1. 8-6 Normal Incidence at a Plane Conducting Boundary
The incident wave travels in a lossless medium
The boundary is an interface with a perfect conductor. y . x z
z=0
Reflected
wave
Medium 2
Perfect conductor Hr Er
anr
Incident wave ( inside medium 1 ) Hi Ei
ani
Incident
wave
Medium 1

2. 8-6 Normal Incidence at a Plane Conducting Boundary
Inside medium 2 , both electric and magnetic fields vanish
No wave is transmitted across the boundary into the z > 0 .
Reflected wave ( inside medium 1 )

3. 8-6 Normal Incidence at a Plane Conducting Boundary
Total wave in medium 1
- continuity of tangential component of the E-field at the boundary z = 0

4. 8-6 Normal Incidence at a Plane Conducting Boundary
The space-time behavior of the total field in medium 1

5. 8-6 Normal Incidence at a Plane Conducting Boundaryz x
E1 versus z
H1 versus z
The total wave in medium 1 is not a traveling wave.
Standing wave.
Note following three points
ⅰ) vanishes on the conducting boundary.
ⅱ) a maximum on the conducting boundary.
ⅲ) The standing waves of and are in time quadrature ( 90˚ phase difference ).

6. 8-7 Oblique Incidence at a Plane Conducting Boundary
8-7.1 Perpendicular Polarization y . x z
z=0
Reflected
wave
Direction of propagation of incidence wave
Medium 2
Perfect conductor Hr Er
anr
Incident wave ( inside medium 1 )
Incident
wave Hi Ei
ani
Medium 1

7. 8-7 Oblique Incidence at a Plane Conducting Boundary
Direction of propagation of reflected wave
Reflected wave ( inside medium 1 )
Boundary condition, z = 0
, for all x
Snell’s law of reflection
» the angle of reflction equals the angle of incidence.

8. 8-7 Oblique Incidence at a Plane Conducting Boundary
Magnetic field of the Reflected wave

9. 8-7 Oblique Incidence at a Plane Conducting Boundary
Total field in medium 1

10. 8-7 Oblique Incidence at a Plane Conducting Boundary
 In z-direction ( x=constant )
 In x-direction ( z=constant )
C = f(z)
, D = g(z)

11. 8-7 Oblique Incidence at a Plane Conducting Boundary
 In x-direction
 when
or when

12. 8-7 Oblique Incidence at a Plane Conducting Boundary
 In x-direction , wave propagate
But, ( not transverse )
∴ TE wave
At A, A’’, O (intersection of the long and short dashed lines) → E=0
At B ( intersections of two long dashed line) → E ( out of page ) is maximum .
At B’ ( intersections of two short dashed line) → E ( into the page ) is maximum .
Thes points travel in the +x direction
Guided wavelength

13. 8-7 Oblique Incidence at a Plane Conducting Boundary
8-7.2 Parallel Polarization y . x z
z=0
Reflected
wave
Direction of propagation of incidence wave
Medium 2
Perfect conductor Hr Er
anr
Incident wave ( inside medium 1 ) Hi Ei
ani
Incident
wave
Medium 1

14. 8-7 Oblique Incidence at a Plane Conducting Boundary
Direction of propagation of reflected wave
Reflected wave ( inside medium 1 )
Boundary Condition
( for all x)

15. 8-7 Oblique Incidence at a Plane Conducting Boundary
Total field in medium 1
 In z-direction : standing-wave
 In x-direction : traveling wave ( phase velocity : )
 nonuniform plane wave
 where
∴ TM wave

16. 8-8 Normal Incidence at a Plane Dielectric Boundary
Incident wave ( inside medium 1 ) y . x z
z=0
Medium 2
Reflected
wave
Transmitted
wave Hr Er
anr Ht Et
ant
Reflected wave ( inside medium 1 )
Incident
wave Hi Ei
ani
Transmitted wave ( inside medium 2 )
Medium 1

17. 8-8 Normal Incidence at a Plane Dielectric Boundary
The tangential components (the x-components)
of the electric and magnetic field intensities
must be continuous. ( at interface z=0 )
Reflection coefficient ( + or - ) ≤ 1
E/H, E=0 perfect conductor !!
H(I)=0 No current !!

18. 8-8 Normal Incidence at a Plane Dielectric Boundary
Transmission coefficient ( + always )
If medium 2  Perfect conductor
 Totally reflected . Standing wave produced in medium 1 .

19. 8-8 Normal Incidence at a Plane Dielectric Boundary
If medium 2 is not a perfect conductor ,
partial reflection will result .
traveling
standing

20. 8-8 Normal Incidence at a Plane Dielectric Boundary
For dissipationless media are real .
However, can be positive or negative. ⅰ)
- Maximum value of is ,
which occures when
- Minimum value of is ,
which occures when

21. 8-8 Normal Incidence at a Plane Dielectric Boundaryⅱ)
- Maximum value of is , at
- Minimum value of is , at
Standing wave Ratio (SWR)
if  = 0, S=1 : No reflection, full power transmission
if  = 1, S=  : Total reflection, no power transmission

22. 8-8 Normal Incidence at a Plane Dielectric Boundary
Transmitted wave