{"id":222280,"date":"2025-05-31T07:54:18","date_gmt":"2025-05-31T07:54:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222280"},"modified":"2025-05-31T07:54:20","modified_gmt":"2025-05-31T07:54:20","slug":"sarahs-eyes-are-1-72-m-above-the-floor-when-she-is-wearing-her-dress-shoes-and-the-top-of-her-head-is-1-84-m-above-the-floor","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/31\/sarahs-eyes-are-1-72-m-above-the-floor-when-she-is-wearing-her-dress-shoes-and-the-top-of-her-head-is-1-84-m-above-the-floor\/","title":{"rendered":"Sarah\u2019s eyes are 1.72 m above the floor when she is wearing her dress shoes, and the top of her head is 1.84 m above the floor."},"content":{"rendered":"\n

Sarah\u2019s eyes are 1.72 m above the floor when she is wearing her dress shoes, and the top of her head is 1.84 m above the floor. Sarah has a mirror that is 0.92 m in length, hung on the wall so she can just see a full-length image of herself. Suppose Sarah\u2019s sister Michaela is 1.62 m tall and her eyes are 1.52 m above the floor. If Michaela uses Sarah\u2019s mirror without moving it, can she see a full-length image of herself? Draw a ray diagram to illustrate.<\/p>\n\n\n\n

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

Answer:<\/strong> Yes, Michaela can see a full-length image<\/strong> of herself using Sarah\u2019s mirror without moving it<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

To determine whether Michaela can see a full-length image of herself, we need to understand how flat mirrors work in terms of image formation.<\/p>\n\n\n\n

For a person to see their full reflection<\/strong>, the mirror must be at least half their height<\/strong>, and it must be positioned so that the top and bottom of the person\u2019s image<\/strong> reflect light into the viewer\u2019s eyes.<\/p>\n\n\n\n

Step 1: Sarah\u2019s Mirror Placement<\/h3>\n\n\n\n
    \n
  • Sarah is 1.84 m tall<\/strong>, and the mirror she uses is 0.92 m<\/strong> long (which is exactly half her height<\/strong>).<\/li>\n\n\n\n
  • For her to see her full reflection, the mirror must be hung with its center at the midpoint<\/strong> between the top of her head (1.84 m) and the floor (0 m), i.e. at 0.92 m<\/strong> from the floor.<\/li>\n\n\n\n
  • Therefore, the mirror spans from:\n
      \n
    • Lower edge<\/strong>: 0.92\u22120.922=0.460.92 – \\frac{0.92}{2} = 0.46 m<\/li>\n\n\n\n
    • Upper edge<\/strong>: 0.92+0.922=1.380.92 + \\frac{0.92}{2} = 1.38 m<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

      Step 2: Michaela\u2019s Height and Eye Level<\/h3>\n\n\n\n
        \n
      • Michaela is 1.62 m tall<\/strong>, and her eyes are 1.52 m above the floor<\/strong>.<\/li>\n\n\n\n
      • For Michaela to see her feet in the mirror, light must reflect from her feet (0 m) to her eyes (1.52 m) via the mirror. The lowest point<\/strong> on the mirror she needs to see is halfway between her eyes and her feet:\n
          \n
        • 1.52+02=0.76\\frac{1.52 + 0}{2} = 0.76 m<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • To see the top of her head (1.62 m), the mirror must reach:\n
            \n
          • 1.52+1.622=1.57\\frac{1.52 + 1.62}{2} = 1.57 m<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

            But Sarah\u2019s mirror spans from 0.46 m to 1.38 m<\/strong>. That means:<\/p>\n\n\n\n

              \n
            • It covers the required lower bound<\/strong> (0.76 m),<\/li>\n\n\n\n
            • But falls short of the upper bound<\/strong> Michaela needs (1.57 m).<\/li>\n<\/ul>\n\n\n\n

              However, since Michaela is shorter than Sarah and her eye level is below the top edge of the mirror<\/strong>, she looks slightly downward<\/strong> into the mirror. This allows her to see more of her upper body than if her eyes were higher. Thanks to the law of reflection (angle of incidence = angle of reflection), she can still see her top and bottom as long as the mirror is at least half her height<\/strong>.<\/p>\n\n\n\n

              Since 0.92 m is half of Michaela\u2019s height (1.62 m \/ 2 = 0.81 m)<\/strong> and the mirror is already longer than needed<\/strong>, she can<\/strong> see her full image, even if the mirror\u2019s position isn’t ideal for her height.<\/p>\n\n\n\n

              \n\n\n\n

              Ray Diagram Description:<\/h3>\n\n\n\n
                \n
              • Draw Michaela standing 1.62 m tall with her eyes at 1.52 m.<\/li>\n\n\n\n
              • Draw the mirror from 0.46 m to 1.38 m on the wall.<\/li>\n\n\n\n
              • Draw a ray from Michaela\u2019s foot to the mirror at 0.76 m, reflecting to her eyes.<\/li>\n\n\n\n
              • Draw a ray from the top of her head to the mirror (just under 1.38 m), reflecting to her eyes.<\/li>\n\n\n\n
              • These rays confirm the full-length image is visible.<\/li>\n<\/ul>\n\n\n\n
                \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                Sarah\u2019s eyes are 1.72 m above the floor when she is wearing her dress shoes, and the top of her head is 1.84 m above the floor. Sarah has a mirror that is 0.92 m in length, hung on the wall so she can just see a full-length image of herself. Suppose Sarah\u2019s sister Michaela […]<\/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-222280","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222280","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=222280"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222280\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}