SISKA ARIANI WA (080913081) SIMULASI OPTIK-DIFRAKSI FRAUNHOFER

Download Pada difraksi fraunhofer jarak celah ke layar lebih panjang karena bayangan ... Fungsi cosinus berarti gelombang yang real, berkas dari cel...

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Simulasi Difraksi Fraunhofer Dalam optika geometri dikenal dua macam difraksi atau hamburan, yaitu fresnel dan fraunhofer. Konsep ini ada dikarenakan cahaya memiliki sifat dapat mengalami hamburan dan interferensi. Yang membedakan keduanya adalah jarak celah ke layar. Pada difraksi fraunhofer jarak celah ke layar lebih panjang karena bayangan harus berada jauh dari celah. Pada difraksi ini, dibuat jarak antara celah ke layar adalah 1meter. Tujuan dasar tugas ini adalah membuat simulasi tentang bagaimana mengolah berkas cahaya yang melewati celah sempit, dari sini lah difraksi akan muncul dimana cahaya dihamburkan saat melewati celah sempit dan ditangkap oleh layar. Pertama yang perlu diperhatikan adalah berkas cahaya merupakan gelombang elektromagnetik, yang dapat dinyatakan dengan persamaan gelombang: =

sin(

+

)

Yang dalam perhitungan ini, beda fase dianggap tetap sehingga:

= Diketahui Dengan

sin(

)

= adalah 1 angstrom, lebar celah 1 mm dan jarak celah ke layar 1 m.

Pertama kita menentukan fungsi gelombang (berkas cahaya) dari sumber ke celah. (1) dengan menggunakan persamaaan gelombang diatas. Kemudian yang kedua kita menentukan fungsi sinus dan cosinus nya. Fungsi cosinus berarti gelombang yang real, berkas dari celah menuju ke layar.

Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

=

cos(

)

Berkas yang kemudian melalui celah sempit menuju layar akan direpresentasikan sebanyak 400pixel. Misalkan kita buat mulai 200 s.d -200 pada sumbu y sehingga skala nol, memungkinkan terjadinya puncak difraksi atau yang biasa kita sebut interferensi maksimum. Yang terakhir untuk mewujudkannya ke dalam grafik, kita membuat fungsi intensitas yang merupakan jumlahan dari fungsi sinus dan cosinus nya. = A sin (

) + A cos (

)

Diolah dengan menggunakan ms.excell sebagai berikut: Column1 200 199 198 197 196 195 194 193 192 191 190 189 188 187 186 185 184 183 182 181 180 179 178 177

x 223.6068 222.7128 221.8197 220.9276 220.0364 219.1461 218.2567 217.3684 216.4809 215.5945 214.7091 213.8247 212.9413 212.059 211.1777 210.2974 209.4182 208.5402 207.6632 206.7873 205.9126 205.039 204.1666 203.2954

Kx 5.257866 5.236845 5.215845 5.194867 5.173911 5.152977 5.132065 5.111176 5.090309 5.069466 5.048647 5.027851 5.007079 4.986331 4.965608 4.94491 4.924238 4.903591 4.88297 4.862375 4.841807 4.821265 4.800751 4.780265

y= A sin (kx) y= A cos (kx) -0.854879959 0.518825843 -0.865596475 0.500742191 -0.875920248 0.482455925 -0.885847772 0.463975996 -0.895375756 0.445311413 -0.904501124 0.426471237 -0.913221014 0.407464574 -0.92153278 0.388300573 -0.929433993 0.368988419 -0.936922439 0.349537327 -0.943996124 0.32995654 -0.950653268 0.310255319 -0.956892312 0.290442942 -0.962711911 0.270528697 -0.968110939 0.250521876 -0.973088485 0.230431771 -0.977643855 0.210267671 -0.981776571 0.19003885 -0.98548637 0.16975457 -0.988773203 0.14942407 -0.991637234 0.129056566 -0.994078838 0.108661238 -0.996098602 0.088247236 -0.997697324 0.067823664

Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

176 175 174 173 172 171 170 169 168 167 166 165 164 163 162 161 160 159 158 157 156 155 154 153 152 151 150 149 148 147 146 145 144 143 142 141 140 139 138 137 136 135 134

202.4253 201.5564 200.6888 199.8224 198.9573 198.0934 197.2308 196.3695 195.5096 194.651 193.7937 192.9378 192.0833 191.2302 190.3786 189.5284 188.6796 187.8324 186.9866 186.1424 185.2998 184.4587 183.6192 182.7813 181.945 181.1105 180.2776 179.4464 178.6169 177.7892 176.9633 176.1391 175.3169 174.4964 173.6779 172.8612 172.0465 171.2338 170.423 169.6143 168.8076 168.003 167.2005

4.759806 4.739376 4.718975 4.698603 4.67826 4.657947 4.637664 4.617412 4.597191 4.577002 4.556844 4.536719 4.516626 4.496567 4.476541 4.456549 4.436592 4.41667 4.396783 4.376933 4.357118 4.337341 4.317601 4.297899 4.278236 4.258612 4.239027 4.219482 4.199979 4.180516 4.161095 4.141717 4.122381 4.10309 4.083842 4.06464 4.045483 4.026372 4.007308 3.988291 3.969323 3.950404 3.931534

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Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

133 132 131 130 129 128 127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112 111 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91

166.4001 165.6019 164.8059 164.0122 163.2207 162.4315 161.6447 160.8602 160.0781 159.2985 158.5213 157.7466 156.9745 156.205 155.4381 154.6739 153.9123 153.1535 152.3975 151.6443 150.894 150.1466 149.4021 148.6607 147.9223 147.187 146.4548 145.7258 145 144.2775 143.5584 142.8426 142.1302 141.4214 140.716 140.0143 139.3162 138.6218 137.9311 137.2443 136.5613 135.8823 135.2072

3.912714 3.893946 3.875229 3.856565 3.837954 3.819397 3.800895 3.782449 3.764059 3.745727 3.727452 3.709237 3.691082 3.672987 3.654954 3.636984 3.619077 3.601235 3.583458 3.565748 3.548105 3.530531 3.513026 3.495591 3.478228 3.460938 3.443722 3.42658 3.409514 3.392526 3.375615 3.358785 3.342035 3.325366 3.308781 3.292281 3.275866 3.259538 3.243298 3.227148 3.211089 3.195122 3.179249

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Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48

134.5362 133.8693 133.2066 132.5481 131.8939 131.244 130.5986 129.9577 129.3213 128.6895 128.0625 127.4402 126.8227 126.2101 125.6025 125 124.4026 123.8103 123.2234 122.6418 122.0656 121.4949 120.9297 120.3703 119.8165 119.2686 118.7266 118.1905 117.6605 117.1367 116.619 116.1077 115.6028 115.1043 114.6124 114.1271 113.6486 113.1769 112.712 112.2542 111.8034 111.3598 110.9234

3.163471 3.147789 3.132206 3.116722 3.101339 3.086058 3.070882 3.055811 3.040847 3.025992 3.011247 2.996615 2.982095 2.967692 2.953405 2.939236 2.925189 2.911263 2.897461 2.883785 2.870236 2.856817 2.843529 2.830373 2.817353 2.804469 2.791724 2.779119 2.766657 2.754339 2.742167 2.730144 2.718271 2.70655 2.694983 2.683573 2.67232 2.661228 2.650298 2.639532 2.628933 2.618502 2.608241

-0.021876103 -0.006196367 0.009386883 0.024868401 0.040243064 0.055505878 0.070651978 0.085676631 0.100575234 0.11534332 0.129976559 0.144470756 0.158821854 0.173025935 0.187079223 0.20097808 0.21471901 0.22829866 0.241713817 0.25496141 0.268038511 0.280942335 0.293670235 0.306219707 0.318588389 0.330774055 0.34277462 0.354588136 0.366212791 0.377646909 0.388888945 0.399937489 0.410791258 0.421449098 0.431909979 0.442172998 0.452237369 0.462102426 0.471767618 0.481232508 0.490496767 0.499560173 0.508422609

