Lecture 2: Electromagnetic Radiation (aka The Nature of Light)

stationary charge has electric field

accelerating charge produces ripples (waves) in electric field

propagation direction perpendicular to E, B fields (E and B perpendicular too)

H = B field in this plot

Five Fundamental Properties

a) speed of propagation, c

b) direction of propagation

c) wavelength

d) polarization (direction !E points)

light from source generally mixture of waves with different b), c), and d) properties

however, c is always cm/sec in vacuum3× 1010

e) intensity

grows as magnitudes of !E and !B grow

one measure is energy/volume:

energy density =1

8π( "E ·

"E + "B ·"B)

=1

8π(E2 + B

2)

another measure is energy flux (energy crossing in some direction/area/time):

!f =c

4π( !E × !B)

f = cEB/4π

flux = c(energy density)

Poynting’s formula

Sidebar: Vector Arithmetic

!A ·!B = ABcosθ

!A

θ

dot product

project length A onto direction B and multiply result

commutative : !A ·!B =

!B ·!A

If !A ⊥ !B, what does !A · !B =?

!B

Sidebar: Vector Arithmetic

cross product

| !A × !B| = ABsinθ

!A

!B

!A × !Bθ

magnitude = area of parallelogram, direction given by right-hand rule

not commutative: !A × !B "= !B × !A

If !A ‖ !B, what does !A × !B =?

The Nature of Light (cont.)

How does a charged particle respond to light?

force exerted on charge q moving at !v through !E, !B

!F = q( !E +!v

c× !B)

from !F = m!a, get !a ∝ q/m

electron oscillates sympathetically with passing EM wave

electron’s oscillation generates waves that reinforceor interfere (refraction or reflection)

why are mirror surfaces made of metal?

Lorentz’s formula

highest a for electrons

Telescopesobservations by collecting and analyzing light

a photon's journey...

• emitted by a source (such as a star)

• perhaps absorbed by interstellar material along the way, perhaps re-emitted...

• crashes through atmosphere, perhaps absorbed (sunsets are red), perhaps scattered (the daytime sky is blue)

• falls onto telescope mirror (bounces on several mirrors)

• is seen by our eye, photographed, or digitally imaged

key points of detecting radiation

• atmosphere limits light that reaches group by absorbing and scattering it, and also blurs image

• telescopes collect light

• optics are used to reflect, refract, or disperse light

• at present, large optical telescopes can improve resolution up to few tenths of an arcsecond

• instruments (computers and detectors) enable photometry and spectroscopy, large and sophisticated on modern telescopes...

• and running them and telescope is computer-intensive activity...

• other ground based observing facilities in infrared and radio wavelength regimes...

• space-based observatories remove constraints of atmosphere (blurring and blocking of certain wavelengths of light)

Hubble Telescope image

ground-based image

1/r2Laws

gravity, electric force, light

let’s look at a radiating source

same amount of energy/time, or luminosity (L) crosses successive spheres at larger r

energy/area/time (energy flux) at distance r = L/4πr2

or, luminosity/surface area

standard candles --> distances