{"id":781,"date":"2026-10-03T15:31:46","date_gmt":"2026-10-03T14:31:46","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/ince-mercek-denklemi-hesaplayici\/"},"modified":"2026-10-03T15:31:46","modified_gmt":"2026-10-03T14:31:46","slug":"ince-mercek-denklemi-hesaplayici","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/fizik\/ince-mercek-denklemi-hesaplayici\/","title":{"rendered":"\u0130nce Mercek Denklemi Hesaplay\u0131c\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Eksik Uzakl\u0131\u011f\u0131 veya Odak Uzakl\u0131\u011f\u0131n\u0131 Bulun<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"781\" data-favorite-title=\"Mercek Denklemi\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/fizik\/ince-mercek-denklemi-hesaplayici\/\" data-favorite-excerpt=\"1\/f = 1\/do + 1\/di ince mercek denklemini g\u00f6r\u00fcnt\u00fc mesafesi, cisim mesafesi veya odak uzakl\u0131\u011f\u0131 i\u00e7in \u00e7\u00f6z\u00fcn. Bilinen iki de\u011feri girin, \u00fc\u00e7\u00fcnc\u00fcs\u00fcn\u00fc ve ayr\u0131ca g\u00f6r\u00fcnt\u00fc t\u00fcr\u00fcn\u00fc, b\u00fcy\u00fctmeyi ve g\u00f6r\u00fcnt\u00fc boyunu \u00f6\u011frenin.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-physic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/fizik\/ince-mercek-denklemi-hesaplayici\/\" method=\"POST\" class=\"calculator\" id=\"calculator-781\" data-post=\"781\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Hesaplanacak b\u00fcy\u00fckl\u00fck<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"hesaplanacak_byklk\"><option value=\"di\" selected>G\u00f6r\u00fcnt\u00fc uzakl\u0131\u011f\u0131 (d\u1d62)<\/option><option value=\"do\">Cisim uzakl\u0131\u011f\u0131 (d\u2092)<\/option><option value=\"f\">Odak uzakl\u0131\u011f\u0131 (f)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field is-single has-term\" id=\"input-2\"><label for=\"field-2\">Cisim uzakl\u0131\u011f\u0131 (d\u2092)<\/label><div class=\"term\">d\u2092<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"cisim_uzakl_d\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 30\" min=\"0\" value=\"30\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm\">mm<\/option><option value=\"cm\" selected>cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-2\">Cisim ile mercek aras\u0131ndaki uzakl\u0131k. Ger\u00e7ek cisim i\u00e7in (ola\u011fan durum) pozitiftir.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-3\" hidden><label for=\"field-4\">G\u00f6r\u00fcnt\u00fc uzakl\u0131\u011f\u0131 (d\u1d62)<\/label><div class=\"term\">d\u1d62<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"number\" name=\"grnt_uzakl_d\" id=\"field-4\" aria-describedby=\"calc-info-4\" placeholder=\"e.g. 15\" step=\"any\" value=\"15\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm\">mm<\/option><option value=\"cm\" selected>cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-4\">Mercek ile g\u00f6r\u00fcnt\u00fc aras\u0131ndaki uzakl\u0131k. Ger\u00e7ek g\u00f6r\u00fcnt\u00fc i\u00e7in pozitif, sanal g\u00f6r\u00fcnt\u00fc i\u00e7in negatiftir.