Simple Nature - Light and Matter

Multiplying these last two equations by each other, we getc 2 ˜BẼ = v 2 Ẽ ˜Bc 2 = v 2v = ±c .This is the desired result. (The plus or minus sign shows that thewave can travel in either direction.)As a byproduct of this calculation, we can find the relationshipbetween the strengths of the electric and magnetic fields in an electromagneticwave. If, instead of multiplying the equations c 2 ˜B = v Ẽand Ẽ = v ˜B, we divide them, we can easily show that Ẽ = c ˜B.o / The electromagnetic spectrum.Figure o shows the complete spectrum of light waves. The wavelengthλ (number of meters per cycle) and frequency f (number ofcycles per second) are related by the equation c = fλ. Maxwell’sequations predict that all light waves have the same structure, regardlessof wavelength and frequency, so even though radio and x-rays, for example, hadn’t been discovered, Maxwell predicted thatsuch waves would have to exist. Maxwell’s 1865 prediction passedan important test in 1888, when Heinrich Hertz published the resultsof experiments in which he showed that radio waves could bemanipulated in the same ways as visible light waves. Hertz showed,for example, that radio waves could be reflected from a flat surface,and that the directions of the reflected and incoming waves wererelated in the same way as with light waves, forming equal angleswith the surface. Likewise, light waves can be focused with a curved,dish-shaped mirror, and Hertz demonstrated the same thing with adish-shaped radio antenna.Momentum of light wavesA light wave consists of electric and magnetic fields, and fieldscontain energy. Thus a light wave carries energy with it when it travelsfrom one place to another. If a material object has kinetic energyand moves from one place to another, it must also have momentum,so it is logical to ask whether light waves have momentum as well.It can be proved based on relativity that it does, and that the momentumand energy are related by the equation U = p/c, where pSection 11.6 Maxwell’s Equations 703