Reflection and Refraction of EM waves at dielectric-dielectric and dielectric-conductor interfaces

1. Course: Electromagnetic Theory
paper code: EC 501
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
Topic: Reflection and Refraction at Dielectric-Dielectric
and Dielectric-Conductor Interfaces
07-10-2025 Arpan Deyasi, EM Thoery 1
Arpan Deyasi
Electromagnetic
Theory

2. Consider interface between two dielectrics Ei
Er
Et
Hr
Hi
Ht
η1
η2
1
1
1

 =

2
2
2

 =

Media are characterized by
i 1 i
E H
=  r 1 r
E H
= −
t 2 t
E H
= 
Reflection and Transmission Coefficients for Dielectric-Dielectric Interface
Arpan Deyasi
Electromagnetic
Theory

3. Reflection and Transmission Coefficients for Dielectric-Dielectric Interface
From the continuity equation of magnetic field intensity
i r t
E E E
+ = i r t
H H H
+ =
According to the continuity of tangential components
i r t
H H H
+ =
t
i r
1 1 2
E
E E
− =
  
i r i r
1 2
E E E E
− +
=
 
Arpan Deyasi
Electromagnetic
Theory

4. r 2 1
i 2 1
E
E
 − 
=
 + 
Reflection and Transmission Coefficients for Dielectric-Dielectric Interface
2 1
E
2 1
R
 − 
=
 + 
Reflection coefficient for Electric Field
t i r r 2 1
i i i 2 1
E E E E
1 1
E E E
+  − 
= = + = +
 + 
Arpan Deyasi
Electromagnetic
Theory

5. Reflection and Transmission Coefficients for Dielectric-Dielectric Interface
t 2
i 2 1
E 2
E

=
 + 
2
E
2 1
2
T

=
 + 
t i r r 2 1
i i i 2 1
E E E E
1 1
E E E
+  − 
= = + = +
 + 
Transmission coefficient for Electric Field
Arpan Deyasi
Electromagnetic
Theory

6. Reflection and Transmission Coefficients for Dielectric-Dielectric Interface
t
t t 1
2
i
i i 2
1
E
H E
E
H E


= =


t 2 1 1
i 2 1 2 2 1
H 2 2
H
  
=  =
 +    + 
1
H
2 1
2
T

=
 + 
Transmission coefficient for
Magnetic Field Intensity
Arpan Deyasi
Electromagnetic
Theory

7. Reflection and Transmission Coefficients for Dielectric-Dielectric Interface
r r 1 2
i i 1 2
H E
H E
 − 
= − =
 + 
1 2
H
1 2
R
 − 
=
 + 
Reflection coefficient for
Magnetic Field Intensity
Arpan Deyasi
Electromagnetic
Theory

8. Reflection and Transmission Coefficients for Dielectric-Dielectric Interface
For non-magnetic dielectrics
1 2 0
 =  = 
1 2
E
1 2
R
 − 
=
 + 
2 1
E
2 1
R
 − 
=
 + 
1
E
1 2
2
T

=
 + 
2
H
1 2
2
T

=
 + 
Arpan Deyasi
Electromagnetic
Theory

9. Reflection and Transmission Coefficients for Dielectric-Conductor Interface
Ei
Er
Et
Hr
Hi
Ht
η1
conductor
2 0
 =
E
R 1
= − E
T 0
=
H
T 2
=
H
R 1
=
Arpan Deyasi
Electromagnetic
Theory

10. Reflection and Transmission Coefficients for Dielectric-Conductor Interface
Magnetic field of incident wave
Magnetic field of reflected wave
Resultant electric field
j z j z
i i
E e E e
 − 
= −
( )
i
2jE sin z
= −  ( ) ( )
i
2E sin z sin t
=  
Electric field exhibits standing wave
j z
i
H e− 
=
j z
i
H e 
=
Arpan Deyasi
Electromagnetic
Theory

11. Reflection and Transmission Coefficients for Dielectric-Conductor Interface
Magnetic field of incident wave
j z
i
E e− 
=
Magnetic field of reflected wave
Resultant magnetic field
( ) ( )
i
2H cos z cos t
=  
Magnetic field exhibits standing wave
( )
i
2H cos z
= 
j z j z
i i
H e H e
 − 
= +
Arpan Deyasi
Electromagnetic
Theory