Diffraction and Polarization
Diffraction
Diffraction from narrow slits
Resolution issues
The diffraction grating
Polarization
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Diffraction and Polarization: Understanding Wave Interference and Light Properties - Prof., Study notes of Physics
The concepts of diffraction and polarization of light waves. It covers topics such as fraunhofer diffraction, diffraction from narrow slits, interference patterns, resolution issues, and polarization. The document also includes problem-solving exercises and concept questions related to spectroscopy, x-ray diffraction, and polarization.
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Pre 2010
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Diffraction and Polarization
Diffraction
Diffraction from narrow slits
Resolution issues
The diffraction grating
Polarization
Diffraction
Light rays canbend aroundcorners
No sharp boundary existsbetween the dark andbright parts on the screen
Diffraction From Narrow Slits
Each portion of the slit acts as a wave source.
sin 2
a
λ^ a
sin
λ a
sin
λ a
sin
Divide slit into two parts
Now divide it into four parts
And into six parts
… so in general for destructive interference
a m
sin
m
a
m
m
λ
θ
sin
y^ m^ L
m
tan
sin
tan
y^ L
a m
m
≈
m
L a
y
m
m
Positions of Dark Fringes
Two-Slit Diffraction Pattern
Interference and diffraction occur simultaneously
(^
)^
2
2
max
sin
sin
sin
sin
cos
⎤ ⎥ ⎦
⎡⎞⎟⎢⎠⎣
⎛⎜ ⎝
=
λ θ
π
λ θ
π
λ
θ
π
a
a
d
I
I
Resolution of Single Slit andCircular Apertures
When the central maximum of one image falls on the first minimum of theother Image, the images are said to be just resolved. This limiting conditionis called the
Rayleigh’s Criterion
For a given lens diameter, which light gives thebest resolution in a microscope? 1. red 2. yellow 3. green 4. blue 5. All give the same resolution.
Concept Question
Limiting Resolution of aMicroscope
cm
D
nm (^9).
5890 =^ = λ
rad
D
5
(^92)
min
10
(^98). 7
10
(^9). 0
10
589
(^22). 1
(^22). 1
−
− −
×
=
× ×
=
=
λ
θ
nm
400
λ
rad 5
(^92)
min
10
(^42). 5
10
(^9). 0
10
400
(^22). 1
−
− −
×
=
× ×
=
θ
(^33). 1 =
water n
rad nm
nm
n vacuum^ water
water
5
(^92)
min
10
6
10
(^9). 0
10
443
(^22). 1
443
(^33). 1 589
−
− −
×
=
× ×
=
=
=
=
θ
λ
λ
Diffraction Gratings
A device with closely spaced slits (or grooves).
Light passing through the slits will interfere with each other toproduce a multiple slit interference pattern
The position of the constructive peaks will be dependent onwavelength.
m
d
sin
Spectrometers
Problem 38.
2 3
N
d
1
d
m
λ
θ =
sin
θ
(^
)^
(^
nm
N
d
nm
v^
sin
3
θ
nm nm
v r
λ λ
(^
)^
(^
nm
N
d
nm
r^
sin
2
θ
2
3
2
3
sin
sin
r
v
r
v^ θ
θ
θ
θ =
N
X-Ray Diffraction
An X-ray has a wavelength onthe order of the atomicseparation in crystals (~0.1 nm).
Successive layers of atoms actas a diffraction grating for the X-ray and create an interferencepattern.
The pattern is a characteristic ofthe crystal structure.
sin
m
m
d
θ 2
max
cos
I
I
= Malus’ Law
Polarization by SelectiveAbsorption ^
These polarizers workby transmitting lightalong their transmissionaxis.
The transmitted light willhave a polarizationalong the transmissionaxis.
Unpolarized light will betransmitted as a linearlypolarized wave at halfthe intensity.
When a ray of light is incident on two polarizers with theirpolarization axes perpendicular, no light is transmitted. If athird polarizer is inserted between these two with itspolarization axis at 45° to that of the other two, does any lightget through to point
P
?
- yes 2. no