1. Electromagnetic spectrum & visible portion
Violet (400 nm)  Red (700 nm)
White = ROYGBV
(can be separated by dispersion)

2. Electromagnetic waves (visible light, X-rays, etc.)
Wave Theory
Wavelength l = Distance between peaks
Frequency = no. of waves/sec to pass a given point (hertz)
frequency = v/l , v = velocity f

3. Pertinent Units
Wavelength: nm (=mμ) = 10-9m;
old units, Å = 10-8m
Frequency: hz (cycles/sec)
Energy units (at the atomic scale) are also sometimes used. Energy in eV = ћν, where ћ is Planck,s constant. 1Å is equivalent to 1.24x10-24eV.

4. Polarization Non-polarized (“usual”) light:
Each photon vibrates as a wave form in a single plane. Vibration refers to the rise and fall of the sine wave.
Light beam is composed of numerous photons, each vibrating in a different plane.
Vibration occurs in all directions ~ perpendicular to propagation direction

5. Polarization Plane of interface = surface of crystal
Plane of incidence = T-N-U-V-M-S-O
Plane of incidence contains incident, reflected and refracted ray paths as well angles i, l and r

6. Refraction Incident ray and reflected ray: Refracted ray:
1)  of incidence i =  of reflection r
2) coplanar in the plane of incidence
Refracted ray:
1) Slower in water or glass
2) r (refraction)   i (incidence)
Depends on D v
Incident i
Reflected r
air
water r
Refracted

7. Index of refraction For a substance x: nx = vvacuum/vx nair = 1.0003
light is slower in water, glass, crystals
Is nwater greater or less than 1?
Larger n associated with slower v !
Snell’s Law (1621):
ni sin i = nr sin r
for two known media (air/water),
sin i/sin r = nr / ni = const.
So can predict angle change (or use it to determine nr)

8. Polarization Note symbolization used:
incoming ray is non-polarized
reflected and refracted rays
both become polarized
Note symbolization used:
Reflected ray polarized perpendicular to the plane of incidence.
Refracted ray polarized in plane of incidence.

9. Interference
Fig 7-1 Bloss, Optical Crystallography, MSA
A: Particles in phase if displaced from rest position by same amount in same direction
a1 - a2 - a3 are all in phase
b1 - b2 - b3 are also all in phase (but not with a1…)
particles perfectly out of phase: equal-but-opposite displacement
b1 and c1 are not perfectly out of phase

10. Interference
Fig 7-1 Bloss, Optical Crystallography, MSA
path difference (D) = distance between any 2 points on a wave form
usually expressed as xl
D between any 2 points in phase = il (i=any integer)
D between any 2 points perfectly out of phase = ((2i+1)/2) l/2