1 Polarization Light can be constrained to vibrate in a particular planeLight can be constrained to vibrate in a particular plane When two light rays combine, their vibration vectors add (vector-wise)When two light rays combine, their vibration vectors add (vector-wise) A B C A+B=CA+B=C

2 Polarization Polaroid film (in the polarizer & analyzer on your scope) absorbs light vibrating perpendicular to it’s directionPolaroid film (in the polarizer & analyzer on your scope) absorbs light vibrating perpendicular to it’s direction incoming ray polarizer direction transmitted component

3 Anisotropic materials Cause light to split into 2 rays vibrating 90° to each otherCause light to split into 2 rays vibrating 90° to each other Two rays “see” a different crystal environmentTwo rays “see” a different crystal environment –different indices of refraction different speeds of lightdifferent speeds of light –different colors, potentiall –different paths produces double refractionproduces double refraction this effect is tiny in most mineralsthis effect is tiny in most minerals polarized

4 monochromatic! Retardation fast & slow rays are 45° from polarizerfast & slow rays are 45° from polarizer Δ = d (n s - n f ) Δ = d (n s - n f ) –distance, nm Note: Colors are not real hereNote: Colors are not real here 1  1.5  fast slow Δ=  /2 d

5 Interference Retarded rays get vector-combined in analyzer (“XP”)Retarded rays get vector-combined in analyzer (“XP”) fast slow Δ=  /2 Retardation of  /2 causes change in vibration direction of 90° (full transmission)

6 Interference If Δ=n  (n=1,2,3...), no ray passes analyzerIf Δ=n  (n=1,2,3...), no ray passes analyzer Retardation of  causes change in vibration direction of 180° (no transmission) fast slow Δ=Δ=

7 Recap: Retardation / Interference The slow ray is held back, so at the analyzer they combine with a new net vibration direction (retardation changes vibration direction)The slow ray is held back, so at the analyzer they combine with a new net vibration direction (retardation changes vibration direction) The relationship between the retardation distance, grain thickness, and indices of refraction is:The relationship between the retardation distance, grain thickness, and indices of refraction is: – Δ = d (n s - n f ) If the new vibration direction is E-W (0° or 180° from the incoming), the ray is canceled at the analyzer (upper polar)If the new vibration direction is E-W (0° or 180° from the incoming), the ray is canceled at the analyzer (upper polar) –when Δ= , or Δ=2 , or Δ=3 , or Δ=4 , etc. If the new vibration direction is N-S (90° or 270° from the incoming), the ray is transmitted through the analyzer (upper polar)If the new vibration direction is N-S (90° or 270° from the incoming), the ray is transmitted through the analyzer (upper polar) –when Δ= , or Δ=3 , or Δ=5 , or Δ=7 , etc.

8 When fast or slow direction || polarizerWhen fast or slow direction || polarizer –will occur every 90° of stage rotation Calcite demoCalcite demo fast slowExtinction