{"id":531,"date":"2026-10-03T14:34:02","date_gmt":"2026-10-03T13:34:02","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/buyutme-hesaplayici\/"},"modified":"2026-10-03T14:34:02","modified_gmt":"2026-10-03T13:34:02","slug":"buyutme-hesaplayici","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/fizik\/buyutme-hesaplayici\/","title":{"rendered":"B\u00fcy\u00fctme 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\">Lens veya Aynan\u0131n B\u00fcy\u00fctmesini Bulun<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"531\" data-favorite-title=\"B\u00fcy\u00fctme\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/fizik\/buyutme-hesaplayici\/\" data-favorite-excerpt=\"Cisim ve g\u00f6r\u00fcnt\u00fc y\u00fcksekliklerini ya da bir merce\u011fe veya aynaya olan uzakl\u0131klar\u0131n\u0131 girerek do\u011frusal b\u00fcy\u00fctmeyi, g\u00f6r\u00fcnt\u00fc boyutunu ve g\u00f6r\u00fcnt\u00fcn\u00fcn d\u00fcz m\u00fc ters mi oldu\u011funu \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\/buyutme-hesaplayici\/\" method=\"POST\" class=\"calculator\" id=\"calculator-531\" data-post=\"531\"><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\">Hesaplama modu<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"hesaplama_modu\"><option value=\"height\" selected>Nesne ve g\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fi<\/option><option value=\"distance\">Nesne ve g\u00f6r\u00fcnt\u00fc uzakl\u0131\u011f\u0131<\/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\">Nesne y\u00fcksekli\u011fi (h)<\/label><div class=\"term\">h<\/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=\"nesne_ykseklii_h\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0\" value=\"5\"\/><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\">Nesnenin y\u00fcksekli\u011fi. Y\u00fckseklik modunda do\u011frudan kullan\u0131l\u0131r; uzakl\u0131k modunda iste\u011fe ba\u011fl\u0131d\u0131r ve hesaplay\u0131c\u0131n\u0131n g\u00f6r\u00fcnt\u00fc boyutunu bulmas\u0131n\u0131 sa\u011flar.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-3\" hidden><label for=\"field-4\">G\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fi (h\u2032)<\/label><div class=\"term\">h\u2032<\/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_ykseklii_h\" id=\"field-4\" aria-describedby=\"calc-info-4\" placeholder=\"e.g. -10\" step=\"any\" value=\"-10\"\/><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\">G\u00f6r\u00fcnt\u00fcn\u00fcn y\u00fcksekli\u011fi. Negatif de\u011fer, g\u00f6r\u00fcnt\u00fcn\u00fcn ters (ba\u015f a\u015fa\u011f\u0131) oldu\u011funu g\u00f6sterir.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-4\" hidden><label for=\"field-6\">Nesne uzakl\u0131\u011f\u0131 (u)<\/label><div class=\"term\">u<\/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=\"nesne_uzakl_u\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 20\" min=\"0\" value=\"20\"\/><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\">Lens veya aynadan nesneye olan uzakl\u0131k. Ger\u00e7ek bir nesne i\u00e7in pozitif olmal\u0131d\u0131r.