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 snd Intensity of a wave Poynting vector Radiation Pressure produced by E/M wave
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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)
U is the energy
carried by a wave
Relation of intensity and power for a Spherical Wave - Variation of Intensity with distanceA 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
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
However, electrons can travel faster than light in water.
And when the do the electrons emit light called
Momentum = p
What is the change in momentum of the paper over some time interval?
1) Black paper absorbs all the light
2) Suppose light is 100% reflected
From this we define the pressure
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
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
Resolved into its y and z-components
The sum of the y-components and
z components are equal
Pass though a
aligned to pass
only the y-component
One Half Rule
Half the intensity out
Intensity is proportional to
square of amplitude
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
Rotate sun glass 2 90 deg and no light gets through
because cos 90 = 0
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
Dispersion: Different wavelengths have different velocities and therefore different indices of refraction. This leads to differentrefractive angles for different wavelengths. Thus the light is dispersed.The frequency does not change when n changes.
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?
47. In the figure, a 2.00-m-long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. What is the length of the shadow of the pole on the level bottom of the pool?
Consider a ray that grazes the top of the pole, as shown in the diagram below. Here 1 = 35o, l1 = 0.50 m, and l2 = 1.50 m.
The length of the shadow is x + L.
x is given by
x = l1tan1 = (0.50m)tan35o = 0.35 m.
L is given by
Use Snells Law to find
L is given by
Calculation of L
According to the law of refraction, n2sin2 = n1sin1. We take n1 = 1 and n2 = 1.33
The length of the shadow is L+x.
L+x = 0.35m + 0.72 m = 1.07 m.
Sin θrefr= 0.7nλ
Polarization by Reflection: Brewsters Law
Index of refraction
Hot road causes gradient in the index of refraction that increases
as you increase the distance from the road