vi < vr

vywater
refracted ray
Property 5: Refraction
normal line

• wave (E&M) ?
incident wave
air

surface                                           surfac
e
water

refracted wave
normal line
Property 5: Refraction
crest of following wave
• wave (E&M) ?
crest of wave
incident wave
air                                           crest of preceding wave
air           air
surface                      x
water
water

refracted wave
normal line
Property 5: Refraction
• particle (photon) theory: vwater > vair
• wave (E&M) theory:        vwater < vair
• experiment ?
Property 5: Refraction
• particle (photon) theory: vwater > vair
• wave (E&M) theory:        vwater < vair
• experiment:               vwater < vair
wave theory works!
particle theory fails!
Properties 1, 2 & 5

Speed, Color and Refraction
• Speed of light changes in different materials
• Speed is related to frequency and
wavelength: v = f
• If speed changes, does wavelength change,
frequency change, or BOTH?
Properties 1, 2 & 5
• Speed, Color and Refraction
• Speed of light changes in different materials
• Speed is related to frequency and
wavelength: v = f
• What changes with speed?
– Frequency remains constant regardless
of speed
– Wavelength changes with speed
Refraction and Thin Lenses
Can use refraction to try to control rays of
light to go where we want them to go.

Let’s see if we can FOCUS light.
Refraction and Thin Lenses
What kind of shape do we need to focus light
from a point source to a point?
lens with some shape for front & back

point
source
of light                                                screen
s’ = image distance
s = object distance
Refraction and Thin Lenses
Let’s try a simple (easy to make) shape:
SPHERICAL.

Play with the lens that is handed out
Does it act like a magnifying glass?
Refraction and Thin Lenses
Let’s try a simple (easy to make) shape:
SPHERICAL.

Play with the lens that is handed out
Does it act like a magnifying glass?
Does it focus light from the night light?
Refraction and Thin Lenses
Let’s try a simple (easy to make) shape:
SPHERICAL
Play with the lens that is handed out
Does it act like a magnifying glass?
Does it focus light from the night light?
Does the image distance depend on the shape
different shaped lens)
Refraction and Thin Lenses
Spherical shape is specified by a radius.
The smaller the sphere (smaller the radius),
the more curved is the surface!
R
R                         R1
R2
Refraction and the Lens-users Eq.
f>0
1   1   1                                s > 0 AND s > f
=   +
f   s   s'
s’ > 0 AND s’ > f

f                     f

s
s’
Example: f = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10
Refraction and the Lens-users Eq.
1   1   1                                as s gets bigger,
=   +
f   s   s'                               s’ gets smaller

f                     f

s
s’
Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm: 1/40 + 1/13.3 = 1/10
Refraction and the Lens-users Eq.
1   1   1                                 as s approaches infinity
=   +
f   s   s'                                s’ approaches f

f                    f

s
s’
Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm: 1/100 + 1/11.1 = 1/10
Refraction and the Lens-users Eq.
f>0
1   1   1                                s > 0 AND s > f
=   +
f   s   s'
s’ > 0 AND s’ > f

f                     f

s
s’
Example: f = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10
Refraction and the Lens-users Eq.
1   1   1
=   +                                     as s gets smaller,
f   s   s'                                  s’ gets larger

f                     f

s
s’
Example: f = 10 cm; s = 13.3 cm; s’ = 40 cm: 1/13.3 + 1/40 = 1/10
Refraction and the Lens-users Eq.
1   1   1
=   +                                     as s approaches f,
f   s   s'                                  s’ approaches infinity

f                    f

s
s’
Example: f = 10 cm; s = 11.1 cm; s’ = 100 cm: 1/11.1 + 1/100 = 1/10
Refraction and the Lens-users Eq.
Before we see what happens when s gets
smaller than f, let’s use what we already
know to see how the lens will work.
Refraction and the Lens-users Eq.
– Any ray that goes through the focal point
on its way to the lens, will come out
parallel to the optical axis. (ray 1)

f              f
ray
1
Refraction and the Lens-users Eq.
– Any ray that goes through the focal point
on its way from the lens, must go into the
lens parallel to the optical axis. (ray 2)

f               f
ray
1
ray 2
Refraction and the Lens-users Eq.
– Any ray that goes through the center of
the lens must go essentially undeflected.
(ray 3)
object

image
f               ray
f
1
ray 3

ray 2
Refraction and the Lens-users Eq.
– Note that a real image is formed.
– Note that the image is up-side-down.
object

image
f               ray
f
1
ray 3

ray 2
Refraction and the Lens-users Eq.
– By looking at ray 3 alone, we can see
by similar triangles that M = h’/h = -s’/s.
object
h                                 s
image
’
f       h’<0
s      f
ray 3

Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm:    note h’ is up-side-down
and so is <0
M = -13.3/40 = -0.33 X
Refraction and the Lens-users Eq.
This is the situation when the lens is used
in a camera or a projector. Image is REAL.
object

image
f               ray
f
1
ray 3

ray 2
Refraction and the Lens-users Eq.
What happens when the object distance, s,
changes?

object

image
f               ray
f
1
ray 3

ray 2
Refraction and the Lens-users Eq.
Notice that as s gets bigger, s’ gets closer to f
and |h’| gets smaller.

