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Contactless Calliper
Reporter – Giga Khizanishvili
01/05/2023Giga Khizanishvili 2
CONTACTLESS CALLIPER
Invent and construct an optical device that uses a laser pointer and allows contactless determination of thickness, refractive index, and other properties of a glass sheet.
01/05/2023Giga Khizanishvili 3
PLAN Problem Theoretical model Experiments The margin of error Compare of theory and experiments Conclusion
01/05/2023Giga Khizanishvili 4
𝛽 𝛽
𝛼 𝛼
THEORETICAL MODEL
d
𝑠
n2
n1
𝑥s=𝑥∗𝑠𝑖𝑛𝑎𝑠
01/05/2023Giga Khizanishvili 5
Refractive index 1,0002926
𝒔𝒊𝒏𝜶𝒔𝒊𝒏 𝜷=
𝒏𝟐𝒏𝟏
n1 (Air) 1n1
n2 𝒔𝒊𝒏𝜶=𝒔𝒊𝒏 𝜷∗𝒏
01/05/2023Giga Khizanishvili 6
cos𝛼=𝑠𝑙
𝑐𝑡𝑔 𝛽=2𝑑𝑙 𝑙= 2𝑑
𝑐𝑡𝑔 𝛽
𝑐𝑜𝑠𝛼=𝑠∗𝑐𝑡𝑔 𝛽2𝑑
𝑑=𝑠∗𝑐𝑡𝑔 𝛽2∗𝑐𝑜𝑠𝑎 = 𝑠∗𝑐𝑜𝑠 𝛽
2∗𝑐𝑜𝑠𝛼∗𝑠𝑖𝑛 𝛽= 𝑠∗√1−𝑠𝑖𝑛2𝛽2∗𝑐𝑜𝑠𝛼∗𝑠𝑖𝑛 𝛽
⇒ 𝑠𝑖𝑛𝛽=𝑠𝑖𝑛𝑎𝑛
𝑑=𝑠∗𝑛∗√1− 𝑠𝑖𝑛2𝑎𝑛2
𝑠𝑖𝑛 2𝑎
01/05/2023Giga Khizanishvili 7
dn
𝑠1
1 𝑎1𝑠1
𝑎1
𝐹𝑖𝑟𝑠𝑡 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡
01/05/2023Giga Khizanishvili 8
dn
𝑠2
𝑎 2 𝑎 2𝑠2
𝑎1
𝑎 2
𝑆𝑒𝑐𝑜𝑛𝑑 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡
01/05/2023Giga Khizanishvili 9
𝑑=s1∗n∗√1− 𝑠𝑖𝑛2𝑎1𝑛2
𝑠𝑖𝑛2𝑎1 𝑑=s2∗n∗√1− 𝑠𝑖𝑛2𝑎 2𝑛2
𝑠𝑖𝑛2𝑎2
s1∗n∗√1− 𝑠𝑖𝑛2𝑎 1𝑛2𝑠𝑖𝑛2𝑎1 =
s2∗n∗√1− 𝑠𝑖𝑛2𝑎2𝑛2𝑠𝑖𝑛2𝑎2
𝒏=√𝐬𝟏𝟐∗ 𝒔𝒊𝒏𝟐𝒂𝟏∗ 𝒔𝒊𝒏𝟐𝟐𝒂𝟐−𝐬𝟐𝟐∗𝒔𝒊𝒏𝟐𝒂𝟐∗𝒔𝒊𝒏𝟐𝟐𝒂𝟏𝐬𝟏𝟐∗ 𝒔𝒊𝒏𝟐𝟐𝒂𝟐−𝐬𝟐𝟐∗𝒔𝒊𝒏𝟐𝟐𝒂𝟏
01/05/2023Giga Khizanishvili 10