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-4\"><label for=\"field-6\">Odak uzakl\u0131\u011f\u0131 (f)<\/label><div class=\"term\">f<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"number\" name=\"odak_uzakl_f\" id=\"field-6\" aria-describedby=\"calc-info-6\" placeholder=\"e.g. 10\" step=\"any\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm\">mm<\/option><option value=\"cm\" selected>cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-6\">Yak\u0131nsak (d\u0131\u015fb\u00fckey) mercek i\u00e7in pozitif, \u0131raksak (i\u00e7b\u00fckey) mercek i\u00e7in negatiftir.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-5\"><label for=\"field-8\">Cisim y\u00fcksekli\u011fi (h\u2092) \u2014 iste\u011fe ba\u011fl\u0131<\/label><div class=\"term\">h\u2092<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"number\" name=\"cisim_ykseklii_h_istee_bal\" id=\"field-8\" aria-describedby=\"calc-info-8\" placeholder=\"e.g. 5\" step=\"any\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm\">mm<\/option><option value=\"cm\" selected>cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-8\">Cismin iste\u011fe ba\u011fl\u0131 y\u00fcksekli\u011fi. Yaln\u0131zca uzakl\u0131klar\u0131, g\u00f6r\u00fcnt\u00fc t\u00fcr\u00fcn\u00fc ve b\u00fcy\u00fctmeyi hesaplamak i\u00e7in bo\u015f b\u0131rak\u0131n.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"781\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> \u0130nce Mercek Sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>\u00c7\u00f6z\u00fclen b\u00fcy\u00fckl\u00fck ve hesaplama ad\u0131mlar\u0131<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>G\u00f6r\u00fcnt\u00fc t\u00fcr\u00fc, b\u00fcy\u00fctme ve g\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fi<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"781\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Mercek Denklemi Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\\[ \\frac{1}{f} = \\frac{1}{d_o} + \\frac{1}{d_i} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(f\\) \u2014 merce\u011fin odak uzakl\u0131\u011f\u0131 (m)<\/li>\n<li>\\(d_o\\) \u2014 cisim mesafesi: cisimden merce\u011fe olan uzakl\u0131k (m)<\/li>\n<li>\\(d_i\\) \u2014 g\u00f6r\u00fcnt\u00fc mesafesi: mercekten g\u00f6r\u00fcnt\u00fcye olan uzakl\u0131k (m)<\/li>\n<\/ul>\n<p>Eksik b\u00fcy\u00fckl\u00fc\u011f\u00fc \u00e7\u00f6zmek, denklemde \u00fc\u00e7 e\u015fit yeniden d\u00fczenleme verir: \\(d_i = \\dfrac{d_o f}{d_o - f}\\), \\(d_o = \\dfrac{d_i f}{d_i - f}\\) ve \\(f = \\dfrac{d_o d_i}{d_o + d_i}\\). \u00dc\u00e7 mesafe de bilindi\u011finde, enine b\u00fcy\u00fctme \\(m = -\\dfrac{d_i}{d_o}\\), g\u00f6r\u00fcnt\u00fc boyu ise \\(h_i = m\\,h_o\\) ba\u011f\u0131nt\u0131s\u0131ndan bulunur.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Mercek Denklemi \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> bir cisim, odak uzakl\u0131\u011f\u0131 10 cm olan bir yak\u0131nsak merce\u011fin 30 cm \u00f6n\u00fcnde duruyor ve cismin boyu 5 cm. G\u00f6r\u00fcnt\u00fc nerede olu\u015fur ve nas\u0131l bir g\u00f6r\u00fcnt\u00fcd\u00fcr?