Phys 0 Lecture 6 Electromagnetic wave energy & polarization
Today we will... Learn about properties p of electromagnetic waves Energy density & intensity Polarization linear, circular, unpolarized Apply those concepts Linear polarizers Optical activity Circular dichroism Phys. 0, Lecture 6, Slide
E & B field energy density There is energy stored in an E & B field B d E A Parallel l plate capacitor Recall Lect. 6 Solenoid U ε A Ed ε E Ad d 0 = CV ( ) = = 0 ( ) C 0 Volume containing E field It is convenient to define energy density = energy per volume [J/m 3 ] ue = ε0e ub = B These expressions are correct μ0 for any E & B field in a vacuum Phys. 0, Lecture 6, Slide 3
EM wave energy There is energy stored in an EM wave in oscillating E & B fields E 0 B(t) B 0 E(t) Since E and B oscillate, we measure the average energy density ue = ε0 E ub = ε0e rms Erms = = 0 B = B rms Brms = B0 μ0 μ0 u = ε E + B = ε0 E rms = tot 0 + rms μ rms 0 B rms μ 0 E E & B field amplitudes Recall that Et () = cbt () c = ε μ 0 0 Phys. 0, Lecture 6, Slide 4
Calculation: EM power A light bulb emits an average 60 W of power. Calculate E rms & B rms at a distance r = m from bulb. (Assume all electric power goes into EM wave) r = m By energy conservation, power emitted = power through spherical surface at r = m What is rate of EM energy flow through surface? Δ U u 4 tot πr cδt P = = Δ t Δt cδt u tot 0 rms = ε E so Phys. 0, Lecture 6, Slide 5
ACT: EM wave E field E P is the rms E field at a distance r = m from the 60W light bulb. r = m E P r = 4 m? What is the rms E field at a distance r = 4m? A. 4E P B. E P C. E P / D. E P /4 Phys. 0, Lecture 6, Slide 6
EM wave intensity The same power from point source of light flows through surfaces at larger distances, but spread over a larger surface area A. g, p g It is useful to define intensity (I or S): I P = S Units: W/m A Since P = u Ac tot I = S = utot c Intensity corresponds to brightness of light (light is dimmer the further from a point source) I decreases as /r^ Phys. 0, Lecture 6, Slide 7
CheckPoint..7 Longitudinal waves: oscillations are to direction or propagation Transverse waves: oscillations are to direction of propagation λ DEMO λ Ex: Sound Ex: Light Radio waves X rays Microwaves Water waves The wave Phys. 0, Lecture 6, Slide 8
Polarization EM waves are transverse and have polarization by convention, the direction of the E field oscillation z Linear x z Circular E B E z y x Ex: Vertical polarization z y x x B Ex: Left circular polarization Unpolarized direction is random For convenience we will stop showing the B field Phys. 0, Lecture 6, Slide 9
Linear polarizers Linear polarizers consist of metal lines that absorb E field. Transmission axis () is defined in direction that E field passes E E : no light passes E E : light passes What happens for other angles between polarization and? Phys. 0, Lecture 6, Slide 0
E inc Law of Malus Given angle θ between and polarization of incident EM wave: θ E inc E trans θ Component of E field to axis is absorbed: E inc E abs Etrans = Einc cosθ Since I = u c E tot I trans I inc θ E trans I = I cos θ trans inc 0 80 360 θ Light emerges with polarization to axis Phys. 0, Lecture 6, Slide
ACT: polarizer A vertically polarized EM wave passes through a linear polarizer with at 45 E inc What is the direction of the B field after the polarizer? A. B. C. D. What is the magnitude? Phys. 0, Lecture 6, Slide
Calculation: unpolarized light Unpolarized light is incident on a linear polarizer. What is the transmitted intensity? E inc E trans Unpolarized light has an equal mixture of all possible θ s I trans I inc trans inc cos g I I θ I inc / Itrans = θ 0 80 360 Light emerges with polarization to axis = average over all θ: I inc Phys. 0, Lecture 6, Slide 3
ACT: CheckPoint. Unpolarized light passes through a linear polarizer with a vertical. I 0 What is the intensity of light when it emerges? A. zero B. / what it was before C. /4 what it was before D. /3 what it was before Phys. 0, Lecture 6, Slide 4
ACT: CheckPoint. Now the light that emerged from the previous polarizer passes through a second linear polarizer with a horizontal. I 0 What isthe intensity of light when it emerges? A. zero B. / what it was before C. /4 what it was before D. /3 what it was before Phys. 0, Lecture 6, Slide 5
ACT: 3 polarizers Now suppose we add a third polarizer between the two outer polarizers. The polarizer is tilted from vertical. 3 I 0 What is the intensity of the light that emerges? A. zero, same as before B. more than what htit was before bf DEMO C. need more information Phys. 0, Lecture 6, Slide 6
Calculation: 3 polarizers 3 I 0 Phys. 0, Lecture 6, Slide 7
Chirality & optical activity Many organic molecules are chiral they have handedness L alanine D alanine (unnatural enantiometer) Chiral molecules rotate linearly polarized light optical activity DEMO Dextrorotary CW rotation Levorotary CCW rotation Phys. 0, Lecture 6, Slide 8
Circular dichroism Chiral molecules also absorb left vs. right circularly polarized light differently Circular dichroism (CD) measures difference in absorption Tool to distinguish chiral features in biomolecules CD spectra α helix (right handed helix) Phys. 0, Lecture 6, Slide 9
ACT: Law of Malus A B I 0 I 0 Compare the light emerging from the two polarizers in A and B: A. I A B A B A B > I B. I = I C. I < I Phys. 0, Lecture 6, Slide 0
Summary of today s lecture Electromagnetic waves Carry energy in E and B fields energy density & intensity Are transverse & polarized linear, circular, unpolarized Applications Linear polarizers Law of Malus Optical activity Circular dichroism Phys. 0, Lecture 6, Slide