F𝑎
𝑎𝑥
𝑦
𝑦=𝑥∗𝑠𝑖𝑛𝑎
𝑠
𝐹𝑑
cos (90−𝑎)−𝑥∗𝑐𝑜𝑠𝑎
2∗𝐹∗ cos (90−𝑎)𝑑−𝑥∗ 𝑠𝑖𝑛2𝑎 = 𝑠
𝑥∗𝑐𝑜𝑠𝑎
𝑠=2∗ F∗ cos (90−𝑎)∗𝑥∗𝑐𝑜𝑠𝑎𝑑−𝑥∗ 𝑠𝑖𝑛2𝑎
𝑑
𝑠=𝐹∗ 𝑥∗𝑠𝑖𝑛2𝑎𝑑−𝑥 ∗𝑠𝑖𝑛2𝑎
¿ 𝑠𝑦
01/05/2023Giga Khizanishvili 11
THE MARGIN OF ERROR
0,03%
The margin of error of the refractive index of the air
01/05/2023Giga Khizanishvili 12
The margin of the error of the angle (
THE MARGIN OF ERROR
𝑙
h=132±0,5cm
𝑥
𝑎
𝑥=126±0.5 cm
h
𝑡𝑔𝑎 (𝑚𝑎𝑥 )= 126+0.5132−0.5=0,96 1965
𝑡𝑔𝑎 (𝑚𝑖𝑛)=126−0.5132+0.5 =0.9 4749
01/05/2023Giga Khizanishvili 13
The margin of the error of the angle (
𝑙
𝑥
𝑎
h
𝑎𝑟𝑐𝑡𝑔 (0,961965 )=43.88 °
𝑡𝑔𝑎 (𝑚𝑖𝑛)=126−0.5132+0.5 =0.94749
𝑎𝑟𝑐𝑡𝑔 (0.94749 )=43.45 °
𝑎=𝑎 (𝑚𝑎𝑥 )+𝑎 (𝑚𝑖𝑛)
2= 43.88+43.45
2=43.665 ° ±0. 215 °
∆𝑎𝑎 =
0.215 °43.665 ° ≈0.005≈0.5%
𝑡𝑔𝑎 (𝑚𝑎𝑥 )= 126+0.5132−0.5=0,96 1965
THE MARGIN OF ERROR
01/05/2023Giga Khizanishvili 14
The margin of the error of the angle (
𝑙
𝑥
𝑎
h
h=130±0,5𝑐𝑚
𝑥=81±0,5𝑐𝑚
𝑎=𝑎 (𝑚𝑎𝑥 )+𝑎 (𝑚𝑖𝑛)
2=32.44 °+31 ,4 °
2=31.92° ±0. 26 °
∆𝑎𝑎 =
0. 26 °31.95 ° ≈0.008 ≈0.8%
𝑎 (𝑚𝑎𝑥 )=32.18 °
𝑎 (𝑚𝑖𝑛 )=31 ,66 °
THE MARGIN OF ERROR
01/05/2023Giga Khizanishvili 15
𝑑=s∗n∗√1− 𝑠𝑖𝑛2𝑎𝑛2
𝑠𝑖𝑛2𝑎
∆ 𝑑𝑑 =4.8%⇒
∆𝑎1𝑎1 =0.5%
∆𝑎 2𝑎2 =0.8%
THE ERROR OF THE GLASS SHEET’S THICKNESS
01/05/2023Giga Khizanishvili 16
DI ELECTRICAL PERMEABILITY𝑐=
1√𝜇0∗𝜀 0
𝑣=1
√𝜇𝜇0∗𝜀 0𝜀
𝑐=𝑣∗𝑛 𝑐𝑛=𝑣⇒
𝑛∗√𝜇 0∗𝜀 0=√𝜇𝜇0∗𝜀 0 𝜀
𝑛=√𝜀 𝑛2=𝜀⇒