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Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5

110.4943 110.0727 109.6586 109.252 108.8531 108.462 108.0787 107.7033 107.3359 106.9766 106.6255 106.2826 105.9481 105.622 105.3043 104.9952 104.6948 104.4031 104.1201 103.846 103.5809 103.3247 103.0776 102.8397 102.6109 102.3914 102.1812 101.9804 101.789 101.6071 101.4347 101.2719 101.1187 100.9752 100.8415 100.7174 100.6032 100.4988 100.4042 100.3195 100.2447 100.1798 100.1249

2.598152 2.588238 2.578499 2.56894 2.55956 2.550363 2.54135 2.532524 2.523885 2.515437 2.507181 2.499118 2.491252 2.483583 2.476114 2.468847 2.461782 2.454922 2.448269 2.441824 2.43559 2.429566 2.423756 2.418161 2.412782 2.40762 2.402678 2.397956 2.393455 2.389178 2.385125 2.381297 2.377695 2.374321 2.371175 2.368259 2.365572 2.363117 2.360893 2.358902 2.357143 2.355618 2.354327

0.517084054 0.525544587 0.533804379 0.541863689 0.54972286 0.55738232 0.56484257 0.572104186 0.579167814 0.586034161 0.592703997 0.599178146 0.605457485 0.611542936 0.617435463 0.623136069 0.628645788 0.633965683 0.639096841 0.644040368 0.648797383 0.653369017 0.657756403 0.661960679 0.665982974 0.669824415 0.673486111 0.676969158 0.68027463 0.683403576 0.686357017 0.689135942 0.691741303 0.694174014 0.696434945 0.698524922 0.700444719 0.702195063 0.703776622 0.705190012 0.706435787 0.707514442 0.70842641

-0.855934624 -0.850766059 -0.845607997 -0.840466384 -0.8353471 -0.830255954 -0.825198686 -0.820180956 -0.815208344 -0.810286346 -0.80542037 -0.800615731 -0.79587765 -0.791211247 -0.786621541 -0.782113444 -0.77769176 -0.773361179 -0.769126276 -0.764991506 -0.760961205 -0.757039582 -0.753230718 -0.749538565 -0.745966941 -0.742519531 -0.739199877 -0.736011385 -0.732957317 -0.730040788 -0.72726477 -0.724632082 -0.722145394 -0.719807223 -0.717619932 -0.715585728 -0.713706659 -0.711984616 -0.71042133 -0.709018369 -0.707777139 -0.706698885 -0.705784685

Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 -27 -28 -29 -30 -31 -32 -33 -34 -35 -36 -37 -38

100.08 100.045 100.02 100.005 100 100.005 100.02 100.045 100.08 100.1249 100.1798 100.2447 100.3195 100.4042 100.4988 100.6032 100.7174 100.8415 100.9752 101.1187 101.2719 101.4347 101.6071 101.789 101.9804 102.1812 102.3914 102.6109 102.8397 103.0776 103.3247 103.5809 103.846 104.1201 104.4031 104.6948 104.9952 105.3043 105.622 105.9481 106.2826 106.6255 106.9766

2.353269 2.352447 2.351859 2.351507 2.351389 2.351507 2.351859 2.352447 2.353269 2.354327 2.355618 2.357143 2.358902 2.360893 2.363117 2.365572 2.368259 2.371175 2.374321 2.377695 2.381297 2.385125 2.389178 2.393455 2.397956 2.402678 2.40762 2.412782 2.418161 2.423756 2.429566 2.43559 2.441824 2.448269 2.454922 2.461782 2.468847 2.476114 2.483583 2.491252 2.499118 2.507181 2.515437

