Geo 406 Lecture 02 - Reflection, Refraction, Lenses, Relief, Becke Line

Reading: p. 7-15

next: Ch. 3-4

Goals

Finish waves

Understand refraction

Understand critical angle

Learn Snell's Law

Understand lenses (generally)

Learn about relief (high, low, positive, negative)

Learn about Becke Line

Materials

Prisms

Laser

thin sections of varying relief

grain mount

thin sections

Positive and negative relief grain mounts

biotite-bearing thin sections

Waves

Wave front

Propagation direction

Wave normal

In non-isometric crystals, propagation ≠ wave normal

Reflection

Incoming angle = reflected angle

measured relative to surface normal

Refraction

If light is moving into slower material, how will it bend?

draw wave fronts

light is slowed, but frequency stays the same

Bends towards slower material (higher n)

If light is moving into faster material, how will it bend?

draw wave fronts

Bends towards slower material (higher n)!

Snell's Law gives precise angles (Eq. 1.3, p. 9):

n₁/n₂ = sin q₂ / sin q₁

Critical Angle & Total internal reflection

How big can q₁ be, when going from higher n to lower?

If q₂ > 90°, then there is no refracted light - all reflected (Total Internal Reflection)

When q₂ = 90°, then q₁ is the critical angle.

Example: if light is going from ruby (corundum, n ~ 1.78) to air (n ~ 1.0), then figure out the critical angle.

T.I.R. is important for gem faceting - desirable

Refraction and polarization

When q₁ is between 0 and the critical angle, then there will be both a reflected and refracted ray

Both are, in general, partially polarized

reflected: in line || to surface, and normal to wave normal

refracted: in line normal to vibration direction of reflected light

Polarization is strongest when angle between reflected & refracted is 90°. The angle between the incoming ray and the surface normal is then Brewster’s angle.

Lenses

Work because of refraction

Relief (“Shagreen”)

Demonstrate differences in relief

Why does this happen?

Need to understand construction of thin section

Grains are rough

Light scattered at surfaces through refraction

Angles of refraction depend on difference in n

So, relief depends on n of medium

Thin section epoxy has n=1.54

Relief can be high or low

Depends on difference between n_mineral & n_medium

Relief can be positive or negative

Depends on n_mineral - n_medium

Relief is different in different media

Leads to immersion method for determining n

Becke line

[Demonstrate]

Medium objective

Low light (iris)

Lower stage, and line moves into material with higher n

Becke line is produced by two factors

Reflection from vertical grain boundaries

Lensing from curved grain boundaries

Oblique Illumination

Relies on same features as Becke line

Partially obscure the light below the substage with a paper or card, and see where the shadows go.

Need to calibrate your scope to be sure.