01/05/2023Giga Khizanishvili 17
DI ELECTRICAL PERMEABILITY OF A GLASS SHEET
I Exp
II Exp
III Exp
IV exp
V Exp
Vi asfas
0 0.5 1 1.5 2 2.5
2.37
2.28
2.19
2.28
2.2
0.0001
Di electrical permeability
01/05/2023Giga Khizanishvili 18
EXPERIMENTS
01/05/2023Giga Khizanishvili 19
DECLINATION OF LASER
Angle of laser’s declination - 𝛼1 = 43,7 Angle of laser’s declination - 𝛼2= 32
01/05/2023Giga Khizanishvili 20
REFRACTIVE INDEX OF A GLASS SHEET
𝑠1=2.8𝑚𝑚
𝒏=√𝐬𝟏𝟐∗ 𝒔𝒊𝒏𝟐𝒂𝟏∗ 𝒔𝒊𝒏𝟐𝟐𝒂𝟐−𝐬𝟐𝟐∗𝒔𝒊𝒏𝟐𝒂𝟐∗𝒔𝒊𝒏𝟐𝟐𝒂𝟏𝐬𝟏𝟐∗ 𝒔𝒊𝒏𝟐𝟐𝒂𝟐−𝐬𝟐𝟐∗𝒔𝒊𝒏𝟐𝟐𝒂𝟏
𝑠2=2.4𝑚𝑚𝑎1=43.7 °𝑎 2=32 °
⇒ 𝑛=1.53
01/05/2023Giga Khizanishvili 21
THICKNESS OF GLASS SHEET
𝑑=s∗n∗√1− 𝑠𝑖𝑛2𝑎𝑛2
𝑠𝑖𝑛2𝑎
𝑛=1.53𝑠𝑖𝑛𝑎=0.69𝑠𝑖𝑛2𝑎=0.99
01/05/2023Giga Khizanishvili 22
F𝑎
𝑎𝑥
𝑦
𝑠
𝑑
𝑑1
𝑑2
𝑑1=953 cm
𝑑2=𝐹∗𝑠𝑖𝑛𝑎
𝑑=𝑑 1+𝑑 2
𝑑=953+15∗0.69
𝑑=953+10.35
𝑑=963cm
01/05/2023 23
THICKNESS OF GLASS SHEET
Giga Khizanishvili
𝑛=1.55𝑠𝑖𝑛𝑎=0.69
𝑠𝑖𝑛2𝑎=0.9989
𝑠=𝐹∗ 𝑥∗𝑠𝑖𝑛2𝑎𝑑−𝑥 ∗𝑠𝑖𝑛2𝑎
𝐹=15𝑐𝑚𝑑=963𝑐𝑚
𝑑=s∗n∗√1− 𝑠𝑖𝑛2𝑎𝑛2
𝑠𝑖𝑛2𝑎
𝑠𝑖𝑛2𝑎=0.99
𝑥=¿
𝑠=15∗0.999∗6.5172.35∗2 =2.8𝑚𝑚⇒𝑥=36𝑐𝑚
𝑥=36𝑐𝑚
01/05/2023Giga Khizanishvili 24
THICKNESS OF GLASS SHEET
𝑛=1.53𝑠𝑖𝑛𝑎=0.69𝑠𝑖𝑛2𝑎=0.9989
𝑑=s∗n∗√1− 𝑠𝑖𝑛2𝑎𝑛2
𝑠𝑖𝑛2𝑎
𝑠=2.8𝑚𝑚𝑛=1.53
𝑠𝑖𝑛2𝑎=0.999𝑠𝑖𝑛𝑎=0.69
𝑑=2.8∗1.55∗√1− 0.476792.4
0.999=4.39∗√0.8=3.83𝑚𝑚
01/05/2023Giga Khizanishvili 25
COMPARE OF THEORY AND EXPERIMENTS
𝑑=3.83𝑚𝑚𝑛=1.53 𝐶𝑎𝑙𝑙𝑖𝑝𝑒𝑟
01/05/2023Giga Khizanishvili 26
