basic characteristics of electromagnetic radiation.astro.346/notes/lec4.pdf · basic...

Basic Characteristics of Electromagnetic Radiation.Brief review of EM waves, with a view towards astronomical application.

From notes for MIT Physics 8.02,Electricity and Magnetism

I. Traveling wave characteristics

E&M radiation consists of transverse waveswith alternating electric and magnetic fields,and amplitudes given by:

r E =

r E o sin

2πλ( x − ct )

where: Eo is the electric amplitude, λ is thewavelength, and c is the propagation speed.

The wavelength and frequency are related by the

Dispersion relation: λν = c, in vacuo.

From Wikipedia: electromagnetic spectrum

Wavelengths and frequencies: the EM spectrum

Atmospheric transmission.

From NASA Goddard Space Flight Center

Important wave-like properties:

Diffraction:Waves bend around obstacles.

Every unobstructed point on a wavefront will act a source ofsecondary spherical waves. The new wavefront is the surfacetangent to all the secondary spherical waves.

From notes for MIT Physics 8.02, Electricity and Magnetism

Interference:

e.g., double-slit (Young’s) pattern of interfering waves.

The amplitudes of the overlapping waves add directly, but the brightness or intensitydepends on the square of the sum (where a 1-d. equation is used for simplicity).

I ∝ E1 sin2πλ( x1 − ct )

+ E2 sin

2πλ(x 2 − ct )

2

II. Light Rays, Geometric Optics.

is often a convenient way to look at EM wave propagation. The ‘rays’ arestraight normals to local wave fronts, with the following properties.

Reflection: Equal angles of incidence and reflection as measured from a normal to thesurface. This principle allows mirrors to focus light.

Refraction (dispersion): Generally light rays are bent as they pass through theboundary between two media, or through a medium with a temperature or pressuregradient. Dispersion results whern the bending (or index of refraction) depends onwavelength.

Ray optics + Huygens’ wave principle help us better understand diffraction andinterference.

2 slits again -

Δx = λ

Δx = λ/2

Δx = 0

Intensity

Mirror reflection:

Δx = 0Δx = λ

Reverse diffraction pattern

Width of centraldiffraction peak:

θ ≈ λ/d,

where d is theaperature size. Thisgives,

θ = 5 x 10-7 rad =0.1 arcsecond for a1 m diametertelescope.

III. Particle Aspect of Electromagnetic Radiation.

In addition to its wave nature, electromagnetic radiation also seems to comein discrete bundles of energy called ‘photons.’ The energy of a photondepends on the frequency of the radiation via Planck’s law:

ε = hν = hc/λ.This relation connects the wave-particle dual characteristics of EM radiation.

The particle aspect is most relevant at high energies, or very low light levels,i.e., where there are few photons.

The Doppler EffectOften explained by analogy to sound or water waves. See squeezed wavediagram below.

Full special relativistic expression for wavelength of light from a moving sourceis,

€

λλo

=1+ v /c1− v /c

1/ 2

.

When v/c << 1, we can approximate this by,

€

λ /λo ≈ 1+ 12vc( ) 1− (− 1

2vc )( ) ≈1+ v /c,

so, Δλλo

=λ − λoλo

=λλo−1 ≈ v /c.

Doppler

Intensity and FluxTo describe the flow (and scattering) of radiation we need the definitions ofintensity and flux, which quantify the idea of a directed, density of radiation.

Monochromatic intensity - is the amount of energy in the frequency interval (ν,ν+Δν) flowing through a unit area, per unit time, into a cone of unit solid angle,in a given direction.

€

r I ν =

ΔEΔνΔAΔtΔΩ

ˆ n Js ⋅m2 ⋅Hz ⋅ ster

.

ΔΩ

Monochromatic flux - is easier to define! Integrate intensity in solid angle overa hemisphere. Thus, flux is the energy in frequency range (ν, ν+Δν) flowingthrough a unit area per unit time, and into ‘any’ direction (of the hemisphere).

ΔA

__________________________________Alternately, the flux received at a detector is the total incoming energy perunit time, etc., from any angle (though often from a single point source).