II BO’LIM. HISOBLASH ISHLARI




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MANGUBEK LITIUM IODATE2

II BO’LIM. HISOBLASH ISHLARI


    1. Lityum yodat (LiIO3) kristali uchun hisob kitob ishlari

Kurs loyiha ishining hisob kitob ishlari bo‘limida biz optik sistemaning fokus masofasining to'lqin uzunlikka va nurlanish chastotasiga bog'liqligi nazariy tahlil qilishni
o‘rganamiz. Bizda berilgan masalada:
Radiuslari 1 m va 1.2 m bo’lgan bir tarafi yassi va o’zaro yopishtirilgan linzalarning natijaviy fokus masofasining chatotaga bog’liqligi hisoblansin (Bunda
birinchi linza shishadan ikkinchi linza Lithium Iodatedan tayyorlangan)
Nur sindirish ko’rsatgiching to’lqin uzunliga bog’liqligini quyidagi formula yordamida hisoblaymiz. Bu bog’liqlikning ikki turi mavjud yani oddiy va g’ayrioddiy nur
uchun. Oddiy nur uchun quyidagi formula:


0.0476
Щ = 3.4132 + — --0.0077 * A2
N A2 - 0.0338
G’ayrioddiy nur uchun esa quyidagi formuladan foydalanamiz:



no =


M
0.0346
2.9211 + — -- 0.0042 * A2
A2 -0.032

Oddiy va g’ayrioddiy nur to’lqin uzunligiga bog’liqligining hisoblangan qiymatlarini pastdagi jadvalga yozamiz.



X, (mkm)







R1

R2

v(Hz)

D,(dptr)

F, (m)

