Download Where is the image?

Last unit we focused on waves that need a medium or substance to
travel through. We now look at a wave that can travel through a
vacuum
LIGHT
For a long time people believed that light was just a beam or a ray,
but people saw light do things that only WAVES can do.
Light does some
neat stuff
White light
entering a prism
Early views held that we saw because our eyes
beamed out light
They believed that if you were in a perfectly
sealed room with no light source, that you
could still see but only dimly.
Could you?
How fast does light travel?
Early experiments could not measure its speed,
because it was too…
FAST
First successful attempt was by
Albert Michelson in 1880
telescope
A rotating octagonal mirror
light source
carefully aligned mirror
about 35 km (15 miles)
distant mountain
When the octagonal mirror is at the correct
rotation point a laser beam could enter the
telescope.
carefully aligned mirror
distant mountain
Wheel is at the correct speed
Wheel is at the correct speed
Wheel is at the correct speed
Wheel is at the correct speed
Wheel is at the correct speed
Wheel is at the correct speed
Wheel is at the correct speed
If the wheel is spinning too slow
Wheel is moving too SLOW
Wheel is moving too SLOW
Wheel is moving too SLOW
Wheel is moving too SLOW
Wheel is moving too SLOW
Wheel is moving too SLOW
Wheel is moving too SLOW
Wheel is spinning TOO FAST
Wheel is spinning TOO FAST
Wheel is spinning TOO FAST
Wheel is spinning TOO FAST
Wheel is spinning TOO FAST
Wheel is spinning TOO FAST
Wheel is spinning TOO FAST
Wheel is spinning TOO FAST
To find the speed of light they needed
distance
time
Round trip of light
time for wheel to rotate 45o
1/8 a rotation.
SPEED OF LIGHT
FAST BUT FINITE
Speed of light = 299,792,458 m/s
( in a vacuum )
c = 3.0 x
11,181,300 mph
8
10
m/s
Mechanical waves must travel through some
material
Waves in water
waves on a string
waves in a spring
the people wave
The wave oscillates the material back and forth
picture these waves without the material
Light is also a wave.
What is the material through which is travels?
Light WILL TRAVEL THROUGH NOTHING
It is not a substance which oscillates but a…
electric and magnetic field
Electromagnetic wave applet
People used to believe that light had to travel
through some unknown substance they called:
the ETHER
the ether was like the matrix, constantly
surrounding us but undetectable
michelson-morely applet
The frequency of a sound wave changes its...
Pitch
The frequency of a light wave changes its...
Color
Visible Light is only small band in the types of
all light called ELECTRMAGNETIC RADIATION
Radio
waves
Micro
waves
Infrared
.
Ultraviolet
X-Rays
Gamma
Rays
We can’t see they other types of light,
but we use them
Be able so place these types of “light” in order
from long wavelengths to shorter wavelengths,
(frequencies, energy etc…)
Radio
waves
Micro
waves
Long wavelengths
Low frequencies,
Low energy
Infrared
.
Ultraviolet
X-Rays
Gamma
Rays
short wavelengths
high frequencies,
high energy
What a dandelion looks like looking in the
UV spectrum
visible spectrum
Visible Image
UV Image
Thermal Imaging
Two people in total darkness
Different colors are just different wavelengths light
NOT
Wavelength
TO SCALE
ROYGBIV
Just looking at visible light
White is perceived if Red, Blue, and Green
light are present in equal amounts.
Changing the relative amounts can generate
any visible color. This is how TVs do it.
Remember...
v=lf
For light
c=lf
What is the wavelength of green
light (in a vacuum) which has a
frequency of about 6.0 x 1014 Hz
Remember the Doppler effect?
What did it change about a sound?
What will it change about light?
vs,o
f = (1+- v ) f0
This equation only makes valid approximations if the
source/observer velocity is MUCH slower than c.
