{"id":218406,"date":"2025-05-23T18:02:32","date_gmt":"2025-05-23T18:02:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218406"},"modified":"2025-05-23T18:02:34","modified_gmt":"2025-05-23T18:02:34","slug":"a-concave-mirror-forms-a-real-image-at-35-2-cm-from-the-mirror-surface-along-the-principal-axis","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/23\/a-concave-mirror-forms-a-real-image-at-35-2-cm-from-the-mirror-surface-along-the-principal-axis\/","title":{"rendered":"A concave mirror forms a real image at 35.2 cm from the mirror surface along the principal axis."},"content":{"rendered":"\n

A concave mirror forms a real image at 35.2 cm from the mirror surface along the principal axis. If the corresponding object is at a 12.6-cm distance, what is the mirror\u2019s focal length?<\/p>\n\n\n\n

<\/td>a.<\/td>19.6 cm<\/td><\/tr>
<\/td>b.<\/td>22.6 cm<\/td><\/tr>
<\/td>c.<\/td>10.8 cm<\/td><\/tr>
<\/td>d.<\/td>47.8 cm<\/td><\/tr>
<\/td>e.<\/td>9.28 cm<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s analyze the problem carefully:<\/p>\n\n\n\n

\n\n\n\n

Given:<\/h3>\n\n\n\n
    \n
  • Image distance $v = +35.2 \\text{ cm}$ (Since the image is real and formed by a concave mirror, $v$ is positive)<\/li>\n\n\n\n
  • Object distance $u = -12.6 \\text{ cm}$ (For mirrors, the object distance is taken as negative if the object is in front of the mirror)<\/li>\n\n\n\n
  • Find: Focal length $f$<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Step 1: Use the mirror formula:<\/h3>\n\n\n\n

    $$
    \\frac{1}{f} = \\frac{1}{u} + \\frac{1}{v}
    $$<\/p>\n\n\n\n

    \n\n\n\n

    Step 2: Substitute values<\/h3>\n\n\n\n

    $$
    \\frac{1}{f} = \\frac{1}{-12.6} + \\frac{1}{35.2}
    $$<\/p>\n\n\n\n

    Calculate each term:<\/p>\n\n\n\n

    $$
    \\frac{1}{-12.6} \\approx -0.07937
    $$<\/p>\n\n\n\n

    $$
    \\frac{1}{35.2} \\approx 0.02841
    $$<\/p>\n\n\n\n

    Add them:<\/p>\n\n\n\n

    $$
    \\frac{1}{f} = -0.07937 + 0.02841 = -0.05096
    $$<\/p>\n\n\n\n

    \n\n\n\n

    Step 3: Calculate $f$<\/h3>\n\n\n\n

    $$
    f = \\frac{1}{-0.05096} \\approx -19.63 \\text{ cm}
    $$<\/p>\n\n\n\n

    Since the focal length is negative, it confirms the mirror is concave.<\/p>\n\n\n\n

    \n\n\n\n

    Step 4: Match with options<\/h3>\n\n\n\n

    The magnitude is approximately 19.6 cm<\/strong> (taking absolute value as focal length magnitude).<\/p>\n\n\n\n

    \n\n\n\n

    Answer: (a) 19.6 cm<\/strong><\/h3>\n\n\n\n
    \n\n\n\n

    Explanation:<\/h3>\n\n\n\n

    A concave mirror forms real images when the object is placed outside the focal length. The real image distance $v$ is positive, and the object distance $u$ is negative by the sign convention (object in front of the mirror). Using the mirror formula, we calculate the focal length $f$.<\/p>\n\n\n\n

    Here, the real image is formed 35.2 cm in front of the mirror (positive $v$), and the object is 12.6 cm in front of the mirror (negative $u$). The negative result of $f$ (-19.6 cm) indicates a concave mirror, which aligns with the scenario described.<\/p>\n\n\n\n

    The focal length is the distance from the mirror where parallel rays converge after reflection. It helps determine the nature and position of the images formed by the mirror. This value (19.6 cm) is consistent with the mirror’s geometry and the image formation conditions given.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    A concave mirror forms a real image at 35.2 cm from the mirror surface along the principal axis. If the corresponding object is at a 12.6-cm distance, what is the mirror\u2019s focal length? a. 19.6 cm b. 22.6 cm c. 10.8 cm d. 47.8 cm e. 9.28 cm The Correct Answer and Explanation is: Let’s […]<\/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-218406","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218406","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=218406"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218406\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218406"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218406"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}