last unit we focused on waves that need a medium or substance to travel through. we now look at a...
TRANSCRIPT
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 byAlbert Michelson in 1880
light source
telescope
A rotating octagonal mirror
distant mountain
carefully aligned mirror
about 35 km (15 miles)
When the octagonal mirror is at the correct rotation point a laser beam could enter the telescope.
distant mountain
carefully aligned mirror
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
distancetime
Round trip of light
time for wheel to rotate 45o
1/8 a rotation.
Speed of light = 299,792,458 m/s 11,181,300 mph
SPEED OF LIGHT
FAST BUT FINITE
( in a vacuum )
c = 3.0 x 108 m/s
Mechanical waves must travel through some material
Waves in waterwaves on a stringwaves in a springthe 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...
The frequency of a light wave changes its...
Pitch
Color
Radio waves
Micro waves
Infrared
.
Ultra-violet
X-Rays Gamma Rays
Visible Light is only small band in the types of all light called ELECTRMAGNETIC RADIATION
We can’t see they other types of light, but we use them
Radio waves
Micro waves
Infrared
.
Ultra-violet
X-Rays Gamma Rays
Be able so place these types of “light” in order from long wavelengths to shorter wavelengths, (frequencies, energy etc…)
Long wavelengthsLow frequencies,Low energy
short wavelengthshigh frequencies,high energy
What a dandelion looks like looking in the
visible spectrumUV spectrum
UV Image
Visible Image
Thermal Imaging
Two people in total darkness
Wavelength
Different colors are just different wavelengths light
NOT TO SCALE
R O Y G B I V
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.
v = f
Remember...
For light
c = f
What is the wavelength of green light (in a vacuum) which has a frequency of about 6.0 x 1014 Hz
f = (1vs,ov ) f0+-
What did it change about a sound?What will it change about light?
Remember the Doppler effect?
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
incident wave
reflected 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 is said to be polarized
Polarized Light Demo
Reflected light become partially polarized
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 AirGlassWater
Nothing
Can light travel through
When light passes through a transparent material like glass or water
It is constantly absorbed and emitted by the electrons in the atoms
The electrons only absorb the energy for a short period
Absorbed held emitted etc……
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 longerbefore letting go.
Absorbed holding holding holding emitted
This has two implications
1.) the passage of light through the material slowsif it is transparent
3 x 108 m/s
speed of light in transparent materials like glass (applet)
1.7 x 108 m/s3 x 108 m/s
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
IR light is strongly absorbed by bondsAbsorbed
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
n = v c
Index of refraction
speed of light in the medium
speed of light in a vacuum
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
table on page 696 in book
Which material slows down light the most?
.
.
.
.
Remember when a wave crosses into another material like a lighter rope, 2 waves are formed called the…..
Incident Wave
Reflected Wave
Transmitted Wave
25o
25o
Light also obeys the law of reflection
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
Reflection of sky in water
Which is diffuse?
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 virtualIs 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?
Same guy looking in curved mirrors
Big face reflection
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
RC
The vertex is shown here.
R
C
V
The focus or focal point is half way between the center and the vertex.
R
C FV
Therefore the focal length is the distance from the vertex to the focal point and is half the radius of curvature.
R
CV
F
f = R2
Ray Tracing Rules
C F
Usually an arrow represents the object
There are 4 principle rays to trace on mirror. You only need 2. But sometimes 1 is more convenient than another
C F
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
You only need 2 to determine the image, but a third can check
C F
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
Where is the image?
object distance (do)
image distance (di)
Distances are measured along the principal axis to the vertex. We could use a ruler here or an equation later
C F
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
Example #2
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 virtualIs the image upright or inverted (vertically)What is the height of the image compared to the actual object
C F
Moving it once more
Example #3
C F
Rule #1
Example #3
C F
Rule #2- any ray going through the focal point will exit parallel to the axis
Example #3
?