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-5\" hidden><label for=\"field-8\">G\u00f6r\u00fcnt\u00fc uzakl\u0131\u011f\u0131 (v)<\/label><div class=\"term\">v<\/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_v\" id=\"field-8\" aria-describedby=\"calc-info-8\" placeholder=\"e.g. 40\" step=\"any\" value=\"40\"\/><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\">Lens veya aynadan g\u00f6r\u00fcnt\u00fcye olan uzakl\u0131k. Ger\u00e7ek g\u00f6r\u00fcnt\u00fc i\u00e7in pozitif (lensin kar\u015f\u0131 taraf\u0131nda, aynan\u0131n \u00f6n\u00fcnde), sanal g\u00f6r\u00fcnt\u00fc i\u00e7in negatiftir.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"531\">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> B\u00fcy\u00fctme Sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Do\u011frusal b\u00fcy\u00fctme (m)<\/span><span class=\"result-term\">m<\/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 boyutu ve do\u011fas\u0131<\/span><span class=\"result-term\">h\u2032<\/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=\"531\" 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>B\u00fcy\u00fctme 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\">\n\\[ m = \\frac{h'}{h} = -\\frac{v}{u} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(m\\) \u2014 do\u011frusal (enine) b\u00fcy\u00fctme, birimsiz bir say\u0131<\/li>\n<li>\\(h'\\) \u2014 g\u00f6r\u00fcnt\u00fcn\u00fcn y\u00fcksekli\u011fi; negatif de\u011fer, g\u00f6r\u00fcnt\u00fcn\u00fcn ters oldu\u011funu g\u00f6sterir<\/li>\n<li>\\(h\\) \u2014 cismin y\u00fcksekli\u011fi (ger\u00e7ek bir cisim i\u00e7in her zaman pozitiftir)<\/li>\n<li>\\(v\\) \u2014 g\u00f6r\u00fcnt\u00fcn\u00fcn merce\u011fe veya aynaya olan uzakl\u0131\u011f\u0131; ger\u00e7ek g\u00f6r\u00fcnt\u00fc i\u00e7in pozitif, sanal g\u00f6r\u00fcnt\u00fc i\u00e7in negatiftir<\/li>\n<li>\\(u\\) \u2014 cismin merce\u011fe veya aynaya olan uzakl\u0131\u011f\u0131; ger\u00e7ek bir cisim i\u00e7in pozitiftir<\/li>\n<\/ul>\n<p>Form\u00fcl, cisim, g\u00f6r\u00fcnt\u00fc ve optik merkezden (ya da aynan\u0131n tepe noktas\u0131ndan) ge\u00e7en \u0131\u015f\u0131nlar\u0131n olu\u015fturdu\u011fu benzer \u00fc\u00e7genlerin, y\u00fckseklikler oran\u0131n\u0131 uzakl\u0131klar oran\u0131na e\u015fit k\u0131ld\u0131\u011f\u0131n\u0131 ifade eder. \\(m = -v\/u\\) ifadesindeki eksi i\u015fareti ger\u00e7ek-pozitif i\u015faret kural\u0131na uyar ve ger\u00e7ek, ters bir g\u00f6r\u00fcnt\u00fc i\u00e7in b\u00fcy\u00fctmeyi otomatik olarak negatif yapar.<\/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>B\u00fcy\u00fctme \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> yak\u0131nsak bir merce\u011fin \u00f6n\u00fcnde duran 5 cm y\u00fcksekli\u011findeki cisim, 10 cm y\u00fcksekli\u011finde ters bir g\u00f6r\u00fcnt\u00fc olu\u015fturuyor (ba\u015f a\u015fa\u011f\u0131 oldu\u011fu i\u00e7in g\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fi negatif olarak girilir).