We won’t worry about the doppler effect yet in this
unit, because we need to take into account the theory
of relativity (later this year)
This is what allows a radar gun uses to
check your speed
reflected wave
incident wave
This also allows a radar signal to determine the:
speed and direction of rain (as well as location)
An Electromagnetic Wave has an orientation
Most light sources have a mix of randomly
oriented light
Light can be selectively transmitted
depending on its orientation
Light polarization applet
Light that has been filtered in this way
Polarized Light Demo
Reflected light become partially polari
So the “glare” can be reduced by
polarizing glasses
The only thing that affects the speed
of a wave is the....
Medium
Can light travel through
Air
Glass
Water
Nothing
When light passes through a transparent material like
glass or water
It is constantly absorbed and emitted by the
electrons in the atoms
Absorbed
held
emitted
etc……
The electrons only absorb the energy for a short period
If the frequency of the light is close to the
natural frequency of the electron
the electron tend to hold on to it a little longer
before letting go.
Absorbed
holding
holding
holding
emitted
This has two implications
1.) the passage of light through the material slows
if it is transparent
3x
108
m/s
1.7 x 108 m/s
3 x 108 m/s
speed of light in transparent materials like glass (applet)
This has two implications
2.) the longer an atom has the energy the more
likely it is to bump into another and lose it as heat
Absorbed
holding
holding
holding
lost as heat
UV light is strongly absorbed by electrons in glass
Absorbed
IR light is strongly absorbed by bonds
Visible light passes through but is slowed
When we say a material is transparent…..
glass is transparent to VISIBLE LIGHT
It is opaque to UV an IR
speed of
light in a
vacuum
c
n= v
Index of
refraction
speed of
light in the
medium
Which material
slows down
light the most?
table on page
696 in book
Material
Index
Vacuum
1
Air at STP
1.00029
Ice
1.31
Water at 20 C
1.33
Ethyl alcohol
1.36
Sugar solution(30%)
1.38
Glycerine
1.473
Sugar solution (80%)
1.49
Typical crown glass
1.52
Crown glasses
1.52-1.62
Sodium chloride
1.54
Carbon disulfide
1.63
Flint glasses
1.57-1.75
Sapphire
1.77
Diamond
2.417
Remember when a wave crosses into another
material like a lighter rope, 2 waves are
formed called the…..
Incident Wave
.
Reflected
Wave
.
.
Transmitted
Wave
.
Light also obeys the law of reflection
25o
25o
If light reflects off of all surfaces, not just mirrors.
Why can’t I see myself in a piece of paper?
specular reflection
-Smooth / polished surface
- clear reflection
Diffuse reflection
-Rough surface
- fuzzy reflection
Reflection of
sunset from
clouds
Which is
diffuse?
Reflection of
sky in water
Laser reflecting in a Jello mold
Why do you see two vases?
How we see objects in mirrors.
Our brain makes the assumption
that light travels in straight lines
Reflected
image
Questions that will be popular on an
AP exam.




Where is the image?
Is the image real or virtual
Is the image upright or inverted (vertically)
What is the height of the image
compared to the actual object
Where is the image?
Behind the mirror at a
distance equal to the
distance of the object
from the mirror.
Is the image real or virtual
A screen placed at that
position would produce
no image.
Is the image upright or inverted?
Upright
What is the height of the image
compared to the actual object?
The same, it is not
magnified or
made smaller
All of this can be determined
here from drawing two lines?
Big face
reflection
Same guy
looking in
curved
mirrors
Little face
reflection
Using the rays to predict what an image will
look like is called ray tracing.
Computer Designed
images use RAY
TRACING for realism
Reflections from concave and convex mirrors
Light rays from objects at a distance are mostly
parallel.
Often optics is analyzed with parallel lines.
Will parallel light rays focus in a concave mirror?
However, a spherical concave mirror doesn’t focus them
perfectly. What shape would?
A parabolic one! They are the best at
focusing parallel light rays
A ray like the red one here is called
the principal axis (or optical axis)
Notice color at focal point
Usually, we pretend that all concave mirrors
have an actual focal point. Because, its makes
coming up with questions easier.
And if the mirror isn’t too big compared to its
radius of curvature, it works decently anyhow.
A spherical mirror is like a slice of a sphere
The radius of curvature is the distance to its
imaginary center
R
C
The vertex is shown here.
