Today Ch.36 (Diffraction)
Next week, Dec.6, Review
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Final Exam: (Ch.21-25, 27-29, 32,33,35,36)
Secs.511-515: December 9, Friday: 12:30-2:30 pm
Secs.521-525, 528: December 12, Monday, 8-10 am

Lecture 24 (Ch. 36)
1. Huygen’s principle, bending of the rays
2. Fraunhofer’s diffraction
3. Single slit
4.Two slits with a finite width
5. Resolution of the lens
6. Diffraction grating
7.Spectroscopy
8. x-ray diffraction
9. e diffraction

Huygen’s principle and bending of the rays

Augustin-Jean Fresnel
1788 – 1827
Joseph von Fraunhofer
(1787 – 1826)

Single slit diffraction
How to describe the real picture?

 r
 r
 a sin

Single slit diffraction a
2 sin min :
 a
  sin


2

( 1 st m
 min)
( m

 a sin


1 ,

2 ,...)
  
NB : m
( m

0
  
0 all rays

0 !
parallel to axis
 max!
) for small

; sin
  tan
  y x
, min : y m
 x
 m a

Intensity distribution
R=
1 st max
 
0
E

  k
 r

2

 a sin

E

2

R sin

2
,
 
E
0 ,
R
E


E
0
 sin

2 min max
:

:



2
 m
 a sin

( 2 m

1 )
  m

( m
2

0 )
, I


I
0
{
 sin

2
}
2
2
E

1 st min:
 
2

1 st max:
 
3


I


I
0
{
 sin

2
}
2
; min :
 
2
 m
 a sin
  m

( m

0 )
2

Narrowing of the first fringe with increase of the slit width
 
1
 a

Circular hole diffraction

The photographs of four very small sources of light taken made with a circular aperture in front of the lens

Rayleigh’s criterion for resolution of two point objects : Two objects are barely resolved if the center of one diffraction pattern coincides with the first minimum if the other.
S

L sin
 
1 .
22

D
L
For a microscop
John William Strutt, 3rd Baron Rayleigh
1842 – 1919
CD :
 
780 nm
DVD :

( 0 .
7 gigabytes )

650 nm ( 4 .
7 gigabytes )

Hubble: D=2.4m,

Arecibo: D=300m,



500 nm
75 cm
S
L


L sin
 
1 .
22

D
3 .
8

10
8 m ( to the moon )
S
H
L


77
4 ly ( m , S
A
 nearest
1000 km ( crater star ,
 size
Centaury )
)
1 ly
S
H
 c

1 year

10
7 km ,

3

10
8
D
Jupiter m
 
10
7 s s

10
5 km

10
13 km

D
1
=8.5m, D eq
=24m
 
500 nm

Arrays of telescopes

Two slits with a finite width
Interefere nce
Difraction factor : factor :
E

E
0
(

)


2 E
0
(

)
 cos

2 sin
E
0

2
,
 
,
  kd sin ka sin


2
I


4 I
0
{
 sin

2
}
2 cos
2

2
2

Diffraction grating max :
 
2
 m
 d sin
  m

E
0 t
E ot

NE
0

I ot

N 2 I
0
!

N-1 minima

With increase of N principal maxima becomes narrower and their amplitude grows as N
2

Spectrum of sunlight produced by a diffraction grating has dark absorption lines due to absorption of the corresponding wavelength by the solar atmosphere. It allows to find out a chemical composition of the solar atmosphere.


~ 0 .
1

10 nm
Wilhelm Röntgen (1845 – 1923)
The 1 st Nobel Prize,1901

2 d sin
  n

An x-ray scattering pattern of DNA recorded by
Rosalind Franklin led Watson and Crick to discovery of the DNA double helix structure

Louis de Broglie (1892 – 1987)

Electromagnetically induced transparency (EIT)
Two undistinguishable absorption passes for light result in cancellation of absorption (transparency ).
An electron has the wave property. It may be in a superposition of states 1 and 1’.
Monohromatic light with a frequency resonant either to one or another atomic transition is absorbed.
Bichromatic light containing two resonant frequencies goes through.


1


2
1’
1
O.K., Y.I.Khanin, JETP, 1986; O.K., P. Mandel, Phys. Rev. A. 1990. theory
S.E. Harris, PRL, 1991. experiment

Electromagnetically induced transparency (EIT)
2
1




1’
Two undistinguishable absorption passes for light result in cancellation of absorption (transparency).
An electron has the wave property. It may be in a superposition of states 1 and 1’.
A circular polarized light interacts only with 1-
2 (or 1’-2) state and absorbed. A linear polarized light interacts with both 1-2 and 12’ states and goes through the medium without absorption.
To make medium transparent for light with given circular polarization send through the medium simultaneously light with another circular polarization.


1


2
The same is true for two beams of different frequencies
1’
When the frequency difference coincides with the frequency of the atomic transition 1-
1’.
1
O.K., Y.I.Khanin, JETP, 1986; O.K., P. Mandel, Phys. Rev. A. 1990. theory
S.E. Harris, PRL, 1991. experiment