A farsighted person has a near point located 210 cm from the eyes. Find the focal length of the converging lenses in a pair of contacts that can be used to read a book held 25 cm from the eyes.<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the focal length of the converging lens needed for a farsighted person to read a book at 25 cm, we use the lens formula<\/strong>:<\/p>\n\n\n\n [ where:<\/p>\n\n\n\n Since distances should be in meters for standard SI units: [ [ A farsighted person has difficulty seeing nearby objects because their near point is farther than normal (typically 25 cm for a young person). This means their eye’s lens cannot converge light strongly enough to focus images of close objects onto the retina. A converging (convex) lens<\/strong> helps by pre-converging the light rays<\/strong> before they enter the eye, allowing the image to form at the person’s near point (210 cm) instead of at 25 cm.<\/p>\n\n\n\n The focal length of the lens is +28.4 cm<\/strong>, meaning it is a convex lens<\/strong> with a positive focal length. This corrective lens shifts the focus, enabling the person to read a book at 25 cm comfortably.<\/p>\n","protected":false},"excerpt":{"rendered":" A farsighted person has a near point located 210 cm from the eyes. Find the focal length of the converging lenses in a pair of contacts that can be used to read a book held 25 cm from the eyes. The correct answer and explanation is : To find the focal length of the converging […]<\/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-204836","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204836","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=204836"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204836\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=204836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=204836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=204836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\frac{1}{f} = \\frac{1}{d_o} + \\frac{1}{d_i}
]<\/p>\n\n\n\n\n
Step 1: Convert to meters<\/h3>\n\n\n\n
[
d_o = 25 \\text{ cm} = 0.25 \\text{ m}, \\quad d_i = 210 \\text{ cm} = 2.10 \\text{ m}
]<\/p>\n\n\n\nStep 2: Apply the Lens Formula<\/h3>\n\n\n\n
\\frac{1}{f} = \\frac{1}{0.25} + \\frac{1}{-2.10}
]
[
\\frac{1}{f} = 4 – 0.476
]
[
\\frac{1}{f} = 3.524
]<\/p>\n\n\n\nStep 3: Solve for ( f )<\/h3>\n\n\n\n
f = \\frac{1}{3.524} \\approx 0.284 \\text{ m} = 28.4 \\text{ cm}
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n