1

0,46

1,918147

1,764330359

1

1,2

6,52174E+14

1,683269

0,594082

2

0,462

1,917427

1,763773222

1

1,2

6,49351E+14

1,681949

0,594548

3

0,464

1,916718

1,763224736

1

1,2

6,46552E+14

1,680649

0,595008

4

0,466

1,91602

1,762684712

1

1,2

6,43777E+14

1,67937

0,595461

5

0,468

1,915333

1,762152971

1

1,2

6,41026E+14

1,67811

0,595908

6

0,47

1,914656

1,761629336

1

1,2

6,38298E+14

1,67687

0,596349

7

0,472

1,91399

1,761113635

1

1,2

6,35593E+14

1,675648

0,596784

8

0,474

1,913334

1,760605702

1

1,2

6,32911E+14

1,674445

0,597213

9

0,476

1,912688

1,760105374

1

1,2

6,30252E+14

1,673261

0,597636

10

0,478

1,912051

1,759612494

1

1,2

6,27615E+14

1,672094

0,598053

11

0,48

1,911424

1,759126909

1

1,2

6,25E+14

1,670944

0,598464

12

0,482

1,910806

1,758648468

1

1,2

6,22407E+14

1,669811

0,59887




13

0,484

1,910198

1,758177025

1

1,2

6,19835E+14

1,668696

0,59927

14

0,486

1,909598

1,757712439

1

1,2

6,17284E+14

1,667596

0,599666

15

0,488

1,909007

1,757254572

1

1,2

6,14754E+14

1,666512

0,600056

16

0,49

1,908424

1,75680329

1

1,2

6,12245E+14

1,665444

0,60044

17

0,492

1,90785

1,756358459

1

1,2

6,09756E+14

1,664392

0,60082

18

0,494

1,907284

1,755919954

1

1,2

6,07287E+14

1,663354

0,601195

19

0,496

1,906726

1,75548765

1

1,2

6,04839E+14

1,662332

0,601565

20 0,498

1,906176

1,755061424

1

1,2

6,0241E+14

1,661323

0,60193

21

0,5

1,905634

1,754641159

1

1,2

6E+14

1,660329

0,60229

22

0,502

1,905099

1,754226739

1

1,2

5,9761E+14

1,659349

0,602646

23

0,504

1,904572

1,753818051

1

1,2

5,95238E+14

1,658382

0,602997

24

0,506

1,904052

1,753414986

1

1,2

5,92885E+14

1,657429

0,603344

25

0,508

1,90354

1,753017437

1

1,2

5,90551E+14

1,656489

0,603686

26

0,51

1,903034

1,752625298

1

1,2

5,88235E+14

1,655562

0,604025

27 0,512

1,902535

1,752238469

1

1,2

5,85938E+14

1,654647

0,604358

28

0,514

1,902043

1,751856849

1

1,2

5,83658E+14

1,653745

0,604688

29

0,516

1,901557

1,751480341

1

1,2

5,81395E+14

1,652855

0,605014

30

0,518

1,901078

1,75110885

1

1,2

5,79151E+14

1,651977

0,605335

31

0,52

1,900606

1,750742285

1

1,2

5,76923E+14

1,65111

0,605653

32 0,522

1,900139

1,750380554

1

1,2

5,74713E+14

1,650255

0,605967

33

0,524

1,899679

1,750023569

1

1,2

5,72519E+14

1,649411

0,606277

34

0,526

1,899225

1,749671243

1

1,2

5,70342E+14

1,648579

0,606583

35

0,528

1,898776

1,749323494

1

1,2

5,68182E+14

1,647757

0,606886

36

0,53

1,898334

1,748980238

1

1,2

5,66038E+14

1,646946

0,607185

37

0,532

1,897897

1,748641394

1

1,2

5,6391E+14

1,646145

0,60748

38

0,534

1,897466

1,748306885

1

1,2

5,61798E+14

1,645354

0,607772

39

0,536

1,89704

1,747976634

1

1,2

5,59701E+14

1,644574

0,60806

40

0,538

1,89662

1,747650564

1

1,2

5,57621E+14

1,643803

0,608345

41 0,54

1,896205

1,747328605

1

1,2

5,55556E+14

1,643043

0,608627

42

0,542

1,895795

1,747010682

1

1,2

5,53506E+14

1,642292

0,608905

43

0,544

1,895391

1,746696727

1

1,2

5,51471E+14

1,64155

0,60918

44

0,546

1,894991

1,74638667

1

1,2

5,49451E+14

1,640817

0,609452

