physics for scientists and engineers ii, summer semester 2009 1 lecture 28: august 3 rd 2009 physics...
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Physics for Scientists and Engineers II , Summer Semester 2009
1
Lecture 28: August 3rd 2009
Physics for Scientists and Engineers II
Physics for Scientists and Engineers II , Summer Semester 2009
2
The Single Slit Diffraction Pattern (Fraunhofer Diffraction Patters)
L
y1
y2
-y1
-y2
Physics for Scientists and Engineers II , Summer Semester 2009
3
The Single Slit Diffraction Minima
a
2
a
2
a
sin2
a
Huygens Principle: Each part of the slit is a source of light waves.
1
2
31b
2b
3b
a
a
sin
2sin
2 : minimumA
Under these conditions: Ray 1 interferesDestructively with 1b, 2 with 2b, etc…
Physics for Scientists and Engineers II , Summer Semester 2009
4
The Single Slit Diffraction Minima
a
a 2sin
2sin
4 : minimumA
Divide slit into 4 equal parts:
a
a 3sin
2sin
6 : minimumA
Divide slit into 6 equal parts:
am
m
a sin2
sin2
: minimumA
Divide slit into 2m equal parts:
......3,2,1sin ma
mdark
Physics for Scientists and Engineers II , Summer Semester 2009
5
....3,2,1sin
sin0
ma
m
ma
whenI
dark
dark
Intensity Distribution of the Single-Slit Diffraction Pattern
2
max sin
sinsin
a
aII
Physics for Scientists and Engineers II , Summer Semester 2009
6
Single Slit Diffraction Pattern
0
-15
Intensity Distribution of the Single-Slit Diffraction Pattern
2
max sin
sinsin
a
aII
2 323
Physics for Scientists and Engineers II , Summer Semester 2009
7
Intensity Distribution of the Double-Slit Diffraction Pattern
2
2max sin
sinsinsincos
a
adII
Double slit pattern – as discussed before
Each of the two slits exhibits thesingle slit diffraction pattern
Physics for Scientists and Engineers II , Summer Semester 2009
8
Double Slit Diffraction Pattern (with single slit envelope) d/a=5
0
-6
Intensity Distribution of the Double-Slit Diffraction Pattern
2
2max sin
sinsinsincos
a
adII
Physics for Scientists and Engineers II , Summer Semester 2009
9
Suppressed Maxima in the Double Slit Pattern
2
2max sin
sinsinsincos
a
adII
msin d
for Maxima
.....2,1sin a
for Minima
nn
page). previous (See5a
dmat maximumslit double
theerases 5a
dfor slit) single of minimum(first 1n :Example
minimum.slit single aon fallsit because erased is
maximumslit double n the and m of ratios For thesesin a
sin d
a
d
n
m
n
m
Physics for Scientists and Engineers II , Summer Semester 2009
10
Resolution of Single Slit Apertures
S1
S2
S1
S2 Unresolved center maximafor smaller angle.
Just barely resolved center maxima (max.of S1 falls on first min.of S2.(Rayleigh’s criterion)
Physics for Scientists and Engineers II , Summer Semester 2009
11
Resolution of Single Slit Apertures
S1
S2
angles) smallfor (approx.
:a width ofslit afor resolution of angle Limiting
sin :minimumfirst ofLocation
min a
a
Just barely resolved center maxima (max.of S1 falls on first min.of S2.(Rayleigh’s criterion)
Physics for Scientists and Engineers II , Summer Semester 2009
12
Resolution of Single Slit Apertures
D
22.1
:Ddiameter of aperture round afor resolution of angle Limiting
min
Example: Telescopes using mirrors of a certain diameter:The larger the mirror, the smaller the limiting angle of resolution. (Critical in viewing close objects that are far away).
Physics for Scientists and Engineers II , Summer Semester 2009
13
The “Diffraction” (Interference) Grating
s.wavelengthdifferent resolve ability tobetter
widerare minima sharper, a Maxima :However
,....2,1,0sin
:slit double with as angles same at theoccur Maxima
mmλθ d bright
Transmission Grating
d
Physics for Scientists and Engineers II , Summer Semester 2009
14
The “Diffraction” (Interference) Grating
,....2,1,0sin mmλθd bright
Reflection Grating
Physics for Scientists and Engineers II , Summer Semester 2009
15
The Spectrometer
f
Light source
TelescopeEye
Analyze the spectral lines of atoms (learn about electronic energy levels).Identify the composition of gases (e.g., what atoms are sending out light from a distant star (send light through spectrometer and look for “fingerprint”of atoms.
Physics for Scientists and Engineers II , Summer Semester 2009
16
X-Ray Diffraction
atoms) of spacing (e.g., structure crystal examine toUse
!!! atomsbetween spacing as small asely approximat bemust d
1106.017.0
101.0
sin10d
:maximum a of )10 (e.g. angle reasonable aFor
0.1nm :rays- xof Wavelength
99
Angstrommm
d
sind
,....2,1,0sin2
:Law sBragg'
mmλθd reflected
Physics for Scientists and Engineers II , Summer Semester 2009
17
Linearly Polarized Light
y
zx
E
B
c
E
y
B
Linearly polarized light
Physics for Scientists and Engineers II , Summer Semester 2009
18
Unpolarized Light
E
yUnpolarized light (traveling out of the page)Is a superposition of many em waves that have electric fields polarized in different directions.Example: Emitted from an ordinary light bulb.
Physics for Scientists and Engineers II , Summer Semester 2009
19
Polarizing Light By Preferential Absorption
E
y
Polaroid(a material with oriented long-chainedmolecules that selectively transmits lightwhose electric field is orientedalong these molecules and absorbslight that has its E-field oriented perpendicular to these molecules.
E
y
Polarized light
Physics for Scientists and Engineers II , Summer Semester 2009
20
Crossed Polarizers
E
y
Second polarizer oriented the same as first:All the polarized light passes through theSecond polarizer.
E
y
Polarized light
E
y
Physics for Scientists and Engineers II , Summer Semester 2009
21
Crossed Polarizers
E
y
Second polarizer oriented perpendicular to first:All the polarized light is absorbed in the second Polarizer. No light passes through second polarizer.
E
y
Polarized lighty
Physics for Scientists and Engineers II , Summer Semester 2009
22
Crossed Polarizers
E
y
Second polarizer oriented at angle to first:Only the component of E-field in directionof second polarizer gets through Transmitted Intensity is proportional to E2.
E
y
Polarized lighty
2E
law) sMalus'(
cos22 II
cos2 EE
Physics for Scientists and Engineers II , Summer Semester 2009
23
Polarizing Light by Reflection
incident reflected
refracted
2n
1n
Physics for Scientists and Engineers II , Summer Semester 2009
24
Polarizing Light by Reflection
incident Reflected light polarized
refracted
2n
1n90
2212
1
1
2 9018090 ;sin
sin
n
n
PPP when
P
2
1
2
1
2
n
ntantan
cos
sin
90sin
sin
n
n
PP
P
P
P
P
“Brewster Angle”