1. Sources (EM waves) 1

2. a quick recap…

3. electromagnetic waves
In general,
electromagnetic waves
Where  represents E or B
or their components 3

4. Traveling 3D plane wave 4

5. Maxwell’s equations

6. Plane EM waves in vacuum6

7. Polarization

8. Electromagnetic Waves

9. Linear Polarization

10. Circular Polarization
A left-handed/counter-clockwise circularly polarized wave as defined from the point of view of the source. It would be considered right-handed/clockwise circularly polarized if defined from the point of view of the receiver.

11. Elliptical Polarization
Different amplitudes and Phase difference = /2
Elliptical Polarization

12. Elliptical Polarization
Different amplitudes and Phase difference not /2
Elliptical Polarization

13. Electromagnetic spectrum

14. The Radio Milky Way
© NRAO Green Bank

15. Cosmic microwave background fluctuation
Cosmic Background Explorer

16. Ultraviolet Galaxy
©NASA/JPL-Caltech/SSC

17. Energy (EM waves) 17

18. EM waves transport Energy and Momentum
The energy density of the E field (between the plates of a charged capacitor):
Similarly, the energy density of the B field (within a current carrying toroid):
Using: E=cB and
The energy streaming through space in the form of EM wave is shared equally between constituent electric and magnetic fields.

19. S represent the flow of electromagnetic energy associated with a traveling wave.
S symbolizes transport of energy per unit time across a unit area
Assume that the energy flows in the direction of the propagation of wave (in isotropic media)
The magnitude of S is the power per unit area crossing a surface whose normal is parallel to S.

20. B is perpendicular to E 20

21. B, k and E make a right handed Cartesian co-ordinate system21

22. Plane EM waves in vacuum22

23. Given:
Instantaneous flow of energy per unit area per unit time
Time averaged value of the magnitude of the Poynting vector
The Irradiance is proportional to the square of the amplitude of the electric field: 23

24. Reflection and Transmission24

25. In an inhomogeneous medium (Reflection and Transmission)25

28. At the boundary x = 0 the wave must be continuous, (as there are no kinks in it).
Thus we must have

30. We can define the transmission coefficient: (C/A)

31. Rigid End: 2   (2 >> 1) k2  
We can define the Reflection coefficient: (B/A)
Rigid End: 2   (2 >> 1)
k2  
When 2 > 1 ,
r < 0
Change in sign of the reflected pulse
External Reflection

32. Free End: 2  0 (2 << 1) k2  0
When 2 < 1 ,
r > 0
No Change in sign of the reflected pulse
Internal Reflection

33. In either case: tr > 0
No Change in phase of the transmitted pulse

34. It can be seen that
Stoke’s relations
Will be also derived from Principle of Reversibility
The reflectance and transmittance of Intensity is proportional to square of Amplitude

35. Refraction 35

36. Snell’s Law of Refraction
It is used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media.

37. Huygens’s and Fermat’s Principles37 37

38. Huygens’s Principle
Every point on a propagating wavefront serves as a source of spherical secondary wavelets, such that the wavefront at some later time is the envelope of these wavelets.
If the propagating wave has a frequency , and is transmitted through the medium at a frequency t, then the secondary wavelets have that same frequency and speed. 38

39. Huygens’s Principle
Every unobstructed point on a wavefront will act as a source of secondary spherical waves.
The new wavefront is the surface tangent to all the secondary spherical waves. 39

40. Huygens’s Principle : when a part of the wave front is cut off by an obstacle, and the rest admitted through apertures, the wave on the other side is just the result of superposition of the Huygens wavelets emanating from each point of the aperture, ignoring the portions obscured by the opaque regions.

42. Fermat’s Principle
In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light.
From Fermat’s principle, one can derive
the law of reflection [the angle of incidence is equal to the angle of reflection] and
(b) the law of refraction [Snell’s law] 42

43. Law of Reflection The time required for the light to traverse the path
To minimize the time set the derivative to zero

44. Law of Refraction The time required for the light to traverse the path
To minimize the time set the derivative to zero