COMPARE OF THEORY AND EXPERIMENTS
n
d
0 1 2 3 4 5 6
1.5
4.96
1.54
5.09
d = 4.96mm
Experiment Theory
01/05/2023Giga Khizanishvili 27
COMPARE OF THEORY AND EXPERIMENTS
n
d
0 0.5 1 1.5 2 2.5 3
1.5
2.39
1.51
2.44
d = 2.39mm
Experiment Theory
01/05/2023Giga Khizanishvili 28
COMPARE OF THEORY AND EXPERIMENTS
n
d
0 1 2 3 4 5 6 7
1.5
6.21
1.48
6.14
d = 6.21mm
Experiment Theory
01/05/2023Giga Khizanishvili 29
COMPARE OF THEORY AND EXPERIMENTS
n
d
0 0.5 1 1.5 2 2.5 3 3.5
1.5
3.24
1.51
3.28
d = 3.24mm
Experiment Theory
01/05/2023Giga Khizanishvili 30
COMPARE OF THEORY AND EXPERIMENTS
n
d
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
1.5
3.91
1.485
3.85
d = 3.91mm
Experiment Theory
01/05/2023Giga Khizanishvili 31
CONCLUSION We came up with a mechanism that measures the thickness of glass sheet The thickness of a glass sheet depends upon We have derived a formula for the refractive index of glass Experimental Errors we are measured Experiments have been conducted Thickness of glass sheet and refractive index have been determined Theoretical model was compared to experiments We have solved the problem
01/05/2023Giga Khizanishvili 32
USED LITERATURE
Baldwin, G. C.; Solem, J. C. (1997). "Recoilless gamma-ray lasers". Reviews of Modern Physics 69 (4): 1085–1117.
