Lecture 13 Electromagnetic Waves Ch. 33 Cartoon Opening Demo Topics –Electromagnetic waves –Traveling E/M wave - Induced electric and induced magnetic amplitudes –Plane waves and spherical waves –Energy transport snd Intensity of a wave Poynting vector –Radiation Pressure produced by E/M wave –Polarization –Reflection, refraction,Snell’s Law, Internal reflection –Prisms and chromatic dispersion –Polarization by reflection-Brewsters angle Elmo Polling

Electromagnetic Waves

Production of Electromagnetic waves

Spherical waves Plane waves

To investigate further the properties of electromagnetic waves we consider the simplest situation of a plane wave. A single wire with variable current generates propagating electric and magnetic fields with cylindrical symmetry around the wire. If we now stack several wires parallel to each other, and make this stack wide enough (and the wires very close together), we will have a (plane) wave propagating in the z direction, with E-field oriented along x, E = E x (the current direction) and B-field along y B=B y (Transverse waves)

Traveling Electromagnetic Wave

How the fields vary at a Point P in space as the wave goes by

Electromagnetic Wave Self Generation Faraday’s Law of Induction Maxwell’s Law of Induction Changing electric field induces a magnetic field Changing magnetic field induces a electric field

Summary

U is the energy carried by a wave Magnitude of S is like the intensity

A point source of light generates a spherical wave. Light is emitted isotropically and the intensity of it falls off as 1/r 2 Let P be the power of the source in joules per sec. Then the intensity of light at a distance r is Lets look at an example Relation of intensity and power for a Spherical Wave - Variation of Intensity with distance

15. The maximum electric field at a distance of 10 m from an isotropic point light source is 2.0 V/m. Calculate (a) the maximum value of the magnetic field and (b) the average intensity of the light there? (c) What is the power of the source? (a) The magnetic field amplitude of the wave is (b) The average intensity is (c) The power of the source is

Speed of light in Water

Nothing is known to travel faster than light in a vacuum However, electrons can travel faster than light in water. And when the do the electrons emit light called Cerenkov radiation

Momentum and Radiation Pressure c Momentum = p p=U/c paper Light beam 1) Black paper absorbs all the light p=0 What is the change in momentum of the paper over some time interval? 2) Suppose light is 100% reflected From this we define the pressure

Radiation Pressure P r Want to relate the pressure P r felt by the paper to the intensity of light For 100% absorption of light on the paper For 100% reflection of light

Problem 21 What is the radiation pressure 1.5 m away from a 500 Watt lightbulb?

Polarization of Light All we mean by polarization is which direction is the electric vector vibrating. If there is no preferred direction the wave is unpolarized If the preferred direction is vertical, then we say the wave is vertically polarized

Pass though a polarizing sheet aligned to pass only the y-component A polarizing sheet or polaroid filter is special material made up of rows of molecules that only allow light to pass when the electric vector is in one direction.

Resolved into its y and z-components The sum of the y-components and z components are equal Unpolarized light

Pass though a polarizing sheet aligned to pass only the y-component Malus’s Law Intensity I 0 One Half Rule Half the intensity out

y Intensity is proportional to square of amplitude Light comes from here Malus’s Law

Sunglasses are polarized vertically. Light reflected from sky is partially polarized and light reflected from car hoods is polarized in the plane of the hood Sunglass 1 Sunglass 2 Rotate sun glass 2 90 deg and no light gets through because cos 90 = 0

Polaroid Material Yes NoNo Transmits Light

Chapter 33 Problem 33 In the figure, initially unpolarized light is sent through three polarizing sheets whose polarizing directions make angles of  1 = 40 o,  2 = 20 o, and  3 = 40 o with the direction of the y axis. What percentage of the light’s initial intensity is transmitted by the system? (Hint: Be careful with the angles.) The polarizing direction of the third sheet is  3 = 40 o counterclockwise from the y axis. Consequently, the angle between the direction of polarization of the light incident on that sheet and the polarizing direction of the sheet is 20 o + 40 o = 60 o. The transmitted intensity is

Law of Reflection Law of Refraction or Snell’s Law Chromatic Dispersion Brewsters Angle Chapter 33 Properties of Light Continued

33 Lab06 Lab07 Lab08 Lab06

Reflection and Refraction of Light

Dispersion: Different wavelengths have different velocities and therefore different indices of refraction. This leads to different refractive angles for different wavelengths. Thus the light is dispersed. The frequency does not change when n changes.

Snells Law n 2 =1.33 Red n 1 =1.00 θ1θ1 θ2θ2

Chapter 33 Problem 49 In Figure 33-51, a 2.00 m long vertical pole extends from the bottom of a swimming pool to a point 90.0 cm above the water. Sunlight is incident at angle θ = 55.0°. What is the length of the shadow of the pole on the level bottom of the pool?

Chapter In the figure, a 2.00-m-long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. What is the length of the shadow of the pole on the level bottom of the pool? 22 11 l2l2 l1l1 Lx air water shadow

Consider a ray that grazes the top of the pole, as shown in the diagram below. Here  1 = 35 o, l 1 = 0.50 m, and l 2 = 1.50 m. 22 11 l2l2 l1l1 Lx air water shadow x is given by x = l 1 tan  1 = (0.50m)tan35 o = 0.35 m. The length of the shadow is x + L. L is given by L=l 2 tan   Use Snells Law to find  

According to the law of refraction, n 2 sin  2 = n 1 sin  1. We take n 1 = 1 and n 2 = 1.33 L is given by The length of the shadow is L+x. L+x = 0.35m m = 1.07 m. 22 11 l2l2 l1l1 Lx air water shadow Calculation of L

Fiber Cable

Why is light totally reflected inside a fiber optics cable? Internal reflection

Total Internal Reflection

Chromatic Dispersion of light with a prism

45 Equilateral prism dispersing sunlight late afternoon. Sin θ refr = 0.7n λ

How much light is polarized when reflected from a surface? Polarization by Reflection: Brewsters Law

What causes a Mirage sk y eye Hot road causes gradient in the index of refraction that increases as you increase the distance from the road Index of refraction

Inverse Mirage Bend