Optics
Table of Contents
1. Holography
1.1. Holographic Principle
The intensity and phase is recorded on a material, which can be used to reconstruct the exact electromagnetic wave on the entire space.
2. Rainbow
2.1. Caustic
The angle of reflection is maximum at certain angle creating a bright spot.
Moreover, the cross section per radius is greater at the edge making it even brighter.
Smaller wavelength light bends more, attaining its maximum at a smaller angle compared to the longer wavelength light.
They merge in the center making white light, but they separates at the edge.
For a normal rainbow the angle is 42 degree away from the shadow of the eyes.
2.2. Alexander's Dark Bend
Between 42 degree and 50 degree, there's dark bend that no light reflects.
2.3. Supernumerary Rainbow
When the droplets are tenth of milimeters wide, interference occurs between lights going out in slightly different angles. Creating dark region at certain angle, letting other light to stands out.
2.4. Glory
The light incident at the edge is also reflected very near the opposite edge. The droplets becomes a ring source of light with a parallel light.
The light at different angles interferes, and it is different among wavelength, creating a rainbow between the angle of 2 degree to 4 degree.
3. Retroreflective Material
Material that always reflect light to exactly where it came from
The road signs can be backed up by it.
4. Stokes Relations
The derivation relies on the time-reversal symmetry, sometimes referred to as the principle of reversibility in this context. Therefore, this only works when their is no absorption.
The relation between the transmission and reflection coefficients in one direction \( r,t \), and the other direction \( r', t' \) are given by:
\begin{align*} &t't + r^2 = 1, \\ &r = -r'. \end{align*}5. Optical Theorem
\[ \sigma = \frac{4 \pi}{k} \operatorname{Im} f(0) \] where \( \sigma \) is the cross section, \( f(0) \) is the scattering amplitude with an angle of zero, \( k \) is the wave vector in the incident direction.