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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 waves with alternating electric and magnetic fields, and amplitudes given by: r E = r E o sin 2 π λ ( x ct ) where: E o is the electric amplitude, λ is the wavelength, and c is the propagation speed. The wavelength and frequency are related by the Dispersion relation: λν = c, in vacuo.

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Page 1: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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.

Page 2: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

From Wikipedia: electromagnetic spectrum

Wavelengths and frequencies: the EM spectrum

Page 3: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

Atmospheric transmission.

From NASA Goddard Space Flight Center

Page 4: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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

Page 5: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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

Page 6: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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

Page 7: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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.

Page 8: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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.

Page 9: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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.

Page 10: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

Doppler

Page 11: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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

Page 12: Basic Characteristics of Electromagnetic Radiation.astro.346/notes/lec4.pdf · Basic Characteristics of Electromagnetic Radiation. Brief review of EM waves, with a view towards astronomical

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).