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Coherent Sources
Wavefront splitting Interferometer
Young’s Double Slit Experiment
Young’s double slit
© SPK
Path difference: PSSP
2222 22 dxDdxD
dxD ,
1 2 1 22 2
2 2
2 21 1
For 1
1 1n
x d x dD D
D D
y
y nx
222 2
2
2 2
x d x d
D
x d d xd D
For a bright fringe,
For a dark fringe,
SP S P m
2 1 2SP S P m
m: any integer
For two beams of equal irradiance (I0)
204 cos
xdI I
D
Visibility of the fringes (V)
max min
max min
I IV
I I
Maximum and adjacent minimum of the fringe system
Photograph of real fringe pattern for Young’s double slit
The two waves travel the same distance– Therefore, they arrive in phase
S
S'
• The upper wave travels one wavelength farther–Therefore, the waves arrive in phase
S
S'
• The upper wave travels one-half of a wavelength farther than the lower wave.
This is destructive interference
S
S'
• Young’s Double Slit Experiment provides a
method for measuring wavelength of the light• This experiment gave the wave model of light a
great deal of credibility.
Uses for Young’s Double Slit Experiment
Wavefront splitting interferometers
•Young’s double slit
•Fresnel double mirror
•Fresnel double prism
•Lloyd’s mirror
Confocal hyperboloids of revolution in 3D
S
S
Path difference
20, 1, 2, 3
SP S P m
m
- confocal hyperbolae with S and S as common foci
2 2
2 2 2
11 1
( )4 4
x y
d
D=ml
Transverse section –Straight fringes
S
S
d
P
D
O
x
The distance of mth bright fringe from central maxima
Fringe separation/ Fringe width
Dx
d
d
mDDx mm
sin
Longitudinal section –Circular fringes
P
O
rn
S
Sd
D
N
q
Path difference = d
For central bright fringe
0
dm
2 00
cos
2( ) 2 ( )
m
m
SP SP SN d m
m m nn m m
d d
Radius of nth bright ring
For small qm
22 2 2 2n m
D nr D
d
Wavefront splitting interferometers
•Young’s double slit
•Fresnel double mirror
•Fresnel double prism
•Lloyd’s mirror
Interference fringes
Real Virtual Localized Non-localized
Localized fringe
Observed over particular surface
Result of extended source
Non-localized fringe
Exists everywhere
Result of point/line source
Concordance
Discordance
= (q+1/2)
Division of Amplitude
Phase Changes Due To Reflection• An electromagnetic wave undergoes a phase change of 180°
upon reflection from a medium of higher index of refraction than the one in which it was traveling– Analogous to a reflected pulse on a string
21 μ1
μ2
Phase shift 0k
D
nfn1 n2
B
d
A
C
ti
t
t
A
B
C
D
Optical path difference for the first two reflected beams
f 1
t
f
1
n [AB BC] n (AD)
AB BC d /cos
nAD ACsin 2d tan sin
ni t t
f2n dcos t
Condition for maxima
cos (2 1) 0, 1, 2,...4f
f tdn m m
Condition for minima
cos 2 0, 1, 2,...4f
f tdn m m
Fringes of equal thickness
Constant height contour of a topographial map
Wedge between two plates1 2
glassglass
air
Dt
x
Path difference = 2tPhase difference = 2kt - (phase change for 2, but not for 1)
Maxima 2t = (m + ½) o/n
Minima 2t = mo/n
Newton’s Ring• Ray 1 undergoes a phase change of 180 on
reflection, whereas ray 2 undergoes no phase change
R= radius of curvature of lens
r=radius of Newton’s ring
R
r
R
rRR
rRRd
2
2
22
2
1
...2
11
2
12 ( )
2
1 12 ( )
2 2
1 1( ) ( ) , 0,1,2...
2 2
For bright ring
bright
d n
rn
R
r n R n R n
...2,1,0,
n2d
ringdark For
nnRrdark
Reflected Newton’s Ring
Newton’s Ring
1. Optics Author: Eugene Hecht Class no. 535 HEC/O Central library IIT KGP