45

0,548

1,894597

1,746080445

1

1,2

5,47445E+14

1,640094

0,609721

46

0,55

1,894207

1,745777986

1

1,2

5,45455E+14

1,639379

0,609987




47

0,552

1,893822

1,745479228

1

1,2

5,43478E+14

1,638674

0,61025

48

0,554

1,893442

1,74518411

1

1,2

5,41516E+14

1,637977

0,610509

49

0,556

1,893066

1,744892569

1

1,2

5,39568E+14

1,637288

0,610766

50

0,558

1,892695

1,744604546

1

1,2

5,37634E+14

1,636608

0,61102

51

0,56

1,892328

1,744319982

1

1,2

5,35714E+14

1,635935

0,611271

52

0,562

1,891966

1,744038818

1

1,2

5,33808E+14

1,635271

0,611519

53

0,564

1,891608

1,743760999

1

1,2

5,31915E+14

1,634615

0,611765

54 0,566

1,891255

1,74348647

1

1,2

5,30035E+14

1,633967

0,612008

55

0,568

1,890905

1,743215177

1

1,2

5,28169E+14

1,633326

0,612248

56

0,57

1,89056

1,742947066

1

1,2

5,26316E+14

1,632693

0,612485

57

0,572

1,890218

1,742682086

1

1,2

5,24476E+14

1,632067

0,61272

58

0,574

1,889881

1,742420186

1

1,2

5,22648E+14

1,631448

0,612952

59

0,576

1,889547

1,742161317

1

1,2

5,20833E+14

1,630837

0,613182

60

0,578

1,889218

1,74190543

1

1,2

5,19031E+14

1,630233

0,613409

61 0,58

1,888892

1,741652476

1

1,2

5,17241E+14

1,629635

0,613634

62

0,582

1,88857

1,741402411

1

1,2

5,15464E+14

1,629045

0,613857

63

0,584

1,888251

1,741155187

1

1,2

5,13699E+14

1,628461

0,614077

64

0,586

1,887937

1,74091076

1

1,2

5,11945E+14

1,627884

0,614294

65

0,588

1,887625

1,740669086

1

1,2

5,10204E+14

1,627313

0,61451

66 0,59

1,887317

1,740430123

1

1,2

5,08475E+14

1,626749

0,614723

67

0,592

1,887013

1,740193827

1

1,2

5,06757E+14

1,626191

0,614934

68

0,594

1,886712

1,739960157

1

1,2

5,05051E+14

1,625639

0,615143

69

0,596

1,886414

1,739729073

1

1,2

5,03356E+14

1,625093

0,615349

70

0,598

1,88612

1,739500536

1

1,2

5,01672E+14

1,624553

0,615554

71

0,6

1,885829

1,739274505

1

1,2

5E+14

1,62402

0,615756

72

0,602

1,885541

1,739050944

1

1,2

4,98339E+14

1,623492

0,615956

73

0,604

1,885256

1,738829814

1

1,2

4,96689E+14

1,62297

0,616155

74

0,606

1,884974

1,738611078

1

1,2

4,9505E+14

1,622453

0,616351

75 0,608

1,884696

1,738394701

1

1,2

4,93421E+14

1,621942

0,616545

76

0,61

1,88442

1,738180648

1

1,2

4,91803E+14

1,621436

0,616737

77

0,612

1,884147

1,737968883

1

1,2

4,90196E+14

1,620936

0,616927

78

0,614

1,883877

1,737759372

1

1,2

4,88599E+14

1,620442

0,617116

79

0,616

1,88361

1,737552082

1

1,2

4,87013E+14

1,619952

0,617302

80

0,618

1,883346

1,737346981

1

1,2

4,85437E+14

1,619468

0,617487




81

0,62

1,883085

1,737144036

1

1,2

4,83871E+14

1,618988

0,61767

82

0,622

1,882826

1,736943216

1

1,2

4,82315E+14

1,618514

0,617851

83

0,624

1,88257

1,736744489

1

1,2

4,80769E+14

1,618045

0,61803

84

0,626

1,882316

1,736547825

1

1,2

4,79233E+14

1,61758

0,618207

85

0,628

1,882066

1,736353195

1

1,2

4,77707E+14

1,61712

0,618383

86

0,63

1,881818

1,736160568

1

1,2

4,7619E+14

1,616665

0,618557

87

0,632

1,881572

1,735969917

1

1,2

4,74684E+14

1,616215

0,61873

88 0,634

1,881329

1,735781213

1

1,2

4,73186E+14

