{"id":152094,"date":"2024-10-10T17:50:43","date_gmt":"2024-10-10T17:50:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=152094"},"modified":"2024-10-10T17:50:45","modified_gmt":"2024-10-10T17:50:45","slug":"an-object-is-located-20-0-cm-from-a-convex-lens","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/10\/an-object-is-located-20-0-cm-from-a-convex-lens\/","title":{"rendered":"An object is located 20.0 cm from a convex lens."},"content":{"rendered":"\n<p>An object is located 20.0 cm from a convex lens. The lens focuses light at a<br>distance of 10.0 cm. What is the image distance?<\/p>\n\n\n\n<p>A. 6.67 cm<br>B. -6.67 cm<br>C. -20.0 cm<br>D. 20.0 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 solve this problem, we need to use the <strong>lens equation<\/strong>:<\/p>\n\n\n\n<p>[<br>\\frac{1}{f} = \\frac{1}{d_o} + \\frac{1}{d_i}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( f ) is the focal length of the lens,<\/li>\n\n\n\n<li>( d_o ) is the object distance (distance from the object to the lens),<\/li>\n\n\n\n<li>( d_i ) is the image distance (distance from the image to the lens).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( d_o = 20.0 \\, \\text{cm} ) (object distance),<\/li>\n\n\n\n<li>( f = 10.0 \\, \\text{cm} ) (focal length).<\/li>\n<\/ul>\n\n\n\n<p>We need to find the image distance ( d_i ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Rearrange the lens equation to solve for ( d_i ):<\/h3>\n\n\n\n<p>[<br>\\frac{1}{d_i} = \\frac{1}{f} &#8211; \\frac{1}{d_o}<br>]<\/p>\n\n\n\n<p>Substitute the given values into the equation:<\/p>\n\n\n\n<p>[<br>\\frac{1}{d_i} = \\frac{1}{10.0} &#8211; \\frac{1}{20.0}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate:<\/h3>\n\n\n\n<p>[<br>\\frac{1}{d_i} = 0.1 &#8211; 0.05 = 0.05<br>]<\/p>\n\n\n\n<p>Thus:<\/p>\n\n\n\n<p>[<br>d_i = \\frac{1}{0.05} = 20.0 \\, \\text{cm}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Interpretation of the Image Distance:<\/h3>\n\n\n\n<p>Since the value of ( d_i ) is <strong>positive<\/strong>, the image is real and formed on the opposite side of the lens from the object. For a convex lens, a positive image distance indicates a real image, which is inverted. The object is located outside the focal point (20.0 cm is greater than the focal length of 10.0 cm), so the lens forms a real image.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The correct answer is <strong>D. 20.0 cm<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This problem demonstrates how convex lenses (also known as converging lenses) focus light. Convex lenses cause parallel rays of light to converge to a focal point. When the object is located outside the focal point of the lens, the image formed is real, inverted, and on the opposite side of the lens. The focal length ( f ) is positive for convex lenses, and this equation is a fundamental part of geometric optics. Understanding the relationship between object distance, image distance, and focal length helps in analyzing how lenses work in various optical devices such as cameras, glasses, and microscopes.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An object is located 20.0 cm from a convex lens. The lens focuses light at adistance of 10.0 cm. What is the image distance? A. 6.67 cmB. -6.67 cmC. -20.0 cmD. 20.0 cm The correct Answer and Explanation is: To solve this problem, we need to use the lens equation: [\\frac{1}{f} = \\frac{1}{d_o} + \\frac{1}{d_i}] [&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-152094","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152094","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=152094"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152094\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152094"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152094"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152094"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}