Vogel, Werner. Physics of Glass. Wiley, 1985. Bundschuh, Bernhard; Himmel, Jörg: Optische Informationsübertragung.
Oldenbourg Verlag, München, Wien 2003 Baldwin, G. C.; Solem, J. C. (1982). "Is the time ripe? Or must we wait so
long for breakthroughs?". Laser Focus 18
01/05/2023Giga Khizanishvili 33
https://www.google.com/patents/US4902902 http://russianpatents.com/patent/242/2429447.html http://physics.aidio.net/index.php/18-teoria/73-geometriuli-optika-ziritadi-kanonebi http://www.google.com/patents/US7414740 http://vlab.amrita.edu/?sub=1&brch=189&sim=1519&cnt=1 https://www.google.com/patents/US5636027
USED WEB-SPACE
01/05/2023Giga Khizanishvili
Thanks For Your
Attention 34
01/05/2023Giga Khizanishvili 35
Thanks For Your Attention
01/05/2023Giga Khizanishvili 36
Added Slides
01/05/2023
LASERსინათლის გაძლიერება იძულე-ბული გამოსხივების მეშვეობითმოწყობილობა, რომელიც ენერგიას გარდაქმნის მიმარ-თულ სინათლის სხივად.
4
01/05/2023Giga Khizanishvili 38
n2 > n1
n1
n2
სრული შინაგანი არეკვლა
01/05/2023Giga Khizanishvili 39
s12∗(𝑛2−𝑠𝑖𝑛2𝑎1)𝑠𝑖𝑛22𝑎1 =
s22∗(𝑛2−𝑠𝑖𝑛2𝑎2)𝑠𝑖𝑛22𝑎2
s12∗𝑛2−s12∗ 𝑠𝑖𝑛2𝑎1𝑠𝑖𝑛22𝑎1 =
s 22∗𝑛2−s 22∗𝑠𝑖𝑛2𝑎 2𝑠𝑖𝑛22𝑎2
s12∗𝑛2∗𝑠𝑖𝑛 22𝑎 2−s12∗𝑠𝑖𝑛2𝑎 1∗𝑠𝑖𝑛22𝑎 2=s22∗𝑛2∗𝑠𝑖𝑛22𝑎1−s 22∗𝑠𝑖𝑛2𝑎2∗𝑠𝑖𝑛22𝑎1
s12∗𝑛2∗𝑠𝑖𝑛 22𝑎 2−s 22∗𝑛2∗𝑠𝑖𝑛 22𝑎1=s12∗𝑠𝑖𝑛2𝑎1∗ 𝑠𝑖𝑛22𝑎2−s 22∗𝑠𝑖𝑛2𝑎2∗𝑠𝑖𝑛22𝑎1