<\/p>\n<p>\\[ m = \\frac{h'}{h} = \\frac{-10 \\text{ cm}}{5 \\text{ cm}} = -2 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(m = -2\\). G\u00f6r\u00fcnt\u00fc terstir ve cismin iki kat\u0131 y\u00fcksekliktedir (boyutunun %200'\u00fc), yani 10 cm y\u00fcksekli\u011findedir. B\u00fcy\u00fctme negatif oldu\u011fu ve bu tek bir ince mercek oldu\u011fu i\u00e7in g\u00f6r\u00fcnt\u00fc ayn\u0131 zamanda ger\u00e7ektir.<\/p>\n<p><strong>Uzakl\u0131klarla do\u011frulama:<\/strong> ayn\u0131 d\u00fczenek, 20 cm cisim uzakl\u0131\u011f\u0131 ve 40 cm g\u00f6r\u00fcnt\u00fc uzakl\u0131\u011f\u0131 verir (ger\u00e7ek g\u00f6r\u00fcnt\u00fc, dolay\u0131s\u0131yla \\(v &gt; 0\\)):<\/p>\n<p>\\[ m = -\\frac{v}{u} = -\\frac{40 \\text{ cm}}{20 \\text{ cm}} = -2 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> her iki y\u00f6ntem de ayn\u0131 sonucu verir: \\(m = -2\\), g\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fi \\(h' = m \\cdot h = -2 \\times 5\\text{ cm} = -10\\text{ cm}\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>B\u00fcy\u00fctme Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Hesaplama modu<\/strong> a\u00e7\u0131l\u0131r men\u00fcs\u00fcn\u00fc a\u00e7\u0131n ve hangi de\u011fer \u00e7iftini biliyorsan\u0131z ona g\u00f6re <em>Cisim ve g\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fi<\/em> ya da <em>Cisim ve g\u00f6r\u00fcnt\u00fc uzakl\u0131\u011f\u0131<\/em> se\u00e7ene\u011fini belirleyin.<\/li>\n<li>Y\u00fckseklik modunda, <strong>Cisim y\u00fcksekli\u011fini (h)<\/strong> ve <strong>G\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fini (h\u2032)<\/strong> birimleriyle birlikte girin. G\u00f6r\u00fcnt\u00fc ters ise g\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fini negatif say\u0131 olarak yaz\u0131n.<\/li>\n<li>Uzakl\u0131k modunda, <strong>Cisim uzakl\u0131\u011f\u0131n\u0131 (u)<\/strong> ve <strong>G\u00f6r\u00fcnt\u00fc uzakl\u0131\u011f\u0131n\u0131 (v)<\/strong> girin. Ger\u00e7ek g\u00f6r\u00fcnt\u00fc i\u00e7in \\(v\\) pozitif, sanal g\u00f6r\u00fcnt\u00fc i\u00e7in negatif olsun. \u0130sterseniz cisim y\u00fcksekli\u011fini de doldurun; b\u00f6ylece hesaplay\u0131c\u0131 g\u00f6r\u00fcnt\u00fc boyutunu da bildirir.<\/li>\n<li><strong>B\u00fcy\u00fctme Sonu\u00e7lar\u0131<\/strong> b\u00f6l\u00fcm\u00fcn\u00fc okuyun: i\u015faretli b\u00fcy\u00fctme \\(m\\), mutlak de\u011feri \\(|m|\\), g\u00f6r\u00fcnt\u00fc boyutunun cisme y\u00fczde olarak oran\u0131 ve \u2014 cisim y\u00fcksekli\u011fi verildi\u011finde \u2014 g\u00f6r\u00fcnt\u00fc y\u00fcksekli\u011fi \u00e7e\u015fitli birimlerle.<\/li>\n<\/ol>\n<h2>B\u00fcy\u00fctme Nedir?<\/h2>\n<p>B\u00fcy\u00fctme, bir g\u00f6r\u00fcnt\u00fcn\u00fcn onu olu\u015fturan cisme g\u00f6re ne kadar b\u00fcy\u00fck veya k\u00fc\u00e7\u00fck oldu\u011funu ve hangi y\u00f6nde g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc s\u00f6yler. Do\u011frusal (enine) b\u00fcy\u00fctme \\(m\\) bir y\u00fckseklikler oran\u0131 oldu\u011fundan birimi yoktur: \\(m = 3\\), g\u00f6r\u00fcnt\u00fcn\u00fcn cismin \u00fc\u00e7 kat\u0131 y\u00fckseklikte oldu\u011fu; \\(m = 0.5\\) ise yar\u0131s\u0131 kadar oldu\u011fu anlam\u0131na gelir.