1. Electromagnetic Waves

2. Lecture 13 Electromagnetic Waves Ch. 33
Cartoon
Opening Demo
Topics
Electromagnetic waves
Traveling E/M wave - Induced electric and induced magnetic amplitudes
Plane waves and spherical waves
Energy transport Poynting vector
Pressure produced by E/M wave
Polarization
Reflection, refraction,Snell’s Law, Internal reflection
Prisms and chromatic dispersion
Polarization by reflection-Brewsters angle
Elmo
Polling

3. Electromagnetic Waves

4. Eye Sensitivity to Color

5. Production of Electromagnetic waves

6. Spherical waves Plane waves

7. To investigate further the properties of
electromagnetic waves we consider
the simplest situation of a plane wave.
A single wire with variable current
generates propagating electric and
magnetic fields with cylindrical symmetry
around the wire.
If we now stack several wires parallel
to each other, and make this stack
wide enough (and the wires very close
together), we will have a (plane) wave
propagating in the z direction, with
E-field oriented along x, E = Ex
(the current direction) and B-field
along y B=By (Transverse waves)

8. Electromagnetic Wave

9. How the fields vary at a Point P in space as the wave goes by

11. Electromagnetic Wave

12. Electromagnetic Wave Self Generation
Faraday’s Law of Induction
Maxwell’s Law of Induction
Changing electric field induces a magnetic field
Changing magnetic field induces a electric field

13. Summary

14. U is the energy
carried by a wave
Magnitude of S is like the intensity

17. Relation of intensity and power for a Spherical Wave
A point source of light generates a spherical wave. Light is emitted isotropically and the intensity of it falls off as 1/r2
Let P be the power of the source
in joules per sec. Then the intensity
of light at a distance r is
Lets look at an example

18. 15. The maximum electric field at a distance of 10 m from an isotropic point light source is 2.0 V/m. Calculate
(a) the maximum value of the magnetic field and
(b) the average intensity of the light there?
(c) What is the power of the source?
(a) The magnetic field amplitude of the wave is
(b) The average intensity is
(c) The power of the source is

20. Speed of light in Water

21. Nothing is known to travel faster than light in a vacuum
However, electrons can travel faster than light in water.
And when the do the electrons emit light called
Cerenkov radiation

23. Momentum and Radiation Pressure
Momentum = p
What is the change in momentum of the paper over some time interval?
Light beam c
paper
p=U/c
p=0
1) Black paper absorbs all the light
2) Suppose light is 100% reflected
From this we define the pressure

24. Radiation Pressure Pr
Want to relate the pressure Pr felt by the paper to the
intensity of light
For 100% absorption of light on the paper
For 100% reflection of light

25. Problem 21 What is the radiation pressure 1
Problem 21 What is the radiation pressure 1.5 m away from a 500 Watt lightbulb?

26. Radiation pressure: Light carries momentum
Another property of light
Radiation pressure: Light carries momentum
This is the force per unit area felt by an object
that absorbs light. (Black piece of paper))
This is the force per unit area felt by an object
that reflects light backwards.
(Aluminum foil)

27. Polarization of Light
All we mean by polarization is which direction is the electric vector vibrating.
If there is no preferred direction the wave is unpolarized
If the preferred direction is vertical, then we say the wave is vertically polarized

28. A polarizing sheet or polaroid filter is special
material made up of rows of
molecules that only allow light
to pass when the electric
vector is in one direction.
Pass though a polarizing sheet
aligned to pass only the y-component

29. Unpolarized light Resolved into its y and z-components
The sum of the y-components and
z components are equal

30. Intensity I0 One Half Rule Half the intensity out Pass though a
polarizing sheet
aligned to pass
only the y-component
Malus’s Law
One Half Rule
Half the intensity out

31. Polarizer P1
Analyzer P2 y

32. Sunglasses are polarized vertically
Sunglasses are polarized vertically. Light reflected from sky is partially polarized and light reflected from car hoods is polarized in the plane of the hood
Sunglass 1
Sunglass 2
Rotate sun glass 90 deg and no light gets through
because cos 90 = 0

33. 35. In the figure, initially unpolarized light is sent through three polarizing sheets whose polarizing directions make angles of 1 = 40o, 2 = 20o, and 3 = 40o with the direction of the y axis. What percentage of the light’s initial intensity is transmitted by the system? (Hint: Be careful with the angles.)
Let Io be the intensity of the unpolarized light that is incident on the first polarizing sheet. The transmitted intensity of is I1 = (1/2)I0, and the direction of polarization of the transmitted light is 1 = 40o counterclockwise from the y axis in the diagram. The polarizing direction of the second sheet is 2 = 20o clockwise from the y axis, so the angle between the direction of polarization that is incident on that sheet and the the polarizing direction of the sheet is 40o + 20o = 60o. The transmitted intensity is I0 I1 I2 I3
and the direction of polarization of the transmitted light is 20o clockwise from the y axis.

34. 35. In the figure, initially unpolarized light is sent through three polarizing sheets whose polarizing directions make angles of 1 = 40o, 2 = 20o, and 3 = 40o with the direction of the y axis. What percentage of the light’s initial intensity is transmitted by the system? (Hint: Be careful with the angles.)
The polarizing direction of the third sheet is 3 = 40o counterclockwise from the y axis. Consequently, the angle between the direction of polarization of the light incident on that sheet and the polarizing direction of the sheet is 20o + 40o = 60o. The transmitted intensity is
Thus, 3.1% of the light’s
initial intensity is transmitted.

35. Chapter 33 Problem 34
In Figure 33-42, initially unpolarized light is sent into a system of three polarizing sheets whose polarizing directions make angles of θ1 = θ2 = θ3 = 16° with the direction of the y axis. What percentage of the initial intensity is transmitted by the system?
Fig

36. Chapter 33 Problem 49
In Figure 33-51, a 2.00 m long vertical pole extends from the bottom of a swimming pool to a point 90.0 cm above the water. Sunlight is incident at angle θ = 55.0°. What is the length of the shadow of the pole on the level bottom of the pool?
Fig

37. Chapter 33 Problem 62
Suppose the prism of Figure has apex angle ϕ = 69.0° and index of refraction n = 1.59.
Fig
(a) What is the smallest angle of incidence θ for which a ray can enter the left face of the prism and exit the right face?
(b) What angle of incidence θ is required for the ray to exit the prism with an identical angle θ for its refraction, as it does in Figure 33-55?
In Figure 33-51, a 2.00 m long vertical pole extends from the bottom of a swimming pool to a point 90.0 cm above the water. Sunlight is incident at angle θ = 55.0°. What is the length of the shadow of the pole on the level bottom of the pool?