Physics Lecture 28: Diffraction in 202 - Single-Slit, Two-Slit, Circular Apertures, Study notes of Physics

A portion of a university physics lecture on the topics of diffraction, including single-slit diffraction, two-slit interference, and diffraction on circular apertures. The text also covers the rayleigh criterion and the separation between minima for single-slit and circular apertures. Not for examination purposes but serves as a reminder and includes derivations using phasors.

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

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Physics 202, Lecture 28
Today’s Topics
!!Diffraction
!!Reminder of Single-slit Diffraction
!!Reminder of Two-slit Interference
!!Double-Slit Diffraction
!!Diffraction on Circular Apertures
!!The Rayleigh Criterion
Single-Slit Diffraction Pattern Explained
"!The slit is not a point source! Interference
The text also offers a derivation using phasors.
Not to be examed but please read.
!
I=I0
sin(
"
/2)
"
/2
#
$
%
&
'
(
2
"
)2
*
+
Dsin
,
!"
D
#y
$=2%/& ysin! @y"
E0
y
Reminder: Single-slit Diffraction
!
I=I0
sin(
"
/2)
"
/2
#
$
%
&
'
(
2
"
)2
*
+
Dsin
,
D
D
D
D
D
Separation between minima =
!
"
D
Reminder: Two-slit Interference
path length difference
' =dsin! ~ d! ~ d y/l
!
I=Iocos2
"
dsin
#
$
%
&
' (
)
*
Separation between minima =
!
"
d
pf2

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Physics 202, Lecture 28

Today’s Topics

!! Diffraction !! Reminder of Single-slit Diffraction !! Reminder of Two-slit Interference !! Double-Slit Diffraction !! Diffraction on Circular Apertures !! The Rayleigh Criterion

Single-Slit Diffraction Pattern Explained

"!The slit is not a point source! Interference The text also offers a derivation using phasors. Not to be examed but please read.

I = I 0

sin( " / 2 )

2

D sin ,

D^ !"

#y $=2%/& ysin! @y" E 0 y

Reminder: Single-slit Diffraction

I = I 0

sin( " / 2 ) " / 2

2 " )

D sin , D D D D D Separation between minima = !

D

Reminder: Two-slit Interference

path length difference ' =dsin! ~ d! ~ d y/l

I = Io cos

2 " d^ sin^

Separation between minima =^ "^ *

d

Two-slit Diffraction

I = Io cos^2

d sin +

I = I 0

sin( " / 2 ) " / 2

2 " )

D sin , !

I = I 0

sin( " / 2 ) " / 2

2 cos^2

Diffraction on Circular Apertures

"!Light through apertures will produce diffractive patters depending on their shape. For circular apertures the diffractive patters is made of concentric rings Separation between minima = !

D

Resolution of Single-slit and Circular Apparatus

two separate beams each smeared due to diffraction Rayleigh’s Criterion Separable Minimally separable Not separable #!Single slit: !min = &/D #!Circular opening: !min = 1.22 &/D