{"id":168644,"date":"2024-11-17T19:52:44","date_gmt":"2024-11-17T19:52:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168644"},"modified":"2024-11-17T19:52:46","modified_gmt":"2024-11-17T19:52:46","slug":"a-flower-is-placed-at-a-distance-of-7-0-cm-in-front-of-a-thin-lens","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/17\/a-flower-is-placed-at-a-distance-of-7-0-cm-in-front-of-a-thin-lens\/","title":{"rendered":"A flower is placed at a distance of 7.0 cm in front of a thin lens."},"content":{"rendered":"\n<p>A flower is placed at a distance of 7.0 cm in front of a thin lens. The image distance is 12 cm. What is the focal length of the lens? Group of answer choices 5.7 cm 3.6 cm 5.1 cm 4.4 cm<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine the focal length of the lens, we can use the <strong>lens formula<\/strong>:1f=1do+1di\\frac{1}{f} = \\frac{1}{d_o} + \\frac{1}{d_i}f1\u200b=do\u200b1\u200b+di\u200b1\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>fff is the focal length of the lens (the value we are trying to find),<\/li>\n\n\n\n<li>dod_odo\u200b is the object distance (distance from the object to the lens),<\/li>\n\n\n\n<li>did_idi\u200b is the image distance (distance from the image to the lens).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Understand the given information<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The object distance (dod_odo\u200b) is 7.0 cm.<\/li>\n\n\n\n<li>The image distance (did_idi\u200b) is 12 cm.\n<ul class=\"wp-block-list\">\n<li>Since the image is real (assuming the lens is converging), the image distance is positive.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Substitute the given values into the lens formula<\/h3>\n\n\n\n<p>Substitute do=7.0\u2009cmd_o = 7.0 \\, \\text{cm}do\u200b=7.0cm and di=12.0\u2009cmd_i = 12.0 \\, \\text{cm}di\u200b=12.0cm into the lens equation:1f=17.0+112.0\\frac{1}{f} = \\frac{1}{7.0} + \\frac{1}{12.0}f1\u200b=7.01\u200b+12.01\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the right side of the equation<\/h3>\n\n\n\n<p>First, calculate the reciprocal of the object distance:17.0=0.1429\\frac{1}{7.0} = 0.14297.01\u200b=0.1429<\/p>\n\n\n\n<p>Next, calculate the reciprocal of the image distance:112.0=0.0833\\frac{1}{12.0} = 0.083312.01\u200b=0.0833<\/p>\n\n\n\n<p>Now, sum the two values:0.1429+0.0833=0.22620.1429 + 0.0833 = 0.22620.1429+0.0833=0.2262<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve for fff<\/h3>\n\n\n\n<p>Now, solve for fff by taking the reciprocal of 0.2262:f=10.2262=4.42\u2009cmf = \\frac{1}{0.2262} = 4.42 \\, \\text{cm}f=0.22621\u200b=4.42cm<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Round the result<\/h3>\n\n\n\n<p>Rounding to one decimal place, the focal length is approximately <strong>4.4 cm<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The correct answer is <strong>4.4 cm<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The focal length of a lens is determined by the relationship between the object distance and image distance, as described by the lens formula. For a real image formed by a converging lens, the focal length can be found by adding the reciprocals of the object and image distances and then taking the reciprocal of the sum. In this case, after performing the calculations, we determined that the focal length of the lens is approximately 4.4 cm.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A flower is placed at a distance of 7.0 cm in front of a thin lens. The image distance is 12 cm. What is the focal length of the lens? Group of answer choices 5.7 cm 3.6 cm 5.1 cm 4.4 cm The Correct Answer and Explanation is: To determine the focal length of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-168644","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168644","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=168644"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168644\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168644"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168644"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168644"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}