<\/p>\n<p>\\[ d_i = \\frac{d_o f}{d_o - f} = \\frac{0.30 \\times 0.10}{0.30 - 0.10} = \\frac{0.03}{0.20} = 0.15\\ \\text{m} \\]<\/p>\n<p>\\[ m = -\\frac{d_i}{d_o} = -\\frac{0.15}{0.30} = -0.5 \\]<\/p>\n<p>\\[ h_i = m\\,h_o = -0.5 \\times 0.05 = -0.025\\ \\text{m} \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> g\u00f6r\u00fcnt\u00fc merce\u011fin 15 cm arkas\u0131nda olu\u015fur (ger\u00e7ek, \u00e7\u00fcnk\u00fc \\(d_i &gt; 0\\)). B\u00fcy\u00fctme \\(-0.5\\times\\) oldu\u011fundan g\u00f6r\u00fcnt\u00fc terstir ve cismin yar\u0131s\u0131 boyundad\u0131r: 2,5 cm.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r<\/h2>\n<ol>\n<li><strong>\u00c7\u00f6z\u00fclecek b\u00fcy\u00fckl\u00fck<\/strong> a\u00e7\u0131l\u0131r men\u00fcs\u00fcnden hesaplamak istedi\u011finiz niceli\u011fi se\u00e7in: <em>G\u00f6r\u00fcnt\u00fc mesafesi (di)<\/em>, <em>Cisim mesafesi (do)<\/em> veya <em>Odak uzakl\u0131\u011f\u0131 (f)<\/em>. Se\u00e7ilen niceli\u011fin alan\u0131 gizlenir; di\u011fer ikisini girersiniz.<\/li>\n<li>Bilinen iki mesafeyi <strong>Cisim mesafesi (do)<\/strong> ve <strong>Odak uzakl\u0131\u011f\u0131 (f)<\/strong> alanlar\u0131na girin (<em>do<\/em> i\u00e7in \u00e7\u00f6z\u00fcl\u00fcrken <strong>G\u00f6r\u00fcnt\u00fc mesafesi (di)<\/strong> alan\u0131na) ve her biri i\u00e7in birimi (mm, cm, m, in veya ft) se\u00e7in.<\/li>\n<li>\u0130sterseniz g\u00f6r\u00fcnt\u00fc boyunu da hesaplamak i\u00e7in <strong>Cisim boyu (ho)<\/strong> de\u011ferini girin. Bu k\u0131sm\u0131 atlamak i\u00e7in bo\u015f b\u0131rak\u0131n.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: \u00e7\u00f6z\u00fclen mesafe (metre, santimetre, milimetre, in\u00e7 ve fit cinsine d\u00f6n\u00fc\u015ft\u00fcr\u00fclm\u00fc\u015f), mercek t\u00fcr\u00fc, g\u00f6r\u00fcnt\u00fcn\u00fcn ger\u00e7ek mi sanal m\u0131 oldu\u011fu, b\u00fcy\u00fctme, g\u00f6r\u00fcnt\u00fcn\u00fcn y\u00f6n\u00fc ve boyu.<\/li>\n<\/ol>\n<h2>\u0130nce mercek denklemi neyi anlat\u0131r<\/h2>\n<p>\u0130nce mercek denklemi, bir cismin konumunu, g\u00f6r\u00fcnt\u00fcs\u00fcn\u00fcn konumunu ve merce\u011fin odak uzakl\u0131\u011f\u0131n\u0131 birbirine ba\u011flar. Mercek, paralel \u0131\u015f\u0131nlar\u0131n ya bir noktada yak\u0131nsamas\u0131n\u0131 (\\(f &gt; 0\\) olan yak\u0131nsak, yani d\u0131\u015fb\u00fckey mercek) ya da bir noktadan \u0131raks\u0131yor g\u00f6r\u00fcnmesini (\\(f &lt; 0\\) olan \u0131raksak, yani i\u00e7b\u00fckey mercek) sa\u011flar. Odak uzakl\u0131\u011f\u0131, mercekten o noktaya olan mesafedir ve \u2014mercek, ilgili mesafelere k\u0131yasla ince oldu\u011fu s\u00fcrece\u2014 merce\u011fin cisimleri nas\u0131l g\u00f6r\u00fcnt\u00fcledi\u011fini tamamen belirler.