R
C
V
The focus or focal point is half way between the center and
the vertex.
R
C
V
F
Therefore the focal length is the distance from the vertex to
the focal point and is half the radius of curvature.
R
f= 2
R
C
F
V
Ray Tracing Rules
Usually an arrow
represents the object
C
F
There are 4 principle rays to trace
on mirror. You only need 2. But
sometimes 1 is more convenient
than another
1.) Any ray that enters parallel (to the axis) goes
through the focal point
C
F
2.) Any ray that goes through the focal point exits
parallel
C
F
3.) Any ray that goes through center of curvature will
strike perpendicularly and go back on itself
C
F
You only need 2 to determine the image, but a
third can check
4.) Any ray striking the vertex reflects at an angle equal
to the principle axis (I don’t use this one much)
C
F
Note that the image is formed where the REFLECTED
rays meet.
C
F
Distances are measured along the principal axis to the
vertex. We could use a ruler here or an equation later
Where is the image?
object distance (do)
C
F
image distance (di)
Is the image real or virtual?
Would actual rays of light from the object hit that
point?
C
F
Is the image inverted?
C
F
What happens to the image depends on the location of the
object (especially in relation to the center and focus)
C
F
Moving the source object and repeating the
process
C
F
Example #2
Doing our first ray
C
F
Example #2
Doing our 2nd ray
C
F
Example #2
The image is formed where the reflected rays intersect
C
F
Example #2
Where is the image?
Is the image real or virtual
Is the image upright or inverted (vertically)
What is the height of the image compared to the actual object
C
F
Example #2
Moving it once more
C
F
Example #3
Rule #1
C
F
Example #3
Rule #2- any ray going through the focal point will exit
parallel to the axis
C
F
?
Example #3
Rule #2- any ray going through the focal point will exit
parallel to the axis
C
F
Example #3
BUT NOTE THE REFLECTED RAYS NEVER MEET
C
F
Example #3
We extend the reflected rays where they will meet.
C
F
Example #3
Where is the image?
Is the image real or virtual
Is the image upright or inverted (vertically)
What is the height of the image compared to the actual object
C
Anytime you have to trace back
lines, it is virtual
F
Example #3
A couple notes that will be proven later, but match what we
have seen and will see
Real images are always inverted
Virtual images are always upright
Since there are only two choices for each, inverted images
are always real and etc…
Concave mirror applet
What about parallel rays on a convex mirror?
And the focal point will be….
Send a parallel ray
F
C
Then send a ray towards the virtual focus
F
C
Other principle ray, send one to the vertex
F
C
It will reflect at an equal angle from the axis.
Then find the intersection of the reflected rays.
F
C
Another note, you can still use the center of curvature as a line as well.
This is the easiest if it is given…
F
C
Where is the image?
Is the image real or virtual
Is the image upright or inverted (vertically)
What is the height of the image compared to the actual object
F
C
Convex mirror applet
Magnification equation for curved mirrors
Height of image
Distance of image (from vertex)
magnification
hi
di
M= h =do
o
Height of object
The negative sign is just there by convention. Meaning
its just what people agreed on to use.
Distance of object
(from vertex)
hi
di
M= h =do
o
ho
do
F
hi
di
And the mirror equation
1
1
1
+
=
do
di
f
focal length
Same as before
Now a chat about SIGNS,
you don’t get to pick here
For distances and focal length,
REAL  +
Virtual -
1
1
1
+
=
do
di
f
hi
di
M= h =do
o
f (focal length)
If rays would really focus from the object Real
Always +
Always -
Concave
C
=+
Convex
F
F
C
do ,distance of the object
Always +, the object is always real
Convex
C
F
F
C
di ,distance of the image
+ if image is real,
- for virtual
Convex
C
F
F
C
hi and M
+ if image is upright,
- for inverted
C
F
h’s and M ones that
don’t fit the rule
They will ALWAYS
have the same sign.
F
C
ho is always +,
why?
+ if image is upright,
- for inverted
C
F
F
C
An object with a height of 4 cm is placed 30 cm in
front of a concave mirror whose focal length is 10
cm.
