Chapter 23 EM Waves

Electromagnetic Waves Solution of Maxwell's Equations Simple Idea: Changing Electric field creates Magnetic field Changing Magnetic field creates Electric field Both happen simultaneously and propagate

Characteristics of EM waves The wave is transverse: Both and are perpendicular to the direction of propagation of the wave and to each other. All EM waves move with speed c when in vacuum Require no medium. Definite ratio between E and B E=cB

Formed from E and B field orthonormal to each other, propagating in direction E x B at speed of light c (in vacuum). Direction of propagation: 𝑘 =𝛼 𝐸 × 𝐵

Electromagnetic Waves They carry energy This follow from the fact that electric and magnetic fields have energy Electric energy density Magnetic energy density

Electromagnetic Waves In an electromagnetic wave propagating through a vacuum or air, the electric field and the magnetic field carry equal amounts of energy per unit volume of space. It is possible to rewrite the equation for total energy density, , in two additional, but equivalent, forms:

Electromagnetic Waves The fact that the two energy densities are equal implies that the electric and magnetic fields are related. To see how, we set the electric energy density equal to the magnetic energy density and obtain In 1865, Maxwell determined theoretically that electromagnetic waves propagate through a vacuum at a speed given by Hence, from equation (1) it follows that

Electromagnetic Waves There are 2 ways of calculating the intensity: From the electric and magnetic fields 𝐼= 𝑢 𝑡 ×𝑐= 𝜀 𝑜 𝐸 0 2 2 𝑐= 1 2 𝜇 0 𝑐 𝐵 0 2

Electromagnetic Waves From the power emitted by a source I: intensity, P: power emitted, A: surface area the waves propagate over The intensity of an EM wave tells you the average energy flowing across a surface in a span of time

Electromagnetic Waves They carry momentum Without considering this, Newton’s laws would fail in the presence of electromagnetic waves 𝑝= 𝐸 𝑡𝑜𝑡𝑎𝑙 𝑐 Since they carry momentum, they can apply pressure to an object Prad: radiation pressure, I: Intensity, c: vacuum speed of light, α: ratio of light reflected P 𝑟𝑎𝑑 =(1+𝛼) 𝐹 𝐴 =(1+𝛼) 𝐼 𝑐

Polarization Polarization occurs with all transverse waves (e.g., wave on a string). When a wave has only y displacements, we say that it is linearly polarized in the y direction ; similarly, a wave with only z displacements is linearly polarized in the z direction. For mechanical waves, we can build a polarizing filter that permits only waves with a certain polarization direction to pass. In figure c, the string can slide vertically in the slot without friction, but no horizontal motion is possible.

POLARIZED ELECTROMAGNETIC WAVES Linearly polarized wave on a rope.

In polarized light, the electric field fluctuates along a single direction.

Polarized light may be produced from unpolarized light with the aid of polarizing material.

MALUS’ LAW intensity before analyzer intensity after analyzer

Example 7 Using Polarizers and Analyzers What value of θ should be used so the average intensity of the polarized light reaching the photocell is one-tenth the average intensity of the unpolarized light I_0?

The electromagnetic Spectrum All these electromagnetic waves have the general characteristics, including the common propagation speed c = 3.00 x 108 m/s (in vacuum). All are the same in principle; they differ in frequency f and wavelength , but the relation holds for all.

Quiz Question 1 Look at projector. +x -x +y -y +z

Quiz Question 2