<\/p>\n<p>\u0130\u015faret y\u00f6n bilgisini ta\u015f\u0131r. Negatif \\(m\\), g\u00f6r\u00fcnt\u00fcn\u00fcn ters (ba\u015f a\u015fa\u011f\u0131) oldu\u011fu; pozitif \\(m\\), d\u00fcz oldu\u011fu anlam\u0131na gelir. Tek bir ince mercek veya ayna i\u00e7in bu i\u015faret g\u00f6r\u00fcnt\u00fcn\u00fcn t\u00fcr\u00fcn\u00fc de s\u00f6yler: ters g\u00f6r\u00fcnt\u00fc ger\u00e7ektir \u2014 bir perdeye yans\u0131t\u0131labilir \u2014; d\u00fcz g\u00f6r\u00fcnt\u00fc ise sanald\u0131r ve yaln\u0131zca merce\u011fe bakarak veya aynan\u0131n i\u00e7ine bakarak g\u00f6r\u00fclebilir.<\/p>\n<p>Form\u00fcl\u00fcn birbirine e\u015f iki bi\u00e7imi geometriden gelir. Cismin tepesinden merce\u011fin optik merkezinden ge\u00e7en (veya bir aynadan yans\u0131yan) \u0131\u015f\u0131nlar iki benzer \u00fc\u00e7gen olu\u015fturur; dolay\u0131s\u0131yla y\u00fckseklikler oran\u0131 uzakl\u0131klar oran\u0131na e\u015fittir: \\(h'\/h = -v\/u\\). Eksi i\u015fareti, merce\u011fin kar\u015f\u0131 taraf\u0131nda (veya aynan\u0131n \u00f6n\u00fcnde) yer alan ger\u00e7ek g\u00f6r\u00fcnt\u00fcn\u00fcn cisme g\u00f6re ters olmas\u0131ndan kaynaklan\u0131r.<\/p>\n<p>Pratikte b\u00fcy\u00fctme, opti\u011fin yer ald\u0131\u011f\u0131 her alanda \u00f6nemlidir: bir mikroskobun veya teleskobun objektifini se\u00e7erken, bir projeksiyon cihaz\u0131 tasarlarken, bir b\u00fcy\u00fctecin boyutunu belirlerken veya bir foto\u011fraf makinesi merce\u011finin olu\u015fturdu\u011fu g\u00f6r\u00fcnt\u00fcy\u00fc denetlerken. G\u00f6r\u00fcnt\u00fc uzakl\u0131\u011f\u0131yla birlikte kullan\u0131ld\u0131\u011f\u0131nda, yaln\u0131zca cismin boyutundan sens\u00f6r veya perdedeki g\u00f6r\u00fcnt\u00fcn\u00fcn boyutunu da \u00f6ng\u00f6rmenizi sa\u011flar.<\/p>\n<h2>Sonucun Yorumlanmas\u0131<\/h2>\n<table>\n<thead>\n<tr>\n<th>B\u00fcy\u00fctme<\/th>\n<th>G\u00f6r\u00fcnt\u00fc boyutu<\/th>\n<th>Y\u00f6n<\/th>\n<th>T\u00fcr (tek mercek\/ayna)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\\(|m| &lt; 1\\)<\/td>\n<td>K\u00fc\u00e7\u00fclm\u00fc\u015f (cisimden k\u00fc\u00e7\u00fck)<\/td>\n<td>\u0130\u015farete ba\u011fl\u0131<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td>\\(|m| = 1\\)<\/td>\n<td>Cisimle ayn\u0131 boyutta<\/td>\n<td>\u0130\u015farete ba\u011fl\u0131<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td>\\(|m| &gt; 1\\)<\/td>\n<td>B\u00fcy\u00fct\u00fclm\u00fc\u015f (cisimden b\u00fcy\u00fck)<\/td>\n<td>\u0130\u015farete ba\u011fl\u0131<\/td>\n<td>\u2014<\/td>\n<\/tr>\n<tr>\n<td>\\(m &lt; 0\\)<\/td>\n<td>\u2014<\/td>\n<td>Ters<\/td>\n<td>Ger\u00e7ek<\/td>\n<\/tr>\n<tr>\n<td>\\(m &gt; 0\\)<\/td>\n<td>\u2014<\/td>\n<td>D\u00fcz<\/td>\n<td>Sanal<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Varsay\u0131mlar, S\u0131n\u0131rlamalar ve \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li>Form\u00fcller, paraksiyal (k\u00fc\u00e7\u00fck a\u00e7\u0131) yakla\u015f\u0131m\u0131 alt\u0131nda <strong>tek bir ince mercek veya k\u00fcresel ayna<\/strong> i\u00e7in ge\u00e7erlidir. Kal\u0131n mercekler, bile\u015fik sistemler ve geni\u015f a\u00e7\u0131l\u0131 \u0131\u015f\u0131nlar, basit oran\u0131n yakalayamad\u0131\u011f\u0131 sapmalar olu\u015fturur.