{"id":337189,"date":"2023-01-06T09:43:14","date_gmt":"2023-01-06T04:13:14","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/5the-near-point-of-a-hypermetropic-eye-is-1-m-what-is-the-power-of-the-lens-required-to-correct-this-defect-assume-that-the-near-point-of-the-normal-eye-is-25-cm\/"},"modified":"2025-06-26T17:53:18","modified_gmt":"2025-06-26T12:23:18","slug":"5the-near-point-of-a-hypermetropic-eye-is-1-m-what-is-the-power-of-the-lens-required-to-correct-this-defect-assume-that-the-near-point-of-the-normal-eye-is-25-cm","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/5the-near-point-of-a-hypermetropic-eye-is-1m-what-is-the\/","title":{"rendered":"[5]The near point of a hypermetropic eye is 1\u00a0m. What is the power of the lens required to correct this defect? (Assume that the near point of the normal eye is 25\u00a0cm.)"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"[5]The near point of a hypermetropic eye is 1\u00a0m. What is the power of the lens required to correct this defect? (Assume that the near point of the normal eye is 25\u00a0cm.)","custom_permalink":"question\/physics\/5the-near-point-of-a-hypermetropic-eye-is-1m-what-is-the\/"},"categories":[],"acf":{"question":"[5]<\/span><\/a>

The near point of a hypermetropic eye is <\/span>1<\/mn> m<\/mi><\/math>. What is the power of the lens required to correct this defect? (Assume that the near point of the normal eye is <\/span>25<\/mn> cm<\/mi><\/math>.)<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt\">","options":[{"option":"+<\/mo>1<\/mn> D<\/mi><\/math>","correct":false},{"option":"+<\/mo>2<\/mn> D<\/mi><\/math>","correct":false},{"option":"+<\/mo>3<\/mn> D<\/mi><\/math>","correct":true},{"option":"+<\/mo>4<\/mn> D<\/mi><\/math> <\/span>","correct":false}],"solution":"The near point of a hypermetropic eye is <\/span>1<\/mn> m<\/mi><\/math>. The power of the lens required to correct this defect is <\/span>+<\/mo>3<\/mn> D<\/mi><\/math>.<\/span>
To correct this defect, the image of an object<\/span>  <\/span>25<\/mn> cm<\/mi><\/math> should be brought to <\/span>100<\/mn> cm<\/mi><\/math>.<\/span>
Substituting in lens formula, <\/span>1<\/mn><\/mrow>f<\/mi><\/mrow><\/mfrac>=<\/mo> <\/mi>1<\/mn><\/mrow>v<\/mi><\/mrow><\/mfrac>-<\/mo> <\/mi>1<\/mn> <\/mi><\/mrow>u<\/mi><\/mrow><\/mfrac><\/math>
where<\/span> u<\/mi>=<\/mo><\/math> the distance between the object and the pole of the mirror,<\/span> v<\/mi>=<\/mo><\/math>  <\/span>the distance between the image and the pole of the mirror,<\/span> f<\/mi>=<\/mo><\/math> focal length in <\/span>cm<\/mi><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>f<\/mi><\/mrow><\/mfrac>=<\/mo> <\/mi>1<\/mn><\/mrow>-<\/mo>100<\/mn><\/mrow><\/mfrac>-<\/mo> <\/mi>1<\/mn><\/mrow>-<\/mo>25<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>f<\/mi><\/mrow><\/mfrac>=<\/mo> <\/mi>1<\/mn><\/mrow>-<\/mo>100<\/mn><\/mrow><\/mfrac>+<\/mo> <\/mi>1<\/mn><\/mrow>25<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>f<\/mi><\/mrow><\/mfrac>=<\/mo> <\/mi>-<\/mo>1<\/mn>+<\/mo>4<\/mn><\/mrow>100<\/mn><\/mrow><\/mfrac><\/math>
We get, <\/span>
\u21d2<\/mo>f<\/mi>=<\/mo>+<\/mo>100<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>f<\/mi>=<\/mo>+<\/mo>33<\/mn>.<\/mo>3<\/mn> cm<\/mi><\/math>.<\/span>
So, a convex lens of focal length <\/span>+<\/mo>33<\/mn>.<\/mo>3<\/mn> cm<\/mi><\/math> is required. (as<\/span> f<\/mi><\/math> is positive, the lens used will be a convex lens)<\/span>
Power<\/mi>=<\/mo>100<\/mn><\/mrow>f <\/mi>cm<\/mi><\/mrow><\/mfenced><\/mrow><\/mfrac><\/math>
=<\/mo>+<\/mo>100<\/mn><\/mrow>33<\/mn>.<\/mo>3<\/mn><\/mrow><\/mfrac><\/math>
=<\/mo>+<\/mo>3<\/mn> D <\/mi><\/math>
 <\/span>","subject":""},"yoast_head":"\n[5]The near point of a hypermetropic eye is 1\u00a0m. What is the power of the lens required to correct this defect? (Assume that the near point of the normal eye is 25\u00a0cm.) - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"[5]The near point of a hypermetropic eye is 1\u00a0m. What is the power of the lens required to correct this defect? (Assume that the near point of the normal eye is 25\u00a0cm.)\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/5the-near-point-of-a-hypermetropic-eye-is-1m-what-is-the\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[5]The near point of a hypermetropic eye is 1\u00a0m. 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