<\/p>\n<p>\u0130\u015faret kural\u0131 \u00f6nemlidir. Merce\u011fin \u00f6n\u00fcndeki ger\u00e7ek bir cismin \\(d_o &gt; 0\\)'d\u0131r. Pozitif g\u00f6r\u00fcnt\u00fc mesafesi <strong>ger\u00e7ek g\u00f6r\u00fcnt\u00fc<\/strong> anlam\u0131na gelir: \u0131\u015f\u0131k merce\u011fin \u00f6b\u00fcr taraf\u0131nda ger\u00e7ekten yak\u0131nsar, dolay\u0131s\u0131yla g\u00f6r\u00fcnt\u00fcy\u00fc bir perde ya da sens\u00f6r \u00fczerinde yakalayabilirsiniz \u2014 foto\u011fraf makineleri ve projekt\u00f6rler b\u00f6yle \u00e7al\u0131\u015f\u0131r. Negatif g\u00f6r\u00fcnt\u00fc mesafesi <strong>sanal g\u00f6r\u00fcnt\u00fc<\/strong> anlam\u0131na gelir: \u0131\u015f\u0131nlar yaln\u0131zca merce\u011fin cisim taraf\u0131ndaki bir noktadan geliyor gibi g\u00f6r\u00fcn\u00fcr, bu y\u00fczden g\u00f6r\u00fcnt\u00fcy\u00fc g\u00f6rmek i\u00e7in merce\u011fin i\u00e7inden bakman\u0131z gerekir; b\u00fcy\u00fcte\u00e7 ve g\u00f6zl\u00fck camlar\u0131nda oldu\u011fu gibi.<\/p>\n<p>\\(m = -d_i\/d_o\\) b\u00fcy\u00fctmesi, g\u00f6r\u00fcnt\u00fcn\u00fcn cisimle kar\u015f\u0131la\u015ft\u0131rmas\u0131n\u0131 verir. Mutlak de\u011feri boy oran\u0131d\u0131r: \\(|m| = 2\\), g\u00f6r\u00fcnt\u00fcn\u00fcn iki kat uzun oldu\u011funu g\u00f6sterir. \u0130\u015faret y\u00f6n\u00fc verir: negatif \\(m\\) g\u00f6r\u00fcnt\u00fcn\u00fcn ters (ba\u015f a\u015fa\u011f\u0131), pozitif \\(m\\) dik oldu\u011fu anlam\u0131na gelir. Tek bir yak\u0131nsak merce\u011fin olu\u015fturdu\u011fu ger\u00e7ek g\u00f6r\u00fcnt\u00fcler ters, sanal g\u00f6r\u00fcnt\u00fcler diktir.<\/p>\n<p>Ak\u0131lda tutulmaya de\u011fer iki \u00f6zel durum vard\u0131r. Cisim tam odak noktas\u0131ndaysa (\\(d_o = f\\)), g\u00f6r\u00fcnt\u00fc sonsuzda olu\u015fur \u2014 bu, bir arama lambas\u0131n\u0131n ya da kolimat\u00f6r\u00fcn \u00e7al\u0131\u015fma ilkesidir. Cisim \u00e7ok uzaktaysa (\\(d_o \\to \\infty\\)), \\(d_i = f\\) olur: paralel gelen \u0131\u015f\u0131nlar odak noktas\u0131nda toplan\u0131r; foto\u011fraf makinesinin uzaktaki bir manzaray\u0131 sens\u00f6r \u00fczerine odaklamas\u0131 da b\u00f6yle olur.<\/p>\n<h2>\u0130\u015faret kurallar\u0131 bir bak\u0131\u015fta<\/h2>\n<table>\n<thead>\n<tr>\n<th>B\u00fcy\u00fckl\u00fck<\/th>\n<th>Pozitif<\/th>\n<th>Negatif<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Odak uzakl\u0131\u011f\u0131 \\(f\\)<\/td>\n<td>Yak\u0131nsak (d\u0131\u015fb\u00fckey) mercek<\/td>\n<td>Iraksak (i\u00e7b\u00fckey) mercek<\/td>\n<\/tr>\n<tr>\n<td>Cisim mesafesi \\(d_o\\)<\/td>\n<td>Merce\u011fin \u00f6n\u00fcnde ger\u00e7ek cisim<\/td>\n<td>Sanal cisim (nadir; \u00f6rn. mercek sistemlerinde)<\/td>\n<\/tr>\n<tr>\n<td>G\u00f6r\u00fcnt\u00fc mesafesi \\(d_i\\)<\/td>\n<td>Merce\u011fin arkas\u0131nda ger\u00e7ek g\u00f6r\u00fcnt\u00fc (perdeye d\u00fc\u015f\u00fcr\u00fclebilir)<\/td>\n<td>Cismin taraf\u0131nda sanal g\u00f6r\u00fcnt\u00fc<\/td>\n<\/tr>\n<tr>\n<td>B\u00fcy\u00fctme \\(m\\)<\/td>\n<td>Dik g\u00f6r\u00fcnt\u00fc<\/td>\n<td>Ters g\u00f6r\u00fcnt\u00fc<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Varsay\u0131mlar ve s\u0131n\u0131rlamalar<\/h2>\n<ul>\n<li><strong>\u0130nce mercek:<\/strong> mercek kal\u0131nl\u0131\u011f\u0131n\u0131n \\(d_o\\), \\(d_i\\) ve \\(f\\) ile kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda ihmal edilebilir oldu\u011fu varsay\u0131l\u0131r. Kal\u0131n mercekler veya mercek sistemleri i\u00e7in asal d\u00fczlemlerden \u00f6l\u00e7\u00fclen mesafeler k\u00fc\u00e7\u00fck d\u00fczeltmeler verir.