(a) Where is the image
(b) Is it real or virtual
(c) Is it upright or inverted
(d) What is the height of the image
An object with a height of 4 cm is placed 20 cm in
front of a convex mirror whose focal length is 30
cm.
(a) Where is the image
(b) Is it real or virtual
(c) Is it upright or inverted
(d) What is the height of the image
Now that took care of the reflected wave on
the rope
Incident Wave
.
Reflected
Wave
.
.
Transmitted
Wave
.
Now for the transmitted
Light also is transmitted and reflected when it
encounters a new substance. Some of the
light goes through and some of the light
reflects off
And what happens when water waves
reach a boundary at an angle where
they change speed?
For a simple approach, we can think of light as a RAY.
But light does display WAVE behavior.
It REFRACTS
The same bending rules apply as before
(using the pretend sled or lawn mower)
Snell’s Law
n1 sin q1 = n2 sin q2
Again, angles are measured to the normal.
n(air) = 1.0003
n(diamond) = 2.62
A beam of light approaches a piece of glass from
air, at an incident angle of 36o. Give the angles
for the reflected and refracted beams.
How will the other beam be bent?
Both towards the normal line
And when they exit
Both away from the normal line
And parallel to the original beam
Bow fishing is tricky
because…
When underwater the “manhole” effect can
be seen as visible light from above the water
is compressed into a circle with a “radius” of
48.6o.
When the change in density is gradual, light
makes a gradual turn instead a sharp one
Consider the air close to hot pavement.
Which way will the light bend?
cool high density air
hot low density air, light travels faster
Light which exits an optically dense material to a less dense one,
will only exit (transmit) below a certain angle.
After which we see TOTAL INTERNAL REFLECTION
For example
For example
For example
For example
For example
For example
For example
For example
The critical incident angle is that which will
produce a refracted angle of 90o
Refraction applet
any angle larger than this produces TIR
n1 Sin(qC ) = n2 Sin(90 )
n2
Sin(qC ) = n
1
Refraction applet
Why can total internal reflection never occur when
exiting into a material that slows light?
Apparent mirrored surface underwater
You may not be able to see a fish even thought it is there in
crystal clear water
The greater the optical density of the substance the greater
range of angles for internal reflection
Angles
for TIR
49o
TIR in water
Angles
for TIR
22o
TIR in Diamond
Light is usually reflected inside the diamond several times
before escaping
Glass Prisms are used to reflect light in binoculars and periscopes.
The glass is not mirrored
Total INTERNAL REFLECTION is what makes a
fiber optic cable a light pipe
HARDLY ANY LIGHT IS LOST to the outside
A beam of light goes from diamond to water at an incident angle of
27o. What is the angle of reflection, angle of refraction, and the
critical angle
water
27o
Diamond
Refraction is due to light slowing
(or speeding up in a material)
The slowing is due to the light interacting with
(mostly) the electrons in atom.
Not all wavelengths interact as strongly,
blue light tend to be more affected than red
Different colors refract by different amounts
Different colors refract by different amounts
Different colors refract by different amounts
(the actual difference is not this noticeable)
White light
Know that shorter wavelengths have a higher effective
index of refraction (aka are bent more)
Physics of a Rainbow
Physics of a Rainbow
This can be a problem when using
lenses to focus light.
It is called: chromatic aberration
The photo on right has been touched up by software
Using special coatings or lenses with different
indices of refraction can minimize chromatic
aberration.
LENSES
A Convex Lens or
Converging lens
A convex lens has a
real focal point and will
form real images
Focal length
Also note the two rays that just go straight
A Concave Lens, or Diverging Lens
Has a virtual focus and forms virtual images
chromatic aberration is not noticeable here
Ray tracing with lenses
Any ray parallel to the axis,
goes through the focal point.
f
Any ray that goes through the optical center is
undeflected (passes straight through).
Ray tracing with lenses
f
A real, inverted image
An object which is
Beyond c is real and smaller
at c is real and the same
Between the c and f is real and magnified
At f is never focused
Less then f is virtual
Lens applet
For concave lenses…
1.) send a ray through the optical center
2.) send a parallel, and refract away from the virtual focus
f
A virtual, upright image
Same rules apply here.