0.709172058 0.70975169 0.710165543 0.710413787 0.710496524 0.710413787 0.710165543 0.70975169 0.709172058 0.70842641 0.707514442 0.706435787 0.705190012 0.703776622 0.702195063 0.700444719 0.698524922 0.696434945 0.694174014 0.691741303 0.689135942 0.686357017 0.683403576 0.68027463 0.676969158 0.673486111 0.669824415 0.665982974 0.661960679 0.657756403 0.653369017 0.648797383 0.644040368 0.639096841 0.633965683 0.628645788 0.623136069 0.617435463 0.611542936 0.605457485 0.599178146 0.592703997 0.586034161

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Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

-39 -40 -41 -42 -43 -44 -45 -46 -47 -48 -49 -50 -51 -52 -53 -54 -55 -56 -57 -58 -59 -60 -61 -62 -63 -64 -65 -66 -67 -68 -69 -70 -71 -72 -73 -74 -75 -76 -77 -78 -79 -80 -81

107.3359 107.7033 108.0787 108.462 108.8531 109.252 109.6586 110.0727 110.4943 110.9234 111.3598 111.8034 112.2542 112.712 113.1769 113.6486 114.1271 114.6124 115.1043 115.6028 116.1077 116.619 117.1367 117.6605 118.1905 118.7266 119.2686 119.8165 120.3703 120.9297 121.4949 122.0656 122.6418 123.2234 123.8103 124.4026 125 125.6025 126.2101 126.8227 127.4402 128.0625 128.6895

2.523885 2.532524 2.54135 2.550363 2.55956 2.56894 2.578499 2.588238 2.598152 2.608241 2.618502 2.628933 2.639532 2.650298 2.661228 2.67232 2.683573 2.694983 2.70655 2.718271 2.730144 2.742167 2.754339 2.766657 2.779119 2.791724 2.804469 2.817353 2.830373 2.843529 2.856817 2.870236 2.883785 2.897461 2.911263 2.925189 2.939236 2.953405 2.967692 2.982095 2.996615 3.011247 3.025992

0.579167814 0.572104186 0.56484257 0.55738232 0.54972286 0.541863689 0.533804379 0.525544587 0.517084054 0.508422609 0.499560173 0.490496767 0.481232508 0.471767618 0.462102426 0.452237369 0.442172998 0.431909979 0.421449098 0.410791258 0.399937489 0.388888945 0.377646909 0.366212791 0.354588136 0.34277462 0.330774055 0.318588389 0.306219707 0.293670235 0.280942335 0.268038511 0.25496141 0.241713817 0.22829866 0.21471901 0.20097808 0.187079223 0.173025935 0.158821854 0.144470756 0.129976559 0.11534332

-0.815208344 -0.820180956 -0.825198686 -0.830255954 -0.8353471 -0.840466384 -0.845607997 -0.850766059 -0.855934624 -0.861107688 -0.866279189 -0.871443011 -0.876592992 -0.881722924 -0.88682656 -0.891897619 -0.896929785 -0.90191672 -0.90685206 -0.911729424 -0.916542418 -0.92128464 -0.925949681 -0.930531134 -0.935022596 -0.939417671 -0.943709979 -0.947893158 -0.951960866 -0.955906791 -0.95972465 -0.963408198 -0.966951229 -0.970347583 -0.973591147 -0.976675866 -0.979595739 -0.98234483 -0.984917268 -0.987307257 -0.989509071 -0.991517067 -0.993325686

Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

-82 -83 -84 -85 -86 -87 -88 -89 -90 -91 -92 -93 -94 -95 -96 -97 -98 -99 -100 -101 -102 -103 -104 -105 -106 -107 -108 -109 -110 -111 -112 -113 -114 -115 -116 -117 -118 -119 -120 -121 -122 -123 -124