<\/li>\n<li><strong>Paraksiyal \u0131\u015f\u0131nlar:<\/strong> denklem, optik eksene yak\u0131n ve k\u00fc\u00e7\u00fck a\u00e7\u0131larla gelen \u0131\u015f\u0131nlar i\u00e7in ge\u00e7erlidir. Geni\u015f a\u00e7\u0131kl\u0131kl\u0131 merceklerde, ger\u00e7ek oda\u011f\u0131 kayd\u0131ran aberasyonlar olu\u015fur.<\/li>\n<li><strong>Tek dalga boyu:<\/strong> odak uzakl\u0131\u011f\u0131 \u0131\u015f\u0131\u011f\u0131n rengine ba\u011fl\u0131 olarak hafif\u00e7e de\u011fi\u015fir (kromatik aberasyon); bu nedenle sonu\u00e7 yaln\u0131zca tek bir dalga boyu i\u00e7in tamd\u0131r.<\/li>\n<li>Hesaplay\u0131c\u0131 yukar\u0131daki standart i\u015faret kural\u0131n\u0131 varsayar. Ders kitab\u0131n\u0131z farkl\u0131 bir kural kullan\u0131yorsa, sonu\u00e7lar\u0131 kar\u015f\u0131la\u015ft\u0131rmadan \u00f6nce i\u015faretleri d\u00f6n\u00fc\u015ft\u00fcr\u00fcn.<\/li>\n<li>Mesafeler s\u0131f\u0131rdan farkl\u0131 olmal\u0131d\u0131r; \\(d_o = f\\), \\(d_i = f\\) veya \\(d_o = -d_i\\) gibi ayr\u0131k (dejener) durumlar sonsuzdaki g\u00f6r\u00fcnt\u00fclere veya cisimlere kar\u015f\u0131l\u0131k gelir ve hesaplay\u0131c\u0131 bunlar\u0131 a\u00e7\u0131klama g\u00f6stererek reddeder.<\/li>\n<\/ul>\n<h2>\u0130lgili hesaplay\u0131c\u0131lar<\/h2>\n<p>Daha fazla fizik arac\u0131 i\u00e7in hareket problemlerinde <a href=\"https:\/\/wpcalc.com\/tr\/fizik\/kinematik-denklemler-cozucu\/\">Kinematik Denklem \u00c7\u00f6z\u00fcc\u00fc<\/a>'y\u00fc, konum de\u011fi\u015fimlerinde <a href=\"https:\/\/wpcalc.com\/tr\/fizik\/yer-degistirme-hesaplayici\/\">Yer De\u011fi\u015ftirme Hesaplay\u0131c\u0131<\/a>'y\u0131, zamana ba\u011fl\u0131 enerji aktar\u0131m\u0131nda ise <a href=\"https:\/\/wpcalc.com\/tr\/fizik\/guc-hesaplama\/\">G\u00fc\u00e7 Hesaplay\u0131c\u0131<\/a>'y\u0131 deneyin.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1\/f = 1\/do + 1\/di ince mercek denklemini g\u00f6r\u00fcnt\u00fc mesafesi, cisim mesafesi veya odak uzakl\u0131\u011f\u0131 i\u00e7in \u00e7\u00f6z\u00fcn. Bilinen iki de\u011feri girin, \u00fc\u00e7\u00fcnc\u00fcs\u00fcn\u00fc ve ayr\u0131ca g\u00f6r\u00fcnt\u00fc t\u00fcr\u00fcn\u00fc, b\u00fcy\u00fctmeyi ve g\u00f6r\u00fcnt\u00fc boyunu \u00f6\u011frenin.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10],"tags":[55],"class_list":["post-781","post","type-post","status-publish","format-standard","hentry","category-fizik","tag-mekanik"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/781","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=781"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/781\/revisions"}],"predecessor-version":[{"id":3722,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/781\/revisions\/3722"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=781"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=781"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=781"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}