C F
Rule #2- any ray going through the focal point will exit parallel to the axis
Example #3
C F
BUT NOTE THE REFLECTED RAYS NEVER MEET
Example #3
C F
We extend the reflected rays where they will meet.
Example #3
C F
Example #3
Where is the image?Is the image real or virtualIs the image upright or inverted (vertically)What is the height of the image compared to the actual object
Anytime you have to trace back lines, it is virtual
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….
CF
Send a parallel ray
CF
Then send a ray towards the virtual focus
CF
Other principle ray, send one to the vertex
CF
It will reflect at an equal angle from the axis.Then find the intersection of the reflected rays.
CF
Another note, you can still use the center of curvature as a line as well. This is the easiest if it is given…
CF
Where is the image?Is the image real or virtualIs the image upright or inverted (vertically)What is the height of the image compared to the actual object
Convex mirror applet
hi
ho= -
di
doM =
magnification
Height of image Distance of image (from vertex)
Height of object
Distance of object (from vertex)
The negative sign is just there by convention. Meaning its just what people agreed on to use.
Magnification equation for curved mirrors
F
do
di
hi
ho= -
di
do
ho
hi
M =
And the mirror equation
1do
= 1di
+1f
Same as beforefocal length
1do
= 1di
+1f
hi
ho= -
di
doM =
Now a chat about SIGNS, you don’t get to pick here
For distances and focal length,
REAL +Virtual -
CFC F
Concave Convex
f (focal length)
If rays would really focus from the object Real = +
Always + Always -
CFC F
Convex
do ,distance of the object
Always +, the object is always real
CFC F
Convex
di ,distance of the image
+ if image is real, - for virtual
CFC F
hi and M+ if image is upright, - for inverted
h’s and M ones that don’t fit the rule
They will ALWAYS have the same sign.
CFC F
+ if image is upright, - for inverted
ho is always +,why?
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 1 = n2 sin 2
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 lineAnd 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
hot low density air, light travels faster
cool high density air
Consider the air close to hot pavement.
Which way will the light bend?
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 exampleFor example
For example
The critical incident angle is that which will produce a refracted angle of 90o
Refraction applet
n1 Sin(C ) = n2 Sin( )
Sin(C ) = n1
n2
any angle larger than this produces TIR
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
49o
TIR in water 22o
TIR in Diamond
The greater the optical density of the substance the greater range of angles for internal reflection
Angles for TIR Angles
for TIR
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
27o Diamond
water
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
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
Also note the two rays that just go straight
Focal length
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 that goes through the optical center is undeflected (passes straight through).
f
Any ray parallel to the axis, goes through the focal point.
Ray tracing with lenses
f
A real, inverted image
Lens applet
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
For concave lenses…
f
1.) send a ray through the optical center2.) send a parallel, and refract away from the virtual focus
A virtual, upright image
1do
= 1di
+1f
hi
ho= -
di
doM =
Same rules apply here.For distances and focal length,REAL +Virtual -
h,M Upright +Inverted -
do
di
f
hi
ho
M
GUESS THAT SIGN
++
+-+-
do
di
f
hi
ho
M
--
++++
GUESS THAT SIGN
GUESS THAT SIGN
CONVEX LENSES
Object further from lens than focus
Object closer to lens than focus
The power of a lens is defined as the inverse of the focal length.
P = 1f
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?2.) Is it real or virtual?3.) Is it upright or inverted?4.) What is the height of the image5.) What is the power of the lens
53 cm, side opposite object
real, di is +
real images are always inverted
- 13 cm
4.2 D
To predict the focal point of a THIN lens, we use a good approximation known as the
Lensmaker’s equation
1f
= (n-1) 1R1
+ 1R2
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
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.
Huygen’s Principle
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)
Difference in path lengths (l)
Destructive (out of phase)
Constructive (in of phase)
Destructive (out of phase)
So in general… where m is an integer
l = m
(m+½ )
1etc...
