physics for scientists and engineers ii, summer semester 2009 1 lecture 28: august 3 rd 2009 physics...

Physics for Scientists and Engineers II , Summer Semester 2009

1

Lecture 28: August 3rd 2009

Physics for Scientists and Engineers II


2

The Single Slit Diffraction Pattern (Fraunhofer Diffraction Patters)

L

y1

y2

-y1

-y2


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…


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


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


6

Single Slit Diffraction Pattern

0

-15

Intensity Distribution of the Single-Slit Diffraction Pattern

2

max sin

sinsin

a

aII

2 323


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


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


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


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)


11


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)


12


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).


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


14

The “Diffraction” (Interference) Grating

,....2,1,0sin mmλθd bright

Reflection Grating


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.


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


17

Linearly Polarized Light

y

zx

E

B

c

E

y

B

Linearly polarized light


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.


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


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


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


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


23

Polarizing Light by Reflection

incident reflected

refracted

2n

1n


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”

physics for scientists and engineers ii, summer semester 2009 1 lecture 28: august 3 rd 2009 physics...

Documents

summer semester

double slit pattern

xray diffraction slide

polarized light slide

rayleighs criterion

intensity distribution

source of light waves

equal parts