TI-84 Plus CE: Birefringence
Introduction
Essentially, birefringence is the double refraction of light in material, drive by the differences in the refractive indices of both materials. Mathematically, birefringence between two materials is defined as:
B = | n_e – n_o |
n_o: refractive index of light where the ordinary ray originates
n_e: refractive index of light where the extraordinary ray originates
If n_e > n_o, we have positive birefringence, and the wave polarizes quickly.
If n_e < n_o, we have negative birefringence, and the wave polarizes slowly.
The relative retardation (delay or angle in radians) with one ray respected to another is calculated by the equation:
R = T * B
T = the thickness of the material, typically in meters
The program features 10 common materials, with the 11th allowing the user to enter their own refractive index, particularly useful for crystals.
TI-84 Plus CE Program: BIREF
Full
{1,1.000293,1.000132,1.333,1.31,1.46,1.49,1.52,1.69,2.417}→L₁
“ORDEXT”→Str0
For(I,1,2)
ClrHome
Output(9,1,"BIREFRINGENCE")
Output(3,1,"1. VACUUM")
Output(4,1,"2. AIR")
Output(5,1,"3. HYDROGEN")
Output(6,1,"4. WATER")
Output(7,1,"5. ICE")
Output(3,12,"6. QUARTZ")
Output(4,12,"7. PLEXIGLASS")
Output(5,12,"8. WINDOW GLASS")
Output(6,12,"9. FLINT GLASS")
Output(7,12,"10. DIAMOND")
Output(8,12,”11. YOUR OWN”)
Input sub(Str0,3(I-1)+1,3)+” RAY? ”,J
If J=11:Then:
Input “ENTER REF INDEX: “,X
If I=1:Then:X→O
Else:X→E:End
Else
If I=1:Then:L₁(J)→O
Else:L₁(J)→E:End
End
End
Input "THICKNESS? ",T
abs(E-O)→B
T*B→G
ClrHome
If E≥O:Then:Disp "POSITIVE"
Else:Disp "NEGATIVE":End
Disp "BIREFRINGENCE:",B,"DELAY:",G
Note: The Full mode sets the TI-84 to full screen mode.
Examples
Example 1: Diamond (ordinary ray) to Air (extraordinary ray), 0.5 m thick
Negative Birefringence: 1.416707
Delay: 0.7083535 (radians)
Example 2: Air (ordinary ray) to Ice (extraordinary ray), 3.6 m deep
Positive Birefringence: 0.309707
Delay: 1.1149452 (radians)
Sources
Nikon with contributing authors Douglas B. Murphy, Kenneth R. Spring, Thomas J. Fellers, and Michael W. Davidson. “Principles of Birefringence: Introduction to Optical Birefringence” Nikon. MicroscopyU: The Source for Microscopy Education. 2024/2025. Retrieved November 16, 2024. https://www.microscopyu.com/techniques/polarized-light/principles-of-birefringence#:~:text=Birefringence%20is%20formally%20defined%20as,dependent%20differences%20in%20refractive%20index.
“Refractive index.” Wikipedia https://en.wikipedia.org/wiki/Refractive_index At the time of retrieval, it was edited November 17, 2024. Retrieved December 1, 2024.
Eddie
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