129.3213 129.9577 130.5986 131.244 131.8939 132.5481 133.2066 133.8693 134.5362 135.2072 135.8823 136.5613 137.2443 137.9311 138.6218 139.3162 140.0143 140.716 141.4214 142.1302 142.8426 143.5584 144.2775 145 145.7258 146.4548 147.187 147.9223 148.6607 149.4021 150.1466 150.894 151.6443 152.3975 153.1535 153.9123 154.6739 155.4381 156.205 156.9745 157.7466 158.5213 159.2985

3.040847 3.055811 3.070882 3.086058 3.101339 3.116722 3.132206 3.147789 3.163471 3.179249 3.195122 3.211089 3.227148 3.243298 3.259538 3.275866 3.292281 3.308781 3.325366 3.342035 3.358785 3.375615 3.392526 3.409514 3.42658 3.443722 3.460938 3.478228 3.495591 3.513026 3.530531 3.548105 3.565748 3.583458 3.601235 3.619077 3.636984 3.654954 3.672987 3.691082 3.709237 3.727452 3.745727

0.100575234 0.085676631 0.070651978 0.055505878 0.040243064 0.024868401 0.009386883 -0.006196367 -0.021876103 -0.037646955 -0.053503433 -0.069439927 -0.085450712 -0.101529951 -0.117671693 -0.133869884 -0.150118362 -0.166410865 -0.182741031 -0.199102405 -0.215488439 -0.231892495 -0.248307854 -0.264727712 -0.28114519 -0.297553333 -0.313945118 -0.330313454 -0.346651191 -0.362951118 -0.379205971 -0.395408436 -0.411551156 -0.42762673 -0.44362772 -0.459546659 -0.475376047 -0.491108366 -0.506736074 -0.522251618 -0.537647433 -0.55291595 -0.568049599

-0.994929456 -0.996322997 -0.997501027 -0.99845836 -0.99918992 -0.999690733 -0.999955942 -0.999980802 -0.999760689 -0.999291102 -0.998567666 -0.997586135 -0.996342399 -0.994832483 -0.993052553 -0.990998917 -0.988668032 -0.986056501 -0.983161083 -0.97997869 -0.976506392 -0.97274142 -0.96868117 -0.964323202 -0.959665245 -0.954705197 -0.949441132 -0.943871295 -0.937994111 -0.931808181 -0.925312289 -0.918505399 -0.911386661 -0.903955408 -0.896211161 -0.888153629 -0.879782708 -0.871098486 -0.862101242 -0.852791444 -0.843169756 -0.833237032 -0.822994321

Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

-125 -126 -127 -128 -129 -130 -131 -132 -133 -134 -135 -136 -137 -138 -139 -140 -141 -142 -143 -144 -145 -146 -147 -148 -149 -150 -151 -152 -153 -154 -155 -156 -157 -158 -159 -160 -161 -162 -163 -164 -165 -166 -167

160.0781 160.8602 161.6447 162.4315 163.2207 164.0122 164.8059 165.6019 166.4001 167.2005 168.003 168.8076 169.6143 170.423 171.2338 172.0465 172.8612 173.6779 174.4964 175.3169 176.1391 176.9633 177.7892 178.6169 179.4464 180.2776 181.1105 181.945 182.7813 183.6192 184.4587 185.2998 186.1424 186.9866 187.8324 188.6796 189.5284 190.3786 191.2302 192.0833 192.9378 193.7937 194.651

3.764059 3.782449 3.800895 3.819397 3.837954 3.856565 3.875229 3.893946 3.912714 3.931534 3.950404 3.969323 3.988291 4.007308 4.026372 4.045483 4.06464 4.083842 4.10309 4.122381 4.141717 4.161095 4.180516 4.199979 4.219482 4.239027 4.258612 4.278236 4.297899 4.317601 4.337341 4.357118 4.376933 4.396783 4.41667 4.436592 4.456549 4.476541 4.496567 4.516626 4.536719 4.556844 4.577002

