A

What you learned in 123

1 2 1 2 2 1

1 2 1 2 2 12

1

refl trans

i i

E Er t

E En n k k v v

rn n k k v v

R r T R

. .

;   –

“Normal incidence”

We have complete picture in 471:• All angles• Polarization (refers to E direction, not to polarized atoms)• Complex index (next time)

Break linear polarization into two components

Plane of incidencevs interface plane

Equations we must write:

Unknowns we want to solve for:

Any one of these gives us:• Frequency cons.• Reflection law• Snell’s law

Amazing!

n=2n=1

Huygen’s principle and Snell’s law: Each point of space or matter can be imagined as a point source of forward semicircular waves. The sum of the circular wavefronts gives a wavefront of the real wave.

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=16

Points farther down the interface are ahead in phase.They emit waves with different wavelength. wave turns

Photon picture of Snell’s lawPhoton energy

Photon momentum

From our findings for k and w across the interface, which is not conserved?a) Photon energyb) Photon momentum perpendicular to

interfacec) Photon momentum parallel to interfaced) All are conservede) None are conserved

The B field that must accompany Etp is_______.

a) Parallel to Etp

b) antiparallel to Etp

c) Into the paged) Out of the pagee) Along k

ook EB

w

The B field that must accompany Etp

has magnitude _____a) nEt

p/cb) ncEt

p

c) cEtp/n

d) Etp/(cn)

e) Etp/c

ook EB

w

i tt i i t i i t t

st i i t i t i i t t

n nr

n n

sinsin cos sin cos cos cossin cos sin cos sin cos cos

2 2 2t i t i i i

st i i t i t i i t t

nt

n n

sin cos sin cos cos

sin cos sin cos sin cos cos

i tt t i i i t t i

pt t i i i t i t t i

n nr

n n

tancos sin cos sin cos coscos sin cos sin tan cos cos

2 2 2i t i t i i

pt t i i i t i t i t t i

nt

n n

cos sin cos sin cos

cos sin cos sin sin cos cos cos

Fresnel Coefficients

Suppose we have a laser beam entering a piece of glass under special conditions so R = 0.

What is the same for both beams?a) Beam intensityb) Beam powerc) bothd) neither

R and T from r and t

2t t

i i

nT t

n

coscos

2R r

2t t

i i

nT t

n

coscos

References

Wave amplitude, energy and N-photons

The beam is focused to an area A. What is the average amplitude of the E-field?

2

2o

o

n cI E

2

2o

field on

u E

I uv

A laser puts out power P (watts): How many photons per second leave it?

What is the photon density photons/m3 in this case?

Suppose we have a laser beam entering a piece of glass at normal incidence. Assume it’s anti-reflection coated so we can ignore reflection.

In the glass the photons move slower.

The energy density u is ____ than in air.a) largerb) smallerc) the same

Photon picture