Written HW due every week. 32.17, 32.47 Due Fri Jan 18

Physics 262

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SI Jonathan GrossSI sessions M & T at 9, Th at 10

Written HW due every week. 32.17, 32.47 Due Fri Jan 18

Some stuff in physics is best memorized. Remembering some basic facts or equations helps you think better, because you can draw on those tools.

Example: What is the relationship between wave speed v, frequency f, and wavelength ?

a) v = f/ b) v = f c) v = fd) v = f

e) None of these

More waves

• When a wave reflects off a fixed end, the reflection

• A) is inverted

• B) is not inverted

• C) vanishes completely

The electromagnetic field supports waves.This is usually “explained” by induction:

Changing E field “causes” B fieldChanging B field “causes” E field

We will see in a month that there is a better explanation for these waves.

Electromagnetic “Discontinuities” Must Propagate at a speed

€

c =1

ε0μ0

Our wavefrontsatisfies both “Gauss’s laws”because there is noenclosed charge or current, and fields on opposite sides of the box are the same.

There is a changing B flux as the wavefront moves by. This changing flux must be equal to the line integral of the E field. Only the back edge (gh) contributes to this line

integral.

There is a changing E flux also. This gives another reqd relation between E

and B.

Clarification:4 % problem session bonus is for going to 1 per week(Total of 14 or more.)

• Last time: Maxwell’s eqns support spatially varying E fields if:1) The fields move at speed c = 3x108 m/s2) There is an associated B field, B=E/c

We call waves that have the same E, B at every point in a plane “plane waves”

Some plane waves are sinusoidal.Maxwell’s equations also allow for non-plane waves. (Because they are linear, any sum of allowed waves is also allowed. Non-

plane waves can be mathematically shown to be sums of plane waves.)

So these waves can exist. What can make them?Classically, an accelerated charge makes an EM wave.

Consider the E field described by the following equation

What is the direction this wave is moving in?

a) Toward +xb) Toward -xc) Toward +yd) Toward -ye) Impossible to tell

What is the associated B field of

For a given sinusoidal plane wave, you need to be able to tell the direction of propagation and the direction of the associated B field.

More about k and

What is the wavelength of a sinusoidal wave with wavenumber k?

a) 1/k

b) (2)/k

c) 2k

d) None is correct

HW Due next Friday Jan 25 33.57, 33.61

Last time: • Understanding sinusoidal plane waves

Find direction of wave propagationUnderstand allowed polarizationsFind associated B field: cB = EFind wavelength, frequency

• Poynting vector S

Direction = propagationMagnitude is energy per time per areaP = S/c is momentum per time per area = pressure

A few loose ends:

1. What is relationship between k and

P = S/c. Would this be different if light were particles?(This is just for fun…)

The Poynting vector S is proportional to E2 (and/or B2) Consider energy conservation to answer this question:How does E depend on r, the distance from a point source

of radiation?

• E ~ r• E ~ 1/r• E ~ 1/r2

• E ~ ln(r)• E is independent of r

You should also remember the wavelengths of visible light,and the very approximate boundaries between the other EM radiations.

How? Gamma rays are the size of a nucleusX-rays are the size of an atomVisible = 400-700 nmMicrowaves fit in the ovenIR is between microwave & visibleRadio: figure it out from the frequency. KUNM 89.9 MHz

Light (em radiation) of wavelength 2 microns is

A] gamma rayB] x-rayC] visibleD] infraredE] microwave

What is the approximate wavelength of KUNM?

A] 3 nmB] 3 micronsC] 3 mmD] 3 mE] 3 km

Light in materials.

Replace 0 and 0 with and .

€

v =1

εμ=

1

KKm

1

ε0μ0=

c

KKm=c

n

Usually Km = 1, so it is the dielectric constant K that is important.

n is the “index of refraction”

Parting comment:

Maxwell’s equations predict a wave satisfying the wave equation

In this equation, there is no reference to the speed of the observer or the source of the wave. Other waves are much more complicated: for example, consider sound waves on a train flatcar. We need to have a different speed upwind & downwind.

Perhaps Maxwell’s equations are only approximately correct?? Maybe our motion on the earth (around the sun & galaxy) is slow enough (compared to c) that we don’t notice the differences in the upstream and downstream speeds of light?

You can see that, if that were so, the EXACT Maxwell equations would be ugly, not neat, beautiful, elegant, simple, as they are.

Does this matter? Maybe the universe is not so neat!

Albert E., yours truly, and God all favor neatness & elegance.

€

∂2E∂x 2

=1

c 2∂ 2E

∂t 2

Chapter 33 Nature and Propagation of Light

WavesWavefronts - “locus of all points at the same phase”

Here “phase” means that, for a sinusoid, the argument would stay the same. (“phase” = argument of sinusoidal function)

It’s easiest to think of wavefronts as simply the crests of the wave.

Rays are imaginary lines along the direction of wave propagation.

What is the relationship between rays and wavefronts in vacuum?

A) they are parallelB) they are perpendicularC) they are at 45° to each other

Reflection: light bounces off a surface (e.g. mirror, or glass)

Refraction: light bends as it enters a material with a different index(I.e. a material in which the speed of light is different!)

Law of reflection (memorize)

Law of refraction- “Snell’s law” (memorize)

Angles are measured to “normal” Snell predates Newton!

€

θr =θ i

€

na sinθa = nb sinθb

When a beam of light enters a piece of plexiglass, what will be its path? (np > 1)

The wave equation is time-reversal symmetric.

A laser in air shines a beam of light that hits a diver, rightmost path.

The diver has a laser pointer, and wants to hit the air laser. What direction should he point it?

Or choose D: no direction will work.