Let’s try optics again

1. Let’s try optics again

2. What we have learned to date • Refractive Index • Snell’s Law • And how it works • Birefringence or Interference Colors • Absolute value of the difference in refractive indices • Isotropic vs Anisotropic minerals

3. What we covered in lab • Color and pleochroism (plane light) • Anisotropism and interference colors (crossed polars) • Extinction angles • How to recognize twinning • Relief

4. Interference colors - review

5. From Relief to the Becke Line Figures from http://www.gwu.edu/~forchem/BeckeLine/BeckeLinePage.htm

6. N of the oil greater than that of the mineral grain Figures from http://www.gwu.edu/~forchem/BeckeLine/BeckeLinePage.htm

7. Becke line again The Becke line results from the concentration of light either inside or outside of the image of the particle, depending on whether the mineral grain or the oil has the larger index of refraction.  This refraction of light at the boundaries creates an optical halo perceived as the Becke line. This halo is caused by the concentration of refracted light rays along the edge of the particle . As you lower the stage or raise the tube, the Becke line will move toward the region with higher index of refraction. 

8. Something else! • A characteristic of anisotropic minerals is that light passing in most directions is doubly-refracted. This means that light is split into 2 plane-polarized rays that vibrate at right angles to one another. In general the direction along which the light is not split is known as the optic axis. • Uniaxial—1 optic axis • Biaxial 2 optic axes

9. D=retardation fast ray (low n) slow ray (high n) d mineral grain plane polarized light lower polarizer Back to birefringence/interference colors Observation: frequency of light remains unchanged during splitting, regardless of material F= V/l if light speed changes, l must also change l is related to color; if l changes, color changes waves from the two rays can be in phase or out of phase upon leaving the crystal Slide from Jane Selverstone

10. Interference phenomena • When waves are in phase, all light gets cut out • When waves are out of phase, some component of light gets through upper polarizer and the grain displays an interference color; color depends on retardation • When one of the vibration directions is parallel to the lower polarizer, no light gets through the upper polarizer and the grain is “at extinction” (=black) Slide from Jane Selverstone

11. At time t, when slow ray 1st exits crystal: Slow ray has traveled distance d Fast ray has traveled distance d+D D=retardation time = distance/rate fast ray (low n) Slow ray: t = d/Vslow Fast ray: t= d/Vfast + D/Vair Therefore: d/Vslow = d/Vfast + D/Vair D = d(Vair/Vslow - Vair/Vfast) D = d(nslow - nfast) D = d d slow ray (high n) d mineral grain plane polarized light D = thickness of t.s. x birefringence lower polarizer Slide from Jane Selverstone

12. Determining the vibration directions in a crystal D=retardation fast ray (low n) Add to this accessory plate with a known wavelength of 550 nm—eg. quartz –align fast direction of the plate with either the fast or slow direction of the mineral. What will happen? slow ray (high n) d mineral grain plane polarized light D = thickness of t.s. x birefringence lower polarizer Slide from Jane Selverstone

13. You will either add or subtract—this will show in a color change.

14. Let’s revisit calcite • What do we know about calcite to date • a = 4.989Å c = 17.062Å • Light splits into two rays traveling at two different velocities • We can look up that n1=1.486, n2=1.64-1.66 • Thus the birefringence=0.1540-0.1740 • Shows very high interference colors

15. Some new stuff!! • ε –epsilon known as the extraordinary ray • ω omega known as the ordinary ray

16. What we don’t know about calcite • In which directions the rays travel in the mineral. • How are these directions related to the crystal lattice?

17. Where they travel • Ordinary ray ωvibrates perpendicular to the c-axis (which in hexagonal and tetragonal x’ls is the optic axis) • Extraordinary ray εvibrates perpendicular to the ordinary ray in a plane that contains the c-axis • One of these rays travels faster than the other

18. calcite calcite calcite calcite calcite ordinary ray, w (stays stationary) extraordinary ray, e (rotates) What happens in calcite again? Slide from Jane Selverstone

19. What happens if I orient calcite, so light passes only along the C-axis? • I will see only one dot! • The c-axis in calcite coincides with what we call the OPTIC axis. Birefringence is zero for light traveling along the c-axis • In actual fact all hexagonal and tetragonal minerals behave the same way in polarized light. There will be one optic axis—thus known as Uniaxial

20. Some definitions • If n of εis greater than n of ω, then the mineral is positive • If n of εis less than n of ω, then the mineral is negative • Thus in a positive mineral, omega is faster than epsilon (velocity and n are inversely related)

21. How could we determine if calcite were positive or negative? • What information do we need? • Wait until next time