Review - EM Wavesfaculty.tamuc.edu/cbertulani/MecTherm/EM_waves_3.pdf · Review - EM Waves z EM...
Transcript of Review - EM Wavesfaculty.tamuc.edu/cbertulani/MecTherm/EM_waves_3.pdf · Review - EM Waves z EM...
Review - EM WavesEM Waves
Wavelengths of 108 to 10-16 meters (10-1024 Hz)Traveling wave of both Eand B fieldsE field is ⊥ B fieldWave moves in direction ⊥to both E and B fields E and B vary sinusoidally with same frequency
)sin( tkxEE m ω−=
)sin( tkxBB m ω−=
m/s1031 8
00
×====εμ
λfcv
Poynting vector, S – rate of energy transported per unit area:
Instantaneous energy flow rate
Peak intensity (when sin=1) given by
BESrrr
×=0
1μ
)(sin111 22
0
2
00
tkxEc
Ec
EBS m ωμμμ
−===
Review - EM Waves
2
0
1mpeak E
cS
μ=
Express in terms of radiation pressure pr which is force/area
SI unit is N/m2 called pascal Pa
AFpr =
cIpr = c
Ipr2
=
Total absorption Total reflection
EM Waves: Radiation pressure
Source emits EM waves with E field always in same plane wave is polarized
Indicate a wave is polarized by drawing double arrow
Plane containing the E field is called plane of oscillation
EM Waves: Polarization
Source emits EM waves with random planes of oscillation (E field changes direction) is unpolarized
Example, light bulb or Sun
Resolve E field into components Draw unpolarized light as superposition of 2 polarized waves with E fields ⊥ to each other
EM Waves: Polarization
Transform unpolarized light into polarized by using a polarizing sheetSheet contains long molecules embedded in plastic which was stretched to align the molecules in rows
E field component || to polarizing direction of sheet is passed (transmitted), but ⊥ component is absorbedSo after the light goes through the polarizing sheet it is polarized in the same direction as the sheet.
EM Waves: Polarization
What is the intensity, I of the light transmitted by polarizing sheet?For initially polarized light, resolve E into components
Transmitted || component is
Cosine-squared rule: Intensity of polarized wave changes as cos2θ
θ20 cosII =
θcos|| EEEy ==
θθμμ
20
22
0
2||
0
coscos11 IEc
Ec
I ===
EM Waves: Polarization
For unpolarized light, average over cos2
Only light || to polarizer is transmitted
One-half rule: Intensity of unpolarizedwave after a polarizer is half of original
021 II =
EM Waves: Polarization
Have 2 polarizing sheets First one called polarizerSecond one called analyzer
Intensity of unpolarized light going through first polarizer is
Light is now polarized and intensity of light after second analyzer is given by
021
1 II =
EM Waves: Polarization
θθ 202
1212 coscos III ==
An interesting demoEffect of P1 and P3
Take and
After P1
After P3
o01 =θ o903 =θ
021
1 II =
0)90(cos 213 == oII
An interesting demoKeep
Now insert P2 in between P1 and P3 with
After P1
After P2
After P3
o01 =θ o903 =θ
021
1 II =
o452 =θ
0412
12 )45(cos III o ==
0812
23 )45(cos III o ==
ExerciseUnpolarized light hits a polarizer and then an analyzer. The polarizing direction of each sheet is indicated by dashed line. Rank pairs according to fraction of initial intensity which is passed, greatest first.
Look at relative orientation of polarization direction between the 2 sheets.What is the intensity if the sheets are…
Polarized || – all light passesPolarized ⊥ to each other – no light passes For angles in between – get more light if closer to ||
a,d,b,c
Exercise
Optical activity
Certain materials rotate the plane of polarizationThe rotation angle may depends on the frequency (color)This is due to molecular asymmetry - e.g. molecules with spiral shapesKaro syrup