1,615769

0,6189

89

0,636

1,881088

1,735594429

1

1,2

4,71698E+14

1,615328

0,619069

90

0,638

1,88085

1,735409536

1

1,2

4,70219E+14

1,614891

0,619237

91

0,64

1,880614

1,735226509

1

1,2

4,6875E+14

1,614459

0,619403

92

0,642

1,880381

1,73504532

1

1,2

4,6729E+14

1,614031

0,619567

93

0,644

1,880149

1,734865945

1

1,2

4,65839E+14

1,613607

0,619729

94

0,646

1,879921

1,734688358

1

1,2

4,64396E+14

1,613188

0,619891

95 0,648

1,879694

1,734512534

1

1,2

4,62963E+14

1,612772

0,62005

96

0,65

1,87947

1,734338448

1

1,2

4,61538E+14

1,612361

0,620208

97

0,652

1,879248

1,734166077

1

1,2

4,60123E+14

1,611954

0,620365

98

0,654

1,879028

1,733995397

1

1,2

4,58716E+14

1,611551

0,62052

99

0,656

1,87881

1,733826385

1

1,2

4,57317E+14

1,611151

0,620674

100 0,658

1,878594

1,733659017

1

1,2

4,55927E+14

1,610756

0,620827

101

0,66

1,87838

1,733493272

1

1,2

4,54545E+14

1,610364

0,620978

102

0,662

1,878169

1,733329127

1

1,2

4,53172E+14

1,609976

0,621127

103

0,664

1,877959

1,733166562

1

1,2

4,51807E+14

1,609592

0,621275

104

0,666

1,877752

1,733005553

1

1,2

4,5045E+14

1,609211

0,621422

105

0,668

1,877546

1,732846082

1

1,2

4,49102E+14

1,608834

0,621568

106

0,67

1,877342

1,732688126

1

1,2

4,47761E+14

1,608461

0,621712

107

0,672

1,877141

1,732531667

1

1,2

4,46429E+14

1,608091

0,621855

108

0,674

1,876941

1,732376683

1

1,2

4,45104E+14

1,607725

0,621997

109 0,676

1,876743

1,732223156

1

1,2

4,43787E+14

1,607362

0,622137

110

0,678

1,876547

1,732071066

1

1,2

4,42478E+14

1,607002

0,622277

111

0,68

1,876353

1,731920395

1

1,2

4,41176E+14

1,606646

0,622415

112

0,682

1,87616

1,731771123

1

1,2

4,39883E+14

1,606293

0,622551

113

0,684

1,875969

1,731623233

1

1,2

4,38596E+14

1,605944

0,622687

114

0,686

1,87578

1,731476707

1

1,2

4,37318E+14

1,605597

0,622821




115

0,688

1,875593

1,731331526

1

1,2

4,36047E+14

1,605254

0,622954

116

0,69

1,875408

1,731187673

1

1,2

4,34783E+14

1,604914

0,623086

117

0,692

1,875224

1,731045132

1

1,2

4,33526E+14

1,604577

0,623217

118

0,694

1,875041

1,730903886

1

1,2

4,32277E+14

1,604243

0,623347

119

0,696

1,874861

1,730763918

1

1,2

4,31034E+14

1,603912

0,623476

120

0,698

1,874682

1,730625211

1

1,2

4,29799E+14

1,603583

0,623603

121

0,7

1,874505

1,73048775

1

1,2

4,28571E+14

1,603258

0,62373

122 0,702

1,874329

1,730351518

1

1,2

4,2735E+14

1,602936

0,623855

123

0,704

1,874155

1,730216501

1

1,2

4,26136E+14

1,602617

0,62398

124

0,706

1,873982

1,730082684

1

1,2

4,24929E+14

1,6023

0,624103

125

0,708

1,873811

1,72995005

1

1,2

4,23729E+14

1,601986

0,624225

126

0,71

1,873641

1,729818585

1

1,2

4,22535E+14

1,601675

0,624346

127

0,712

1,873473

1,729688275

1

1,2

4,21348E+14

1,601367

0,624467

128

0,714

1,873306

1,729559106

1

1,2

4,20168E+14

1,601061

0,624586

129 0,716

1,873141

1,729431062

1

1,2

4,18994E+14

1,600758

0,624704

130

0,718

1,872977

1,729304131

1

1,2

4,17827E+14

1,600458

0,624821

131

0,72

1,872814

1,729178299

1

1,2

4,16667E+14

1,60016

0,624938

132