-0.583040814 -0.597882038 -0.612565727 -0.627084355 -0.641430418 -0.655596443 -0.669574986 -0.68335864 -0.696940041 -0.710311873 -0.723466867 -0.736397813 -0.749097561 -0.761559026 -0.773775192 -0.78573912 -0.797443947 -0.808882896 -0.820049276 -0.830936491 -0.841538041 -0.851847526 -0.861858655 -0.871565245 -0.880961228 -0.890040655 -0.8987977 -0.907226662 -0.915321974 -0.923078202 -0.930490051 -0.93755237 -0.944260152 -0.950608542 -0.95659284 -0.962208499 -0.967451138 -0.972316536 -0.976800642 -0.980899573 -0.984609623 -0.987927259 -0.990849132

-0.812442865 -0.801584099 -0.790419655 -0.778951354 -0.767181216 -0.755111451 -0.742744464 -0.730082851 -0.717129402 -0.703887096 -0.690359104 -0.676548787 -0.662459693 -0.648095556 -0.6334603 -0.618558029 -0.603393032 -0.587969779 -0.572292919 -0.556367278 -0.540197858 -0.523789836 -0.507148557 -0.490279536 -0.473188455 -0.45588116 -0.438363656 -0.420642108 -0.402722837 -0.384612315 -0.366317164 -0.347844152 -0.329200191 -0.310392331 -0.29142776 -0.272313796 -0.25305789 -0.233667613 -0.214150663 -0.194514852 -0.174768107 -0.154918463 -0.134974062

Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

-168 -169 -170 -171 -172 -173 -174 -175 -176 -177 -178 -179 -180 -181 -182 -183 -184 -185 -186 -187 -188 -189 -190 -191 -192 -193 -194 -195 -196 -197 -198 -199 -200

195.5096 196.3695 197.2308 198.0934 198.9573 199.8224 200.6888 201.5564 202.4253 203.2954 204.1666 205.039 205.9126 206.7873 207.6632 208.5402 209.4182 210.2974 211.1777 212.059 212.9413 213.8247 214.7091 215.5945 216.4809 217.3684 218.2567 219.1461 220.0364 220.9276 221.8197 222.7128 223.6068

4.597191 4.617412 4.637664 4.657947 4.67826 4.698603 4.718975 4.739376 4.759806 4.780265 4.800751 4.821265 4.841807 4.862375 4.88297 4.903591 4.924238 4.94491 4.965608 4.986331 5.007079 5.027851 5.048647 5.069466 5.090309 5.111176 5.132065 5.152977 5.173911 5.194867 5.215845 5.236845 5.257866

-0.993372072 -0.995493095 -0.997209405 -0.998518397 -0.999417658 -0.99990497 -0.999978313 -0.999635865 -0.998876008 -0.997697324 -0.996098602 -0.994078838 -0.991637234 -0.988773203 -0.98548637 -0.981776571 -0.977643855 -0.973088485 -0.968110939 -0.962711911 -0.956892312 -0.950653268 -0.943996124 -0.936922439 -0.929433993 -0.92153278 -0.913221014 -0.904501124 -0.895375756 -0.885847772 -0.875920248 -0.865596475 -0.854879959

-0.114943147 -0.094834058 -0.074655227 -0.054415174 -0.034122504 -0.013785901 0.006585877 0.026984003 0.047399584 0.067823664 0.088247236 0.108661238 0.129056566 0.14942407 0.16975457 0.19003885 0.210267671 0.230431771 0.250521876 0.270528697 0.290442942 0.310255319 0.32995654 0.349537327 0.368988419 0.388300573 0.407464574 0.426471237 0.445311413 0.463975996 0.482455925 0.500742191 0.518825843

Sehingga dihasilkan grafik fungsi intensitas yang tertangkap oleh layar adalah sebagai berikut:

Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

12000.0000000000

10000.0000000000

Intensitas

8000.0000000000

6000.0000000000 pola difraksi 4000.0000000000

Linear (pola difraksi)

2000.0000000000

0.0000000000 -300

-200

-100

0

Layar

Siska Ariani WA (080913081) Simulasi Optik-Difraksi Fraunhofer

100

200

300