½etc...
l =
Constructive interference occurs when the difference in path length is multiples of the wavelength
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 #
m = 0
m = 1m = 1
Notice that the brightness of each fringe decreases as m increases
0
Representing fringes with a curve showing relative intensity
1123 2 3
If the path difference is multiples of a wavelength, they will be in phase at the screen
l = d sin()
Pretty darn close to theta, given that d will be about a mmAnd L will be at least a meter.
How to predict where the bright spots will be?
d sin() = m
Distance between slits
Angle from slits
Order #(integers)
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
d sin() = m
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?
Double slit diffraction applet
Monochromaticlight
Whitelight
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
d sin() = m
What if there are more slits, will the light from the 3rd slit interfere constructively or destructively with the other two
d
d sin() = m
What if there are more slits, will the light from the 3rd slit interfere constructively or destructively with the other two
d
d sin() = 1
Here the extra path 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
2d sin() = 2
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() = m
Central bright spot(m = 0)
What did “d” stand for in a double slit?
d sin() = m
What did “d” stand for with multiple slits?
d
The distance between any 2 slits. (They will be evenly spaced)
This might be the first order bright fringe?
d sin() = m
d
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
d sin() = m
The same equation holds here as well.What will d stand for here?
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
Ripple tank
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
This makes sense from Huygens Principle
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
d
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.
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() = m Slit width
What value of m would you use to find the first dark spot?
0 or 1
What does reference to?
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?
1 = 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
n2 > n1air
glass
know this
When a light wave reflects off a material with a lower index of refraction, it reflects back in phase
n1 > n2air
glass
air
know this
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?
air
water
air
AB
But the key things to remember are that:Beam 1 is inverted upon reflectionBeam 2 has to go a greater distance
air
water
air
1
2
1
2
If the two reflected rays traveled the same distance when they met, they would be out of phase
The 2nd beam has unit wavelengths colored for clarity
Destructive interference (Dark)
Reflected off of water
Reflected off of air
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)
air
water
air
1
2
1
2
Ray 2 has to travel a greater distance
How much extra distance would cause them to be in phase again?
Half a wavelength
1
2
If the extra distance is a full wavelength
1
2
Here
1
2
Here
If the extra path difference (L) is where m is some integer
l = m
(m+½ )
1etc...
½etc...
Destructive interference
Constructive interference
Don’t write this yet
l =
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?
t
l = 2t
If the extra path difference (L) is where m is some integer
2t = m
2t = (m+½ )
1etc...
½etc...
Destructive interference
Constructive interference
Not done yet
What happens to the wavelength as the light enters the glass?
t
n
n =n
Entering from a vacuum or close enough for air
Conditions for thin film interference
2t = m
2t = (m+½ )
1etc...
½etc...
Destructive interference
Constructive interference
OK now
n
n
And if the both rays are inverted or neither ray is inverted… Is this correct?
L = m
L = (m+½ )
1etc...
½etc...
Destructive interference
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
A
B
Paths will be different for angles, and thereforeDifferent colors of light will be reinforced at Different locations on a surface.
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 , 2etc..
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 = /2Then extra path will be
When will the next dark fringe occur.
If thickness = Then extra path will be 2
2t = m n
Given that the index of air is close to 1 and rearranging
t = m 2
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 .
t = m 2
m = 0m = 1m = 2m = 3m = 4
t = 0t = t =
t =
t =
Would the point of contact between the two glass plates be dark or light? Why?
m = 0m = 1m = 2m = 3m = 4
t = 0t = t =
t =
t =
Dark, because the path length difference is zero and the reflections are out of phase.
How thick is the object?
t = m 2
m = 0m = 1m = 2m = 3m = 4
t = 0t = t =
t =
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 = 0m = 1m = 2m = 3m = 4
t = 0t = t =
t =
t =
What will happen to the spacing of the dark fringes if a thicker object is used?
m = 012345
678
91011
12