<\/li>\n<li>Bu hesaplay\u0131c\u0131 <strong>ger\u00e7ek-pozitif i\u015faret kural\u0131n\u0131<\/strong> kullan\u0131r: ger\u00e7ek cisimler ve ger\u00e7ek g\u00f6r\u00fcnt\u00fcler pozitif uzakl\u0131k al\u0131r. Baz\u0131 ders kitaplar\u0131 Kartezyen kural\u0131 kullan\u0131r; orada form\u00fcl \\(m = -v\/u\\) yerine \\(m = v\/u\\) bi\u00e7imindedir \u2014 yan\u0131tlar\u0131 kar\u015f\u0131la\u015ft\u0131rmadan \u00f6nce kursunuzun hangi kural\u0131 kulland\u0131\u011f\u0131n\u0131 kontrol edin.<\/li>\n<li>Y\u00fckseklik modunda g\u00f6r\u00fcnt\u00fcn\u00fcn ger\u00e7ek mi sanal m\u0131 oldu\u011fu yaln\u0131zca y\u00fcksekliklerden kararla\u015ft\u0131r\u0131lamaz; hesaplay\u0131c\u0131 ola\u011fan kural\u0131 belirtir (tek eleman i\u00e7in ters \u2192 ger\u00e7ek, d\u00fcz \u2192 sanal), ancak \u00e7ok mercekli sistemler bu kural\u0131 bozabilir.<\/li>\n<li>Burada hesaplanan <strong>do\u011frusal b\u00fcy\u00fctme<\/strong>, mikroskop ve teleskoplar i\u00e7in verilen <em>a\u00e7\u0131sal<\/em> b\u00fcy\u00fctmeden farkl\u0131d\u0131r; a\u00e7\u0131sal b\u00fcy\u00fctme y\u00fckseklikleri de\u011fil bak\u0131\u015f a\u00e7\u0131lar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131r\u0131r.<\/li>\n<li>Birimleri tutarl\u0131 tutun: hesaplay\u0131c\u0131 her girdiyi se\u00e7ilen birimden d\u00f6n\u00fc\u015ft\u00fcr\u00fcr; dolay\u0131s\u0131yla kar\u0131\u015f\u0131k birimler (\u00f6r. cisim cm, g\u00f6r\u00fcnt\u00fc in\u00e7) do\u011fru \u015fekilde i\u015flenir.<\/li>\n<\/ul>\n<p>Daha fazla fizik arac\u0131 i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/fizik\/kinematik-denklemler-cozucu\/\">Kinematik Denklemler \u00c7\u00f6z\u00fcc\u00fcs\u00fc<\/a> veya <a href=\"https:\/\/wpcalc.com\/tr\/fizik\/enerji-korunumu-hesaplayici\/\">Enerji Korunumu Hesaplay\u0131c\u0131s\u0131<\/a>'n\u0131 deneyin.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cisim ve g\u00f6r\u00fcnt\u00fc y\u00fcksekliklerini ya da bir merce\u011fe veya aynaya olan uzakl\u0131klar\u0131n\u0131 girerek do\u011frusal b\u00fcy\u00fctmeyi, g\u00f6r\u00fcnt\u00fc boyutunu ve g\u00f6r\u00fcnt\u00fcn\u00fcn d\u00fcz m\u00fc ters mi oldu\u011funu \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-531","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\/531","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=531"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/531\/revisions"}],"predecessor-version":[{"id":3624,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/531\/revisions\/3624"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=531"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=531"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}