𝑛2∗(s 12∗𝑠𝑖𝑛22𝑎2−s22∗𝑠𝑖𝑛22𝑎1)=s12∗𝑠𝑖𝑛2𝑎1∗𝑠𝑖𝑛22𝑎2−s22∗ 𝑠𝑖𝑛2𝑎2∗𝑠𝑖𝑛22𝑎1
𝑛2= s12∗𝑠𝑖𝑛2𝑎1∗𝑠𝑖𝑛22𝑎2−s22∗ 𝑠𝑖𝑛2𝑎2∗𝑠𝑖𝑛22𝑎1s12∗𝑠𝑖𝑛22𝑎2−s22∗𝑠𝑖𝑛22𝑎1
𝒏=√𝐬𝟏𝟐∗ 𝒔𝒊𝒏𝟐𝒂𝟏∗ 𝒔𝒊𝒏𝟐𝟐𝒂𝟐−𝐬𝟐𝟐∗𝒔𝒊𝒏𝟐𝒂𝟐∗𝒔𝒊𝒏𝟐𝟐𝒂𝟏𝐬𝟏𝟐∗ 𝒔𝒊𝒏𝟐𝟐𝒂𝟐−𝐬𝟐𝟐∗𝒔𝒊𝒏𝟐𝟐𝒂𝟏
01/05/2023Giga Khizanishvili 40
𝑑=s1∗n∗√1− 𝑠𝑖𝑛2𝑎1𝑛2
𝑠𝑖𝑛2𝑎1 𝑑=s2∗n∗√1− 𝑠𝑖𝑛2𝑎 2𝑛2
𝑠𝑖𝑛2𝑎2
s1∗n∗√1− 𝑠𝑖𝑛2𝑎 1𝑛2𝑠𝑖𝑛2𝑎1 =
s2∗n∗√1− 𝑠𝑖𝑛2𝑎2𝑛2𝑠𝑖𝑛2𝑎2
s12∗n2∗ 𝑛2−𝑠𝑖𝑛2𝑎1
𝑛2𝑠𝑖𝑛22𝑎1 =
s 22∗n2∗𝑛2−𝑠𝑖𝑛2𝑎 2
𝑛2𝑠𝑖𝑛22𝑎2
s12∗(𝑛2−𝑠𝑖𝑛2𝑎1)𝑠𝑖𝑛22𝑎1 =
s22∗(𝑛2−𝑠𝑖𝑛2𝑎2)𝑠𝑖𝑛22𝑎2
01/05/2023 41Giga Khizanishvili
𝒅=𝐬∗𝐧∗√𝟏− 𝒔𝒊𝒏𝟐𝒂
𝒏𝟐𝒔𝒊𝒏𝟐𝒂
𝒏=√𝐬𝟏𝟐∗ 𝒔𝒊𝒏𝟐𝒂𝟏∗ 𝒔𝒊𝒏𝟐𝟐𝒂𝟐−𝐬𝟐𝟐∗𝒔𝒊𝒏𝟐𝒂𝟐∗𝒔𝒊𝒏𝟐𝟐𝒂𝟏𝐬𝟏𝟐∗ 𝒔𝒊𝒏𝟐𝟐𝒂𝟐−𝐬𝟐𝟐∗𝒔𝒊𝒏𝟐𝟐𝒂𝟏
𝑑=
s∗√ 𝑠12∗𝑠𝑖𝑛2𝑎1∗𝑠𝑖𝑛22𝑎2−𝑠22∗𝑠𝑖𝑛2𝑎2∗𝑠𝑖𝑛22𝑎1𝑠12∗𝑠𝑖𝑛22𝑎2−𝑠22∗𝑠𝑖𝑛 22𝑎 1 ∗√1− 𝑠𝑖𝑛2𝑎𝑠12∗𝑠𝑖𝑛2𝑎1∗ 𝑠𝑖𝑛22𝑎2−𝑠 22∗𝑠𝑖𝑛2𝑎2∗𝑠𝑖𝑛22𝑎1
𝑠12∗𝑠𝑖𝑛22𝑎2−𝑠22∗𝑠𝑖𝑛 22𝑎 1𝑠𝑖𝑛2𝑎
01/05/2023Giga Khizanishvili 42
𝒏=√ 𝒙𝟏𝟐∗𝒔𝒊𝒏𝟐𝒂𝟏∗ 𝒔𝒊𝒏𝟐𝒂𝟏∗𝟒∗𝒔𝒊𝒏𝟐𝒂𝟐∗𝒄𝒐𝒔𝟐𝒂𝟐− 𝒙𝟐𝟐∗𝒔𝒊𝒏𝟐𝒂𝟐∗ 𝒔𝒊𝒏𝟐𝒂𝟐∗𝟒∗𝒔𝒊𝒏𝟐𝒂𝟏∗𝒄𝒐𝒔𝟐𝒂𝟏𝒙𝟏𝟐∗𝒔𝒊𝒏𝟐𝒂𝟏∗𝟒∗ 𝒔𝒊𝒏𝟐𝒂𝟐∗𝒄𝒐𝒔𝟐𝒂𝟐−𝒙𝟐𝟐∗𝒔𝒊𝒏𝟐𝒂𝟐∗𝟒∗ 𝒔𝒊𝒏𝟐𝒂𝟏∗ 𝒔𝒊𝒏𝟐𝒂𝟏
𝒏=√𝟒∗𝒔𝒊𝒏𝟐𝒂𝟏∗𝒔𝒊𝒏𝟐𝒂𝟐(𝒙 𝟏𝟐∗ 𝒔𝒊𝒏¿¿𝟐𝒂𝟏∗𝒄𝒐𝒔𝟐𝒂𝟐− 𝒙𝟐𝟐∗ 𝒔𝒊𝒏𝟐𝒂𝟐∗𝒄𝒐𝒔𝟐𝒂𝟏)𝟒∗ 𝒔𝒊𝒏𝟐𝒂𝟏∗𝒔𝒊𝒏𝟐𝒂𝟐(𝒙𝟏𝟐∗𝒄𝒐𝒔𝟐𝒂𝟐−𝒙 𝟐𝟐∗𝒄𝒐𝒔𝟐𝒂𝟏)
¿
𝒏=√ 𝒙𝟏𝟐∗𝒔𝒊𝒏𝟐𝒂𝟏∗𝒄𝒐𝒔𝟐𝒂𝟐− 𝒙𝟐𝟐∗ 𝒔𝒊𝒏𝟐𝒂𝟐∗𝒄𝒐𝒔𝟐𝒂𝟏𝒙𝟏𝟐∗𝒄𝒐𝒔𝟐𝒂𝟐− 𝒙𝟐𝟐∗𝒄𝒐𝒔𝟐𝒂𝟏
s=𝑥∗𝑠𝑖𝑛𝑎⇒
01/05/2023Giga Khizanishvili 43
დახრილი სიბრტყის ცდომილება
𝛼𝑜𝑠
𝑙
𝑙= 𝑠𝑐𝑜𝑠𝑎
∆ 𝑠𝑠 =
𝑠𝑠∗𝑐𝑜𝑠𝑎 −1
∆ 𝑠𝑠 =
𝑙𝑠 −1
∆ 𝑠𝑠 =
1𝑐𝑜𝑠𝑎−1
𝑎=2.5 ° 𝑐𝑜𝑠𝑎=0.999048221582
∆ 𝑠𝑠 =
10.999048221582 −1
∆ 𝑠𝑠 =1.0009526851631775−1
∆ 𝑠𝑠 =0.0009526851631775
∆ 𝑠𝑠 ≈ 0 .01%