For distances and focal length,
REAL  +
Virtual -
h,M
Upright +
Inverted -
1
1
1
+
=
do
di
f
hi
di
M= h =do
o
GUESS THAT SIGN
f +
di +
do +
hi ho +
M-
GUESS THAT SIGN
f di do +
hi +
ho +
M+
GUESS THAT SIGN
CONVEX LENSES
Object further from
lens than focus
Object closer to
lens than focus
CONCAVE LENSES
The power of a lens is defined as the
inverse of the focal length.
1
P=
f
It is measured in Diopters,
1 D = 1 m-1
An object with a height of 11 cm is placed 44 cm in
front of a converging lens with a focal length of 24
cm.
1.) Where is the image? 53 cm, side opposite object
real, d is +
2.) Is it real or virtual?
3.) Is it upright or inverted? real images are always inverted
4.) What is the height of the image - 13 cm
5.) What is the power of the lens 4.2 D
i
Lenses come in all shapes
To predict the focal point of a THIN lens, we use a good
approximation known as the
Lensmaker’s equation
1 = (n-1) 1 1
+
f
R1 R 2
Focal
length
Index of
refraction
of lens
material
The radius of curvature of each
side of the lens.
+ for convex (real)
- For concave
The lens at left is made of glass with an index of
refraction of 1.5. The radius of curvature of the
convex side is 22.4 cm and is 46.2 cm for concave
side. What is the focal length?
87 cm
If a laser beam is shined into a very
small slit, what would the light on the
wall look like?
A dot?
Light reflect and refracts but does it….
Diffract
Huygen’s Principle
Every point of a wave front may be considered the
source of secondary wavelets that spread out in all
directions with a speed equal to the speed of propagation
of the waves.
Refraction explained through HP (applet)
Reflection and refraction by HP applet
Diffraction also occurs when waves
meet an obstacle
If light was shined through two little
slits onto a screen, what would I see
on the screen?
2 dots?
This would make common sense, but NO?
Would I see a smear of light due to
the diffraction????
Getting closer, but still NO
When two waves originating from different locations
reach the same point like on a screen, usually one has
to travel further to get there as in the picture below.
Because the slits are very narrow,
they each act as a single point
source of light that diffracts
Starting in
Phase
Destructive
(out of phase)
l
2
Difference in path lengths (Dl)
Destructive
(out of phase)
l
2
l
Constructive
(in of phase)
Destructive
(out of phase)
3l
2
So in general… where m is an integer
Dl = m l
1l , 2l, etc...
Constructive interference occurs
when the difference in path length
is multiples of the wavelength
Dl = (m+½ ) l
½l , 3/2 l, etc...
Destructive
(here they are off by ½ a
wavelength)
Two slits less than the wavelength of the light
source act like two point sources of light.
What would the light
on the wall look like?
Double slit wave tank video in
folder
LIGHT CAN CANCEL LIGHT?
The bright spots are called interference “fringes”.
m is the order #
Notice that the brightness of each fringe decreases
as m increases
m=0
m=1
m=1
0
3
2
1
1
2
3
Representing fringes with a curve showing relative
intensity
If the path difference is multiples of a wavelength,
they will be in phase at the screen
Dl = d sin(q)
Pretty darn close to theta, given that d will be about a mm
And L will be at least a meter.
90 - q
~q
~q
How to predict where the bright spots will be?
Distance
between slits
Order #
(integers)
d sin(q) = m l
Angle from
slits
Wavelength
of light
A screen containing two slits 0.100 mm apart
is 1.2 m from a viewing screen. Light of with
a wavelength of 500 nm falls on the slits.
How far apart with the 2nd and 3rd brightest
fringes be apart from each other on a given
side?
6.00 mm
What will happen to the distance
between fringes if.
• a longer wavelength of light is used?
• the distance between slits is increased?
• what would the fringes look like if white light
instead of monochromatic light were used?
d sin(q) = m l
Double slit diffraction applet
Monochromatic
light
White
light
Diffraction from an obstruction
The diffraction above is seen from shining laser light
into a fine wire. If white light had been used?
