Light

Physics 202Professor Vogel (Professor Carkner’s & CJV

notes, ed)Lecture 10

Light Electromagnetic wave

oscillating electric and magnetic fields – no material medium that is moving!

energy transfer at speed v (c=3X108 m/s in vacuum)

wavelength = distance between repeats frequency = # repeats per second

f=v

v=c in vacuum

c=3X108 m/s

f

EM Spectrum

The EM Spectrum Radio

> 1 meterpenetrates solid objects

easily

Millimeter (microwave)1 m - 1 mmused for communication

Infrared1 mm - 700 nmwe feel as heat

Visible700-400 nmeyes evolved to see

Ultraviolet400 nm - 100 Ahigher energy, causes

sunburn

X-ray100 A - 0.01 Apenetrates soft things

but not hard

Gamma Ray< 0.01 Ahard to produce and

dangerous

The EM Wave

Lets consider light as a wave What kind of wave is it? What is oscillating?

An EM wave consists of an electric field wave (E) and a magnetic field wave (B) traveling together

The 2 fields are perpendicular to each other and to the direction of travel An EM wave is transverse (like string waves)

The field waves are sinusoidal and in phase

Wave Equations We can generalize the waves as:

E = Em sin (kx -t)

B = Bm sin (kx -t) Nothing is actually moving

There is no string A changing E field induces a B field A changing B field induces an E field

The two fields continuously create each other The speed of the wave is related to the fields:

c = E/B

Traveling EM Wave

Key Constants Two important constants in E and M are the permittivity

constant 0 and the permeability constant 0

Permittivity is the electric force constant:0 = 8.85 X 10-12 F/m

In farads per meter Measure of how electric fields propagate through space

Permeability is the magnetic force constant:0 = 1.26 X 10-6 H/m

In henrys per meter Measure of how magnetic fields propagate through space

The wave speed depends on these constants:c = 1/(0 0)½

Poynting Vector EM waves transport energy The amount of energy delivered per unit

area per unit time is given as flux:flux = W/m2 = J/s/m2

Flux for an EM wave can be given by the Poynting vector:

S = (1/0) EB However, E and B are related by E/B = c so

we can rewrite S as:S = (1/c 0) E2

Intensity

The value of S depends on where the EM wave is in its cycle

We generally are interested in the time averaged value of S, known as the intensity

I = (1/c 0) Erms2

Where Erms is the root-mean-square value of the electric field

Radiation Pressure

EM waves exert a pressure on objects If someone shines a flashlight on you, the

light is trying to push you away like ball bouncing off object pushes object

back The force is very small in most cases

EM pressure is due to the fact that light has momentum which can be transmitted to an object through absorption or reflection

Momentum Transfer The change in momentum due to light is

given by:p = U/c

Where p is the momentum change and U is the energy change The above equation is for absorption

For reflection the momentum change is twice as much:

p = 2U/c

Light Pressure From Newton’s second law

F = p/t The amount of energy delivered in time t

is:U = I A t

where I is the intensity and A is the area Since pressure (pr) is force per unit area the

pressure becomes:pr = I/c (total absorption)

pr = 2I /c (total reflection)

Comet Hale-Bopp

Comet Tails

Light Sail

Color Vision Rods and cones

one type of cone responds to long ’s: “R” one type of cone responds to mid wavelengths:

“G” one type of cone responds to short ’s: “B”

How our eyes view pure waves: red : R-type responds green : G-type responds blue : B-type responds yellow : R- and G-types respond Cyan: G- and B-types respond

Color Addition

How our eyes view mixtures : blue + red: R- and B-types respond

magenta

green + blue : G- and B-types respond indistinguishable from cyan

red + green : R- and G-types respond indistinguishable from yellow

Demo of color addition -- HELP

(Like no pure color)

Color Addition

How our eyes view mixtures : red + green : R- and G-types respond

indistinguishable from yellow

red + green + blue : R-, G-, and B-types respond white

yellow + blue : R-, G-, and B-types respondwhite

Color Subtraction How our eyes view pigments (absorb

light) white - blue: R- and G-types respond

pigment that absorbs blue looks yellow

white - red : G- and B-types respond pigment that absorbs red looks cyan

white - (blue + red): G-type responds pigment that absorbs blue and red looks green

Color Subtraction How our eyes view pigments:

white - (blue + red): pigment that absorbs blue and red looks

greenPigment: yellow + cyan:

pigments that absorb blue and red look greenA demo of subtraction

usflag-neg.gif

Complementary color= white - color

primary color red green blue

Complementary color

cyan magenta yellow