Lecture 1-2 Flashcards
What do Maxwell’s equations describe?
Generation and propagation of light
What are the properties of light?
- Light carries an electric and magnetic field
- Light has a frequency and wavelength so it carries energy
- Light has momentum
- Light is polarized
- Light has coherence
- Light can interact with gravity
- Light can interact with itself (photon-photon interactions)
What are the equations involving light?
c = lamda * v
E = hv = hc/lamda
p = E/c
What are Maxwell’s equations?
Gauss’ law of electric charges: ▽E = p/ε0
Gauss’ law of magnetism: ▽B = 0
Faraday’s law (of induction): ▽E = -ϕB/ϕt
Ampere’s law: ▽B = u0J + μ0ε0(ϕE/ϕt)
What is Gauss’ law of electric charges?
Electric fields are generated by single charges and diverge
What is Gauss’ law of magnetism?
Magnetic fields are generated by dipoles and do not originate in a single point
What’s Faraday’s law?
A time-varying magnetic field always accompanies a spatially varying electric field and vice versa (theory of induction)
What is Ampere’s law?
Magnetic fields are generated either by electric currents and/or by changing electric fields (solenoids = coiled electrical wire which, when current passes through them, create strong uniform magnetic field)
How can classical EM theory describe light?
EM is one of the four main forces in nature (gravity, weak force, EM force, strong force)
Self-propagation of light is composite of 2 waves varying in unison, an electric wave + magnetic wave
2 major acting forces in EM theory: electrostatic forces + magnetic forces
What is an EM wave?
Consists of rapidly varying electric + magnetic fields which propagate through space
Energy from light can only be imparted to objects in photons
Amount of energy a photon can impart is proportional to its frequency
What is lorentz (EM) force
Measures force exerted on charged particle moving through electric + magnetic field
Responsible for binding electrons to nuclei as well as intermolecular interactions
F = qE + qvB
What are the 2 main ways light is generated?
Heat source - thermal radiation (with heat being relative, anything over 0 kelvin)
From emission spectrum of translucent matter interacting with specific spectrum of light
What are the radiative heat loss equations?
Pnet = Pemit - Pabsorb
Pnet = Aσε(T^4 - T0^4)
P: power
A: area
Sigma: Boltzmann constant
T: temperature (to envir. temp)
What are the main ways in which light is generated?
Radiation - from heat sources
Radioactivity - gamma rays
Luminescence - comes from sources other than heat
What kinds of luminescence are there?
Photoluminescence = absorption of another photon (fluorescence, phosphorescence, most scattering events)
Chemiluminescence = chemical reaction
Electroluminescence = electric current (lasers, LEDs, lightning)
Mechanoluminescence = mechanical stress (tribo-, piezo-, sonoluminescence)
How is light generated (in general)?
Electrons are excited to higher energy level by means other than heating for luminescence (chemical reaction, electric current, etc.)
Light is generated on discrete levels depending on what substance’s electrons are being excited
When the excited photon drops to normal state, a photon is released
Explain exponential decay
A quantity is said to decay exponentially if it decreases at a rate proportional to its current value: dN/dt = -lamda*N
Solution of differential equation: N(t) = N0e^(-lamda*t)
N: quantity
t: time
lamda: exponential decay constant
N(t): quantity at time t
N0: initial quantity (t = 0)
Explain mean lifetime and half-life
Mean lifetime of quantity = exponential time constant T = time it takes for quantity to be reduced to 1/e of its initial value
T = 1/lamda = 1/decay constant
Half-life = t(1/2) = time it takes for quantity to be reduced to half its initial value
t(1/2) = ln2/lamda = T*ln2
What is fluorescence?
Property of compound to absorb light in a certain range of wavelengths and emit a different wavelength of light (usually longer) - Stokes shift
Shorter time of re-emission (nanoseconds)
Variable mean lifetime or half-life
What is phosphorescence?
A phosphorescent material does not immediately re-emit absorbed radiation
The transition between excited and ground states in these materials happens very slowly
Light is re-emitted at a lower intensity for up to several hours after original excitation
What are the two kinds of elastic scatterings of light?
Rayleigh: elastic scattering on molecules smaller than incident wavelength
Mie: elastic scattering on molecules similar to or larger than incident wavelength
Both = no energy is lost
What is the inelastic scattering of light?
Raman: inelastic scattering of photons by matter - both an exchange of energy and change in light’s direction
Inelastic: scattered photons have different energy (usually lower) than incident photons
Many biosensors being developed using this phenomenon
How does chemiluminescence work?
Emission of light that occurs from chemical reactions that produces high amounts of energy lost in the form of photons
A + B -> AB* -> Products + Light
AB* = excited state
Light = ground state
How does bioluminescence work?
ATP driven + relate to luciferin (responsible for producing light) + enzyme luciferase
Formula:
Luciferin + O2 -> (Luciferase) -> Oxyluciferin + Light
ATP is hydrolyzed by luciferase enzyme to oxidize luciferin (exciting it) and upon compound’s return to ground state, photon is released