object

image
f                    ray
f
1
ray 3
Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm:
M = -11.1/100 = -0.11 X                                 ray 2
Focusing
To focus a camera, we need to change s’ as s
changes. To focus a projector, we need to
change s as s’ changes. We do this by
screwing the lens closer or further from the
film or slide.
But what about the eye? How do we focus on
objects that are close and then further away
with our eyes? Do we screw our eyes in
and out like the lens on a camera or
projector?
Focusing
But what about the eye? How do we focus on
objects that are close and then further away
with our eyes? Do we screw our eyes in
and out like the lens on a camera or
projector? - NO, instead our eyes
CHANGE SHAPE and hence change f as s
changes, keeping s’ the same!
Refraction and the Lens-users Eq.
Let’s now look at the situation where
s < f (but s is still positive):

s
f              f
Refraction and the Lens-users Eq.
We can still use our three rays. Ray one goes
through the focal point on the left side.
ray 1

s
f              f
Refraction and the Lens-users Eq.
Ray two goes through the focal point on the
right side (and parallel to the axis on the left).
ray 1

s
f                f
ray 2
Refraction and the Lens-users Eq.
Ray three goes through the center of the lens
essentially undeflected.
ray 1

h’

s
f              f
s’                           ray 2

ray 3
Refraction and the Lens-users Eq.
Notice that: s’ is on the “wrong” side, which
means that s’ < 0 , and that |s’| > |s| so f > 0.
ray 1

h’

s
f                     f
s’                                        ray 2

ray 3

Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: 1/7.14 + 1/(-25) = 1/10
Refraction and the Lens-users Eq.
Notice that: h’ right-side-up and so h’ > 0.,
M = h’/h = -s’/s . M > 0 (s’ < 0 but -s’ > 0).

h’

s
f                     f
s’
ray 3
Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm:
M = - (-25)/ 7.14 = 3.5 X
Refraction and the Lens-users Eq.
This is the situation when the lens is used
as a magnifying glass! Image is VIRTUAL.
ray 1

h’

s
f              f
s’                          ray 2

ray 3
Refraction and the Lens-users Eq.
The same lens can be used as:
• a camera lens: s >> f, s > s’,
M < 0, |M| < 1
• a projector lens: s > f, s’ > s,
M < 0, |M| > 1
• a magnifying glass: s < f, s’ < 0,
M > 0, M > 1
Refraction and the Lens-users Eq.
Notes on using a lens as a magnifying glass:
• hold lens very near your eye
• want IMAGE at best viewing distance
which has the nominal value of 25 cm
so that s’ = -25 cm.
Refraction and the Lens-users Eq.
Are there any limits to the magnifying power
we can get from a magnifying glass?
Refraction and the Lens-users Eq.
• Magnifying glass has limits due to size
• As we will see in a little bit, magnifying
glass has limits due to resolving ability
• NEED MICROSCOPE (two lens system)
for near and small things; need
TELESCOPE (two lens system) for far
away things.
Telescope Basics
Light from far away is almost parallel.

objective
lens                                       eyepiece

fe
fo
Telescope Basics:
Get More Light
The telescope collects and concentrates light.

objective
lens                                     eyepiece

fe
fo
Telescope Basics
Light coming in at an angle, in is magnified
to out .
objective
lens                                       eyepiece

x

fo                    fe
Magnification
in = x/fo, out = x/fe; M = out/in = fo/fe

objective
lens                                          eyepiece

x

fo                      fe
Limits on Resolution
telescopes
– magnification: M = out/in = fo /fe
– light gathering: Amt D2
– resolution: 1.22  = D sin(limit) so
in = limit and out = 5 arc minutes
so limit  1/D implies Museful = 60/in * D
where D is in inches
– surface must be smooth on order of 
Limits on Resolution:
calculation
Mmax useful = out/in = eye/limit
= 5 arc min / (1.22 *  / D) radians
= (5/60)*(/180) / (1.22 * 5.5 x 10-7 m / D)
= (2167 / m) * D * (1 m / 100 cm) * (2.54 cm / 1 in)
= (55 / in) * D
Example
What diameter telescope would you need to
from a spy satellite?
Example
• need to resolve an “x” size of about 1 cm
• “s” is on order of 100 miles or 150 km
• limit then must be (in radians)
= 1 cm / 150 km = 7 x 10-8
• limit = 1.22 x 5.5 x 10-7 m / D = 7 x 10-8
so D = 10 m (Hubble has a 2.4 m diameter)
Limits on Resolution: further
examples
• other types of light
– x-ray diffraction (use atoms as slits)
– IR
• surface must be smooth on order of 
Review of Telescope Properties
1. Magnification: M = fo/fe depends on the
focal lengths of the two lenses.
2. Light gathering ability: depends on area
of objective lens, so depends on diameter
of objective lens squared (D2).
3. Resolution ability: depends on diameter
of objective lens: Max magnification = 60
power/in * D.
Types of Telescopes
The type of telescope we have looked at so far, and
the type we have or will have made in the lab is
called a refracting telescope, since it uses the
refraction of light going from air to glass and back
to air. This is the type used by Galileo.
There is a second type of telescope invented by
Newton. It is called the reflecting telescope since
it uses a curved mirror instead of a curved lens for
the objective. There are three main sub-types of
reflectors that we’ll consider: Prime focus,
Newtonian, and Cassegranian.
Refracting Telescope

Two lenses (as we had in the lab)

objective
lens                                      eyepiece

fe
fo
Reflecting Telescope

Light from far away                     mirror
focuses
light

problem: how do we get to focused light without
blocking incoming light?
Reflecting Telescope
Prime Focus
Light from far away
mirror
focues
eyepiece            light

Solution #1: If mirror is big enough (say 100
to 200 inches in diameter), we can sit right in
the middle and we won’t block much light -
this is called the prime focus.
Reflecting Telescope
Newtonian Focus

Light from far away                     eyepiece
primary
mirror
focuses
mirror
light

Solution #2: Use secondary mirror to reflect light out
the side of the telescope- this is called the Newtonian
focus.
Reflecting Telescope
Cassegranian Focus

Light from far away                  primary mirror
focuses
light
mirror
eyepiece

Solution #3: Use secondary mirror to reflect light
out the back of the telescope- this is called the
Cassegranian focus.

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