1. Sources (EM waves) 1

2. Electromagnetic spectrum

3. The Radio Milky Way
© NRAO Green Bank

4. Cosmic microwave background fluctuation
Cosmic Background Explorer

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

6. Energy (EM waves) 6

7. 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.

8. S represent the flow of electromagnetic energy associated with a traveling wave.
S symbolizes transport of energy per unit time across a unit area: Poynting Vector
ct
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.

9. B is perpendicular to E 9

10. B, k and E make a right handed Cartesian co-ordinate system10

11. Plane EM waves in vacuum11

12. 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: 12

13. Reflection and Transmission13

14. In an inhomogeneous medium (Reflection and Transmission)14

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

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

20. 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

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

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

23. 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

24. Refraction 24

25. 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.

26. Waves at Interface
Consider a monochromatic planar light wave incident at an interface:
The most general form for the reflected and transmitted waves

27. Electromagnetic Theory: Boundary Conditions
The component of E (and H) that is tangent to the interface must be continuous across it.
i.e., the total tangential component of E on one side of the surface must equal that on the other.
NOTE: The tangential component of E is always continuous at any boundary, but the normal component is discontinuous by and amount σ/εo.

28. This has to be true for all values of time:
Now:
Prove it to be sure
Hecht (4th Ed.) Chapter 2

29. Law of Reflection
Furthermore:
Snell’s Law

30. Huygens’s and Fermat’s Principles30 30

31. 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. 31

32. 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. 32

33. 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.

35. 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
the law of refraction [Snell’s law] 35

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

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

38. Principle of superposition38

39. Principle of superposition

42. Resultant phasor

45. Superposition of a large number of phasors
Problem
Superposition of a large number of phasors
of equal amplitude a and equal successive
phase difference θ. Find the resultant
phasor.
Remember: The sum of the first n terms of a geometric series is:

46. Addition of Phasors
GP series 46

48. We will revisit!