0,722

1,872653

1,729053551

1

1,2

4,15512E+14

1,599864

0,625053

133

0,724

1,872494

1,728929876

1

1,2

4,14365E+14

1,599572

0,625167

134 0,726

1,872335

1,728807259

1

1,2

4,13223E+14

1,599281

0,625281

135

0,728

1,872178

1,728685689

1

1,2

4,12088E+14

1,598993

0,625393

136

0,73

1,872023

1,728565152

1

1,2

4,10959E+14

1,598708

0,625505

137

0,732

1,871868

1,728445635

1

1,2

4,09836E+14

1,598425

0,625616

138

0,734

1,871715

1,728327128

1

1,2

4,08719E+14

1,598144

0,625726

139

0,736

1,871563

1,728209616

1

1,2

4,07609E+14

1,597866

0,625835

140

0,738

1,871413

1,72809309

1

1,2

4,06504E+14

1,59759

0,625943

141

0,74

1,871263

1,727977536

1

1,2

4,05405E+14

1,597316

0,62605

142

0,742

1,871115

1,727862943

1

1,2

4,04313E+14

1,597045

0,626157

143 0,744

1,870968

1,7277493

1

1,2

4,03226E+14

1,596775

0,626262

144

0,746

1,870823

1,727636596

1

1,2

4,02145E+14

1,596508

0,626367

145

0,748

1,870678

1,72752482

1

1,2

4,0107E+14

1,596243

0,626471

146

0,75

1,870535

1,72741396

1

1,2

4E+14

1,595981

0,626574

147

0,752

1,870393

1,727304006

1

1,2

3,98936E+14

1,59572

0,626676

148

0,754

1,870252

1,727194948

1

1,2

3,97878E+14

1,595462

0,626778




149

0,756

1,870112

1,727086774

1

1,2

3,96825E+14

1,595205

0,626879

150

0,758

1,869973

1,726979476

1

1,2

3,95778E+14

1,594951

0,626979

151

0,76

1,869835

1,726873042

1

1,2

3,94737E+14

1,594698

0,627078

152

0,762

1,869699

1,726767462

1

1,2

3,93701E+14

1,594448

0,627176

153

0,764

1,869563

1,726662728

1

1,2

3,9267E+14

1,5942

0,627274

154

0,766

1,869429

1,726558828

1

1,2

3,91645E+14

1,593953

0,627371

155

0,768

1,869296

1,726455754

1

1,2

3,90625E+14

1,593709

0,627467

156 0,77

1,869163

1,726353497

1

1,2

3,8961E+14

1,593466

0,627563

157

0,772

1,869032

1,726252046

1

1,2

3,88601E+14

1,593225

0,627658

158

0,774

1,868902

1,726151393

1

1,2

3,87597E+14

1,592987

0,627752

159

0,776

1,868772

1,726051528

1

1,2

3,86598E+14

1,59275

0,627845

160

0,778

1,868644

1,725952444

1

1,2

3,85604E+14

1,592514

0,627938

161

0,78

1,868517

1,72585413

1

1,2

3,84615E+14

1,592281

0,62803

162

0,782

1,868391

1,725756579

1

1,2

3,83632E+14

1,592049

0,628121

163 0,784

1,868265

1,725659782

1

1,2

3,82653E+14

1,59182

0,628212

164

0,786

1,868141

1,72556373

1

1,2

3,81679E+14

1,591592

0,628302

165

0,788

1,868017

1,725468416

1

1,2

3,80711E+14

1,591365

0,628391

166

0,79

1,867895

1,725373831

1

1,2

3,79747E+14

1,591141

0,62848

167

0,792

1,867773

1,725279966

1

1,2

3,78788E+14

1,590918

0,628568

168 0,794

1,867653

1,725186815

1

1,2

3,77834E+14

1,590696

0,628655

169

0,796

1,867533

1,725094369

1

1,2

3,76884E+14

1,590477

0,628742

170

0,798

1,867414

1,72500262

1

1,2

3,7594E+14

1,590259

0,628828

171

0,8

1,867296

1,724911561

1

1,2

3,75E+14

1,590042

0,628914

172

0,802

1,867179

1,724821185

1

1,2

3,74065E+14

1,589828

0,628999

173

0,804

1,867062

1,724731484

1

1,2

3,73134E+14

1,589614

0,629083

174

0,806

1,866947

1,72464245

1

1,2

3,72208E+14

1,589403

0,629167

175

0,808

1,866832

