SME
Mineralogy
Optical mineralogy
Use this for “Quartz has birefringence 0.009. What retardation and color order does it show in a 30 μm thin section?”
Diagram
Γ = 1,000tδ = 1,000 × 30 × 0.009
Γ = 270 nm
Order
=
floor(
Γ
550
)
+
1
=
1:
first-order
white.
This is an example. Type your own values to start a new problem.
Γ (nm)
=
1,000
×
t (μm)
×
δ
N
Color order
worked out (not typed)
Formulas
Γ
=
1,000
×
t
×
δ
270 = 1,000 × 30 × 0.009
N
=
floor(
Γ
550
)
+
1
1
=
floor(
270
550
)
+
1
Assumptions
•
δ is nhigh − nlow for the grain as cut, so grains of one mineral show colors up to its maximum δ.
•
Γ = 1,000tδ: 1 μm of thickness is 1,000 nm, and the slow ray falls behind by tδ.
•
Each order of colors spans about 550 nm of retardation; a standard thin section is 30 μm thick.
Step-by-step
WE KNOW
δ = 0.009, t = 30 μm
FIND
retardation (Γ), color order (N)
Step 1 · Find retardation (Γ)
Use Γ = 1,000 × t × δ
The slow ray falls behind by the thickness (1,000 nm per μm) times the birefringence.
Γ
=
1,000
×
30
×
0.009
Γ
=
30,000
×
0.009
Γ
=
270
nm
Step 2 · Find color order (N)
Use N = floor(Γ ÷ 550) + 1
Count
the
whole
550
nm
orders
below
Γ
,
then
add
1:
the
color
sits
in
the
next
order.
N
=
floor(
270
550
)
+
1
N
=
1
Check
Put the numbers back in. Both sides should match.
270 = 1,000 × 30 × 0.009 ✓
1
=
floor(
270
550
)
+
1
✓
Topic check
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