Post on 18-Jul-2020
Reflection, Refraction and Polarization of EM wave
PPN College, Kanpur
Department of Physics, P. P. N. (PG) College,
Kanpur – 208 001, U.P., IndiaEmail: pandeydrdk@rediffmail.com,
dr.dkpandey@gmail.comWebsite: dkpandey.weebly.com
Dharmendra Kumar Pandey
30 May 2020 1
30 May 2020 PPN College, Kanpur 2
Boundary condition for EM wave
1. The normal component of electricdisplacement vector is not continuous atthe interface but changes by an amountequal to the free surface charge density.
2. The normal component of magneticinduction B is continuous across theinterface.
D-D 2n1n
0B-B 2n1n
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 330 May 2020 PPN College, Kanpur 3
Boundary condition for EM wave
3. The tangential component of electric field iscontinuous at the interface.
4. The tangential component of magnetic fieldstrength is not continuous at the interfacebut changes by an amount equal to thecomponent of the surface current densityperpendicular to tangential component of H.
0E-E 2t1t
JH-H S2t1t
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 4
Reflection and Refraction of EM waveFor Incident wave
)tr.1K(i
011 eEE
1
111
EKB
11
111
EKH
For reflected wave)tr.1K(i
011 eEE
1
111
EKB
11
111
EKH
)tr.2K(i
022 eEE
2
222
EKB
11
111
EKH
For refracted wave
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 530 May 2020 PPN College, Kanpur 5
Reflection and Refraction of EM wave
Since, tangential component of electric field iscontinuous at interface .
t2t1t1 )E()E()E(
)t2r.2k(i
t02
)t1r.1k(i
t1o
)t1r.1k(i
t01 e)E(e)E(e)E(
211
)r.2k(i
t02
)r.1k(i
t1o
)r.1k(i
t01 e)E(e)E(e)E(
t02t1ot01 )E()E()E(for ,Therefore
0z20z10z1 )r.k()r.k()r.k(
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 630 May 2020 PPN College, Kanpur 630 May 2020 PPN College, Kanpur 6
Reflection and Refraction of EM wave
11 kk
r1i1 sinxksinxk
0z10z1 )r.k()r.k( ,If
Since wave propagationvector does not vary insame medium thus
ri sinsin
ri
0z20z1 )r.k()r.k( ,If
r2i1 sinxksinxk
1
2
r
i
k
k
sin
sin
2
1
1
2
r
i
v
v
k
k
sin
sin
11
22
2
1
r
i
v
v
sin
sinn
Law of reflection Law of refractionD K
Pan
dey,
PPN Coll
ege,
Kanpu
r
30 May 2020 PPN College, Kanpur 7
Fresnel Equation for Reflection and Refraction of EM wave
A: When E is perpendicular to plane of incidence
r
2
2i
1
1
r
2
2i
1
1
01
01
coscos
coscos
E
E
r
2
2i
1
1
i
1
1
01
02
coscos
cos2
E
E
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 8
)sin(
sincos2
cosncosn
cosn2
E
E
ri
ri
r2i1
i1
01
02
Fresnel Equation…………. contdfor Reflection and Refraction of EM wave
r
i
1
2
1
2021
sin
sin
n
n then if
)sin(
)sin(
cosncosn
cosncosn
E
E
ri
ri
r2i1
r2i1
01
01
For normal incidence ; i=r=0
21
21
01
01
nn
nn
E
E
21
1
01
02
nn
n2
E
E
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 9
Case 1: when (n1/n2)<1 ; wave : rare to densern=Sini / Sinr =(n2/n1)>1 and i > r
Fresnel Equation…………. contdfor Reflection and Refraction of EM wave
2differencePath ; Change Phase ve
E
E
01
01
Reflected and incident wave are in opposite phase.Refracted and incident wave are in same phase.
Case 2: when (n1/n2)>1 ; wave :denser to raren=Sini / Sinr =(n2/n1)<1 and i < r
0 Change Phase veE
E
01
01
Reflected and incident wave are in same phase.Refracted and incident wave are in same phase.
0 Change Phase veE
E
01
02
0 Change Phase veE
E
01
02
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 10
Fresnel Equation…………. contdfor Reflection and Refraction of EM wave
B: When E is parallel to plane of incidence
r
1
1i
2
2
r
1
1i
2
2
01
01
coscos
coscos
E
E
r
1
1i
2
2
i
1
1
01
02
coscos
cos2
E
E
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 11
)cos()sin(
sincos2
cosncosn
cosn2
E
E
riri
ri
r1i2
i1
01
02
r
i
1
2
1
2021
sin
sin
n
n then if
)tan(
)tan(
cosncosn
cosncosn
E
E
ri
ri
r1i2
r1i2
01
01
For normal incidence ; i=r=0
12
12
01
01
nn
nn
E
E
12
1
01
02
nn
n2
E
E
Fresnel Equation…………. contdfor Reflection and Refraction of EM wave
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 12
Fresnel Equation…………. Contd….for Reflection and Refraction of EM wave
Case 1:
Refracted and incident wave are in same phase.
0 Change Phase veE
E
01
02
Case 2: From both cases we found that -
)tan(
)tan(
E
Er
ri
ri
II01
01II
)sin(
)sin(
E
Er ;
ri
ri
01
01
1
21
riBprin
ntan
2 or
2 if
0r and 0rII Thus , if an un-polarized light incidents (rare to denser) at angle p= B thenonly electric vector perpendicular to plane of incidence will be reflected andlight will become polarized. This angle is termed as angle of polarization orBrewster’s angle.D K
Pan
dey,
PPN Coll
ege,
Kanpu
r
30 May 2020 PPN College, Kanpur 13
Fresnel Equation…………. Contd….for Reflection and Refraction of EM wave
Case 3: if em wave travels from denser to rarer medium then it goes away from normal.
)tan(
)tan(
E
Er
ri
ri
II01
01II
)sin(
)sin(
E
Er ;
ri
ri
01
01
1
21
cirn
nsinor
2
1r and 1rII
1rR and 1rR22
IIII
Thus total energy is reflected at the interface of two mediums.This means, as the angle of incident wave increases, the intensity ofreflected wave increases while intensity of refracted wave diminishes. Theintensity of refracted wave becomes zero at i=c. But if i>c then wavecompletely goes in medium Ist, and follows law of reflection. This is TIR.
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 14
Reflection and transmission coefficient
2
01
2
01
2
011
2
011
)E(
)E(
)E(v
)E(v
aveincident w ofIntensity
wavereflected of IntensityR
2
012
2
021
2
011
2
022
)E(k
)E(k
)E(v
)E(v
aveincident w ofIntensity
waveed transmittof IntensityT
2
011
2
022
)E(n
)E(nT
For normal incidence ; i=r=0
12
12
01
01
nn
nn
E
E
12
1
01
02
nn
n2
E
E
1TR
Note : Degree of polarization
)(tan
)(tanR &
)(sin
)(sinR ;
RR
RRP
ri
2
ri
2
II
ri
2
ri
2
II
II
D K P
ande
y, PPN C
olleg
e, Kan
pur
30 May 2020 PPN College, Kanpur 15
Faraday Effect or Faraday Rotation
When an isotropic medium of high refractive index isplaced in strong magnetic field, then it becomesoptically active temporarily.
If a plane polarized EM wave passes through suchmedium then its plane of polarization is rotated. This iscalled as Faraday rotation.
BL
VBL
V=Verdet constant
V
1mL and 1TB ,If
D K P
ande
y, PPN C
olleg
e, Kan
pur
PPN College, Kanpur
A Lot of Thanksfor attention
30 May 2020 16