1,724554076

1

1,2

3,71287E+14

1,589193

0,62925

176

0,81

1,866719

1,724466356

1

1,2

3,7037E+14

1,588984

0,629333

177 0,812

1,866606

1,724379282

1

1,2

3,69458E+14

1,588777

0,629415

178

0,814

1,866494

1,724292848

1

1,2

3,6855E+14

1,588572

0,629496

179

0,816

1,866382

1,724207045

1

1,2

3,67647E+14

1,588367

0,629577

180

0,818

1,866272

1,724121869

1

1,2

3,66748E+14

1,588165

0,629658

181

0,82

1,866162

1,724037312

1

1,2

3,65854E+14

1,587964

0,629737

182

0,822

1,866053

1,723953367

1

1,2

3,64964E+14

1,587764

0,629817




183

0,824

1,865945

1,723870028

1

1,2

3,64078E+14

1,587566

0,629895

184

0,826

1,865837

1,723787289

1

1,2

3,63196E+14

1,587369

0,629973

185

0,828

1,865731

1,723705143

1

1,2

3,62319E+14

1,587173

0,630051

186

0,83

1,865625

1,723623584

1

1,2

3,61446E+14

1,586979

0,630128

187

0,832

1,86552

1,723542606

1

1,2

3,60577E+14

1,586786

0,630205

188

0,834

1,865415

1,723462203

1

1,2

3,59712E+14

1,586595

0,630281

189

0,836

1,865312

1,723382369

1

1,2

3,58852E+14

1,586404

0,630356

190 0,838

1,865209

1,723303098

1

1,2

3,57995E+14

1,586216

0,630431

191

0,84

1,865106

1,723224383

1

1,2

3,57143E+14

1,586028

0,630506

192

0,842

1,865005

1,723146221

1

1,2

3,56295E+14

1,585842

0,63058

193

0,844

1,864904

1,723068603

1

1,2

3,5545E+14

1,585657

0,630653

194

0,846

1,864804

1,722991526

1

1,2

3,5461E+14

1,585473

0,630727

195

0,848

1,864704

1,722914984

1

1,2

3,53774E+14

1,585291

0,630799

196

0,85

1,864605

1,72283897

1

1,2

3,52941E+14

1,585109

0,630871

197 0,852

1,864507

1,72276348

1

1,2

3,52113E+14

1,584929

0,630943

198

0,854

1,864409

1,722688508

1

1,2

3,51288E+14

1,584751

0,631014

199

0,856

1,864313

1,72261405

1

1,2

3,50467E+14

1,584573

0,631085

200

0,858

1,864216

1,722540099

1

1,2

3,4965E+14

1,584397

0,631155

201

0,86

1,864121

1,722466651

1

1,2

3,48837E+14

1,584221

0,631225

Bu yerda no - oddiy nur uchun nur sindirish ko‘rsatkichi ne - g‘ayrioddiy nur uchun nur sindirish ko‘rsatkichi. Nur sindirish ko‘rsatkichini hisoblashda quyidagi chegaraviy shartlardan foydalanamiz. litiy niobat kristali uchun normal sharoitdaoddiy va g‘ayrioddiy nurlar uchun to‘lqin uzunlikni 420 nm dan 860 nm gacha 2 nm interval bilan olamiz. Hisoblash ishlarini kalkulyatordan, ixtiyoriy matematik dasturlardan yoki microsoft office (Excel) dasturlaridan foydalanishimiz mumkin.
Ushbu dastur yordamidan hisoblash ishlarini oson, tez va yuqori aniqlik bilan

Yuqorida olingan grafiklardan tushunarliki nur sindirish ko‘rsatkichi to‘lqin uzunlik ortishi bilan kamayadi va nurlanish chastotasi esa kamayishi bilan kamayadi.

    1. Lityum yodat (LiIO3) kristalidan yasalgan optik sistema fokus masofasining to’lqin uzunlik va chastotaga bog’liqligi.

Hisoblashning ushbu qismida bir tomoni kumushlangan ikkinchi tomoni Lityum yodat kristalidan tuzilgan optic sistema focus masofasining to’lqin uzunlik va chastotaga bog’liqligi o’rganiladi. Bunda quyidagi formulalardan foydalanamiz:


Bu yerda R1= 1m ga, R2 =1.2 m teng. n- ga yuqoridagi n0 formulasining qiymatlarini olamiz.

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