Electromagnetic Waves (Text 2.1)1. Electromagnetic radiation follows classical wave equation nicely because of Maxwell’s work.

2. Electromagnetic radiation is determined by frequency (ν), or wave length (λ). Both frequency and wavelength are wave properties.

c= λν

Electromagnetic wave has a broad spectrum. Its frequency can be as fast as 1022 Hz (Gamma wave) to as slow as 103 Hz (radio wave). Visible light has a snallwindow in between, it has a frequency between 4.3× 1014 Hz (red, λ=700nm) to 7.5× 1014 Hz (violet, λ=400nm).

00

1 cµε

=

Electromagnetic Waves (Text 2.1)

Electromagnetic Waves (Text 2.1)3. In classical wave description, the “displacement” from equilibrium (Ψ) is a function of position (x) and time (t).

4. In one dimension,Ψ(x,t) = A cos (kx-ωt) + B sin (kx-ωt)

or more conveniently,Ψ(x,t) = A e i(kx-ωt+ϕ)

5. k is know as the wave number, and it is interchangeable withwavelength:

ω is the angular frequency, and it is interchangeable with frequency and period:

λπ2 k =

T1 and 2 == νπνω

Electromagnetic Waves (Text 2.1)6. In three dimension,

Ψ( r ,t) = A cos (k ⋅ r-ωt)k is now a vector and it is called the wave vector. Its is pointing in

the direction of wave propagation, and its magnitude is related to wavelength as

λπ2 k =

r

7. Principle of superposition:

ΨTotal( r, t)= Ψ1 ( r , t) + Ψ2( r , t)

8. For electromagnet wave, Ψ is either the electric field E or magnetic field B.

Electromagnetic Waves (Text 2.1)9. Wave theory of light is well supported by experiments in physical optics, like the Young’s experiment and diffraction experiments. All these experimentsinvolve superposition of waves: When two or more waves of the same nature travel past a point at the same time, the instantaneous amplitude there is the sum of the instantaneous amplitudes of the individual waves (same as note 6 above.

Blackbody radiation (Text 2.2)A blackbody absorbs all radiation incident upon it. In reverse, it radiates electromagnetic wave when it is heated. The radiation spectrum depends on the temperature of the blackbody.

A model blackbody

Blackbody radiation (Text 2.2)Some basic properties of blackbody radiation

1. Wien’s Displacement Law gives the peak position:

T or K m 10 7685(51) 2.897 T

max

–3max

∝⋅×=

νλ

2. Stefan’s Law gives the area under curve:

black sonot for 1 blackperfect for 1 emissivity

KmJs105.670400 T

apower /Areradiation Total

4-2-1-8-

4

<==×=

=

εσ

σε

Blackbody radiation (Text 2.2)Blackbody radiation in real life

pyrometer

hottest

Blackbody radiation (Text 2.2)Some basic properties of blackbody radiation

Exact form?

3. Wien’s Law (thermodynamicalderivation):

5

)()(uλλλ Tf

=

(but infinite possible equations can satisfy this requirement!)

Attempt to get the exact equation of the spectral distribution ⇒

Rayleigh-Jeans Theory