Formulae and Constants: e = 1.60 x 10-19 Coulombs 1 eV

advertisement

Formulae and Constants: e = 1.60 x 10 -19

E = h f = hc /

λ

Coulombs

& momentum, p = h /

λ

1 eV = 1.60 x 10 -19 J h = Planck’s const = 6.63 x 10

= 4.14 x 10 -15 eV•s

____ c = “speed of light” = 1 / √ (

ε

0

µ hc = 1240 eV•nm

0

) = 3 x 10 8 m/s c =

λ f

-34 J•s

Traveling wave equation : y(x,t) = A sin [k(x - vt)] = A sin (kx - ω t) = A sin [ (2 π / λ ) x - ( 2 π / T) t ] where k = 2 π / λ ω = 2 π f = 2 π / T v = ω / k

Polarization

• intensity of polarized light transmitted proportional to the amplitude squared:

Malus’ Law I = I

0

cos 2 θ

• by reflection -- Brewster’s angle = polarizing angle -- tan

θ p

= n

2

/n

1

• by scattering

For a crystal with thickness d, the phase difference between the 2 rays (ordinary and extraordinary) is

Φ

= [2 π /

λ

0

] * |n

-n

||

| * d

Photoelectric Effect hf =

φ

+ E k or hc /

λ

=

φ

+ eV

0 or hc /

λ

= hc /

λ c

+ eV

0

Blackbody Radiation :

Wien displacement law

λ max

T = 2.880 x 10 6 nm•K

Stefan-Boltzmann law energy / (time•area) =

σ

T 4

σ

= 5.67 x 10 -8 W / (m 2 K 4 )

Bohr Model of Atom

Allowed energy levels: E n

= -13.6 eV / n 2

Energies of photons that can be emitted or absorbed = [exactly] | E n1

-E n2

|

Reflection/refraction n = c / v

Snell’s Law: n

1

sin

θ

1

λ n

= λ / n

= n

2

sin

θ

2

For step-index fibers

Numerical Aperture = N.A. = n o

sin

θ m

___________

___________

= √ n

1

2 -n

2

2

Skip distance = L s

= n

2

d / √ n

1

2 -n

2

2

# of modes = ( 1 /

2

) [ π d (N.A.) /

λ ] 2 in order to be single-mode, a fiber diameter d must be:

d < 2.4 λ / π (N.A.)

For fibers in general :

Loss of power in dB =

α

L = 10 dB log

10

(P

1

/ P

2

where α is the attenuation coefficient

)

Lenses/Mirrors

Textbook sign conventions: [these assume light is coming from the left !]

• if the object/image is to the left of the vertex (where lens/mirror crosses axis), its distance u/v is negative

• radii of curvature follow the same rule as above, so diverging mirrors have positive f = focal lengths, but diverging lenses have negative focal lengths

Object/image location

Magnification

Mirror Equations

1/u + 1/v = 2/r = 1/f m = h i

/ h o

= - v / u

Lens Equations

- 1/u + 1/v = 1/f m = h i

/ h o

= v / u

For Mirrors: f = radius of curvature / 2

Lens Maker’s Equation: 1/f = [(n

2

- n

1

) / n

1

] [ 1/r

1

3 standard rays for ray diagrams:

• in thru focus, out parallel to axis

• in parallel, out thru focus

• in thru center, undeviated

-1/r

2

]

Download