The Propagation of Light

목차

1. Introduction

2. Rayleigh Scattering

3. Reflection(반사)
1) internal and external reflection
2) the Law of Reflection
3) Light rays
4) Refraction
5) Huygens`s principle

4. Fermat`s Principle
1) optical path length (OPD):
2) Fermat`s Principle:
3) Explanation of reflection and refraction by Fermat`s Principle

5. The Electromagnetic Approach
1) Waves at an interface (for monochromatic plane waves)
2) Derivation of the Fresnel Equations
3) Interpretation of the Fresnel Equations
4) Total internal reflection (내부 전반사)

6. Optical Properties of Metals

7. Familiar Aspects of the Interaction of Light and Matter

8. The Stokes Treatment of Reflection and Refraction

9. Photons, Waves, and Probability

본문내용

theta_i}}
,
r_⊥ ~=~ {cos theta_i ``-`` sqrt{n_ti^2 ``-`` sin^2 theta_i}} over {cos theta_i ``+`` sqrt{n_ti^2 ``-`` sin^2 theta_i}}
(
n_ti ~=~ n_t ``/`` n_i
; relative refractive index)
① critical angle and total internal reflection
In the case of internal reflection (nti < 1)
if
n_ti ~<~ sin theta_i
i.e.
theta_i ~>~ sin^-1 n_ti
r_∥ ~=~ {n_ti^2 ``cos theta_i ``-`` i sqrt{sin^2 theta_i ``-`` n_ti^2}} over {n_ti^2 ``cos theta_i ``+`` i sqrt{sin^2 theta_i ``-`` n_ti^2}}
,
r_⊥ ~=~ {cos theta_i ``-`` i sqrt{sin^2 theta_i ``-`` n_ti^2}} over {cos theta_i ``+`` i sqrt{sin^2 theta_i ``-`` n_ti^2}}
∴
R_∥ ~=~ vert r_∥ vert^2 ~=~ 1
,
R_⊥ ~=~ vert r_⊥ vert^2 ~=~ 1
total reflection
critical angle (임계각)
theta_c ~=~ theta_i vert_min
② evanescent wave
Although there must be a transmitted wave , it cannot, on the average, carry energy across the boundary.
The wave function for the transmitted electric field
{vecE}_t ~=~ {vecE}_ot ``exp i({veck}_t · vecr ``-`` omega`t)
{veck}_t · vecr ~=~ k_tx `x ``+`` k_ty `y
( no z-component : assumption)
k_tx ~=~ k_t sin theta_t ~=~ k_t sin theta_i ``/`` n_ti
k_ty ~=~ k_t cos theta_t ~=~ ± i k left( {sin^2 theta_i} over n_ti^2 ``-`` 1 right )^1/2 ~=~ ± i beta
{vecE}_t ~=~ {vecE}_ot ``e^{± `beta `y} e^{i ( k_t `x ``sin theta_i `/` n_ti ``-`` omega `t)}
==> Its amplitude decays rapidly in the y-direction. Actually the energy circulates back and forth across the interface.
(Application : Prism coupler.)
4.8 Optical Properties of Metals
4.9 Familiar Aspects of the Interaction of Light and Matter
-. white light : light that contains a roughly equal amount of every frequency in the visible region of the spectrum.
* a reflecting surface with the characteristics of highly reflecting, frequency-independent, diffusely scattering is perceived as white.
* When the distribution of energy in a beam of light is not effectively uniform across the spectrum, the light appears colored.
-. primary colors
\"a broad range of colors can be generated by mixing three beams of light.\"
red (R), green (G), blue (B) ---
R ``+`` B ``+`` G ~=~ W``
magenta (M) --- reddish purple
M ``+`` G ~=~ W``
cyan (C) --- bluish green or turquoise
C ``+`` R ~=~ W``
yellow (Y)
Y ``+`` B ~=~ W``
* complimentary : sum of two colors becomes white
* saturated : when a color is superimposed on a background of white.
예)
M ``+`` Y ``=`` (R ``+`` B) ``+`` (R ``+`` G) ~=~ W ``+`` R``
┌ subtractive coloration
└ additive coloration
-. reflection from a metal
R ``=`` {(n_R ``-`` 1)^2 ``+`` n_I^2} over {(n_R ``+`` 1)^2 ``+`` n_I^2}
(in the case of normal incidence)
4.10 The Stokes Treatment of Reflection and Refraction
the principle of reversibility :
A ray going from P to S will trace the same route as one from S to P.\"
E_i `t `t\' ``+`` E_i `r `r\' ~=~ E_i
,
E_i `r `t ``+`` E_i `t `r\' ~=~ 0
Stokes relation
t `t\' ``+`` r `r ~=~ 1 #
r\' ~=~ - r
==> There is a 180o phase difference between the waves (internally and) externally reflected.
4.11 Photons, Waves, and Probability

키워드

Propagation,   Light,   빛,   경계면,   전파