Diffraction lines around a razor blade
Diffraction of white light on a DVD
Pits on a cd
and dvd
Lets say a point on the screen where the two light beams
interfere constructively such that
d sin(q) = m l
d
What if there are more slits, will the light from the 3rd slit
interfere constructively or destructively with the other two
d
d sin(q) = m l
What if there are more slits, will the light from the 3rd slit
interfere constructively or destructively with the other two
d sin(q) = 1 l
d
Here the extra pat
is 1 wavelength
What if there are more slits, will the light from the 3rd slit
interfere constructively or destructively with the other two
2d sin(q) = 2 l
2d
Here the extra path
is 2 wavelengths
Still in phase
So anyway the equation still holds for multiple slits or
even finely spaced lines (a diffraction grating)
d sin(q) = m l
Central
bright spot
(m = 0)
What did “d” stand for in a double slit?
What did “d” stand for with multiple slits?
d sin(q) = m l
d
The distance between any 2 slits.
(They will be evenly spaced)
This might be the first order bright fringe?
d sin(q) = m l
d
q
Multiple slit diffraction patterns follow the same equations as double
slit.
However the additional interference from multiple slit sources causes
a tighter fringe pattern. ( and is superior)
A diffraction grating has finely
spaced lines to diffract the light.
They might be described as
having 500 lines/cm
The same equation holds here as well.
What will d stand for here?
d sin(q) = m l
Demo - Diffraction from small dots
on a transparency
Diffraction through a diffraction
grating.
A diffraction grating has 500 lines/cm.
If 640 nm light is shined through it,
how far will the first order fringe be
from the center line on a screen 2 m
away?
X-ray diffraction, seeing molecules
Computers take these
patterns and solve to
determine the molecular
structure
single slit diffraction
This makes sense from Huygens Principle
If the slit is small compared to the
wavelength you see a point source.
If the slit is larger compared to the
wavelength you see something different
Ripple tank
Single slit diffraction applet
Applet #2
The opening is four wavelengths wide,
what do you see at the opening?
It looks like 4
point sources.
Huygen’s principle states that wave front can be thought
of being made of a bunch of teeny wavelets capable of
each a point source for a spherical wave.
The new wave front is
tangent to the “wavelets”
Flat here
But curved at the
edges
Huygen’s principle states that wave front can be thought
of being made of a bunch of teeny wavelets capable of
each a point source for a spherical wave
When we looked at double slits we didn’t worry about
Huygen’s principle because we used very narrow slits.
So the slits behaved like single light sources.
d
But if we use a wider slit (as compared to the
wavelength), it acts like multiple sources
single slit wave tank video in folder
I am not going to get into the derivation of this formula for several
reasons. Were just going to have it and use it (its easy though)
#1 Probably the most important thing about single slit
diffraction is just that it occurs and verifies Huygen’s Principle
#2 I was hesitant to discuss single slit diffraction because the
formula yield opposite results for double slit which is more
important. Explanations are conceptually difficult
The same equation is used for single slit diffraction BUT it
tells you where the DARK SPOTS (minima) are
d sin(q) = m l
Slit width
What does q reference to?
What value of m would you
use to find the first dark spot?
0 or 1
Light of 750 nm passes through a slit 1.0x10-3 mm wide.
How wide is the central bright spot (maximum)
(a) In degrees, and (b) in cm on a screen 20 cm away?
q1 = 49o
(a) = 98o
(b) = 0.46 m
Is gasoline or soapy water a
colorful material?
Similary the vibrant colors you see are
not the color of the animal’s feathers or
shells
Iridescence
When a light wave reflects off a material with a higher
index of refraction, it reflects back out of phase
know this
air
glass
n2 > n 1
When a light wave reflects off a material with a lower
index of refraction, it reflects back in phase
know this
air
glass
air
n1 > n 2
A light beam strikes a thin film of a bubble. Some
is reflected at the 1st boundary and some at the 2nd
boundary
air
water
air
Which ray is phase changed upon reflection?
A B or Both?
