Resonant motion: amplitude and phase

What resonances to electrons in atoms have?

Lorentz model of spring-like oscillating dipoles

A

2 e

e

i k r t

o o

qr r r E e

m

e2 2

e

oo

o

q Er

m i

if all identical (in text notation )o o

NP Nqr N

V

2e

2 2e

1o

o o o o

P q N

E m i

2

2

2 2

11 1 e

e o o

q Nn i

m i

Lorentz model of spring-like oscillating dipoles

0 0.5 1 1.5 2 2.5-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10

-6

(1016 rad/sec)

disp

lace

men

t xo

magnitude

real

imaginary

Lorentz model of spring-like oscillating dipoles

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

(1016 rad/sec)

Phase

of x o

vs

E

P2. Clear, colorless glass has no resonances in the visible, but does have them in the UV, which is at a higher w.

Hence in clear glass, index n _________ with as w increases for visible light

a) increasesb) decreases

P3. If we increase the density of a gas (N), index n a) increases for all w b) decreases for all w c) increases with density below resonance, decreases above d) decreases with density below resonance, increases above

Hint: what would these curves look like in the limit

of N 0?

Common optical glass indices vs wavelength

P4. In a glass that absorbs green lightthe index , real index n is probably greatest for ______ light. a) redb) yellowc) greend) bluee) violet

P5. In a glass that absorbs green lightthe index , imaginary index k is greatest for ______ (same choices)

Organic semiconductor for solar cell: visible n,k

Glass: changes in the IR n, k due to vibrating atoms

Complex index, dielectric constant, k

A

P. Near a resonance frequency, materials with atomic dipoles might have for example n = 2 and k = 3

When the wave has moved into the material by a distance of one vacuum wavelength, by what factor is the wave amplitude reduced?

a) exp(-2p)b) exp(-3p)b) exp(-4p)d) exp(-6p)

P4. What is the phase change of the wave after traveling this distance?

1

2 2

2

vac

vac

n

nk n

c

cv f

n kf

n

Wave equation

f x t f x ct ( , ) ( )P. is a solution to

It is also a solution to ____:1)

2)

a) eqn 1b) eqn 2c) bothd) neither

2 2

2 2 2

10

f x tf x t

x c t

( , )

( , )

3 3

3 3 3

10

f x tf x t

x c t

( , )

( , )

4 4

4 4 4

10

f x tf x t

x c t

( , )

( , )