A
air
water
air
B
But the key things to remember are that:
Beam 1 is inverted upon reflection
Beam 2 has to go a greater distance
1
2
air
water
air
If the two reflected rays traveled the same distance
when they met, they would be out of phase
Reflected off of
water
1
Reflected off of
air
2
The 2nd beam has unit wavelengths colored for clarity
Destructive interference (Dark)
But remember ray 2 has to travel a greater distance
before exiting the water (we’ll just consider this based
on the thickness of a thin film of water (like a bubble)
1
2
air
water
air
Ray 2 has to travel a greater distance
1
2
How much extra distance would cause them to
be in phase again?
Half a wavelength
If the extra distance is a full wavelength
1
2
Here
1
2
Here
1
2
If the extra path difference (L) is where m
is some integer
Dl = m l
1l , 2l, etc...
Don’t write this yet
Destructive interference
Dl = (m+½ ) l
½l , 3/2 l, etc...
Constructive interference
Usually, the problems will have the light enter head on
instead of at an angle. What is the extra path distance
compared to the thickness of the film?
Dl = 2t
t
If the extra path difference (L) is where m
is some integer
2t = m l
Not done yet
Destructive interference
1l , 2l, etc...
2t = (m+½ ) l Constructive interference
½l , 3/2 l, etc...
What happens to the wavelength as the light enters the
glass?
l
ln = n
l
t
ln
Entering from a vacuum
or close enough for air
Conditions for thin film interference
ml
2t = n
OK now
Destructive interference
1l , 2l, etc...
(m+½ ) l
2t =
n
Constructive interference
½l , 3/2 l, etc...
And if the both rays are inverted or neither ray is
inverted… Is this correct?
L=ml
1l , 2l, etc...
Destructive interference
L = (m+½ ) l
½l , 3/2 l, etc...
Constructive interference
For a red light wave wavelength of 500
nm entering a thin film of water (n =
1.33)
What is the minimum thickness to
intensify the color and to cancel the
color.
Thin film interference applet
Paths will be different for angles, and therefore
Different colors of light will be reinforced at
Different locations on a surface.
A
B
I think that is why a repeating color pattern is
seen here.
When two glass plates are placed on top of
each other the same effect is observed.
What is the thin film involved.
This can be used to determine the thickness of
something very thin.
Just looking at the air wedge boundaries, how will the thickness
of the air relate to the wavelength at the dark spots? (assume
that the light goes straight through the air thickness)
Light is inverted so l, 2l, etc..
One ray is flipped and the other isn’t so if the extra
distance is a whole wavelength multiple… out of phase
and dark spot.
How thick will the air gap be for the first dark fringe.
If thickness = l/2
Then extra path will be l
When will the next dark fringe occur.
If thickness = l
Then extra path will be 2l
ml
2t = n
ml
t= 2
Given that the
index of air is
close to 1 and
rearranging
Dark lines will occur when
the air gap thickness is some
multiple of ½ wavelengths
Dark fringes will occur every time the thickness increases
by 1/2 l .
ml
t= 2
m=4
4l
t=
2
m=3
3l
t=
2
m=2
2l
t=
2
m=1
m=0
l
2
t=0
t=
Would the point of contact between the two glass plates be
dark or light? Why?
Dark, because the path length
difference is zero and the
reflections are out of phase.
m=4
4l
t=
2
m=3
3l
t=
2
m=2
2l
t=
2
m=1
m=0
l
2
t=0
t=
How thick is the object?
m=4
4l
t=
2
m=3
3l
t=
2
ml
t= 2
m=2
2l
t=
2
m=1
m=0
l
2
t=0
t=
A piece of plastic is wedged between two flat glass plates.
If light with a wavelength of 470 nm produces the dark
fringes below, how thick is the plastic?
What will happen to the spacing of the dark fringes if a
thicker object is used?
m=4
4l
t=
2
m=3
3l
t=
2
m=2
2l
t=
2
m=1
m=0
l
2
t=0
t=
What will happen to the spacing of the dark fringes if a
thicker object is used?
12
11 10
9
8
7
6
5
4
3
2
1
m=0