{"id":87493,"date":"2025-06-01T06:45:23","date_gmt":"2025-06-01T06:45:23","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87493"},"modified":"2025-06-01T06:45:23","modified_gmt":"2025-06-01T06:45:23","slug":"the-radii-of-curvature-of-the-faces-of-a-double-convex-lens-are-10-cm","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-radii-of-curvature-of-the-faces-of-a-double-convex-lens-are-10-cm\/","title":{"rendered":"The radii of curvature of the faces of a double convex lens are 10 cm"},"content":{"rendered":"

The radii of curvature of the faces of a double convex lens are 10 cm and 20 cm. The refractive index of the glass is 1.5. What is the power of this lens (in units of dioptre) ?<\/p>\n

[amp_mcq option1=”+7\u00b75 D” option2=”\u20137\u00b75 D” option3=”+2\u00b75 D” option4=”+5\u00b70 D” correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is +7.5 D.
\n<\/section>\n
\nFor a thin lens, the power (P) is given by the reciprocal of the focal length (f) in meters, P = 1\/f. The focal length of a lens in air can be calculated using the lensmaker’s formula: 1\/f = (n – 1) * (1\/R\u2081 – 1\/R\u2082), where n is the refractive index of the lens material, and R\u2081 and R\u2082 are the radii of curvature of the two surfaces. For a double convex lens, assuming light comes from the left, the first surface is convex (R\u2081 > 0) and the second surface is also convex but faces the opposite direction (R\u2082 < 0).\n<\/section>\n
\nGiven: R\u2081 = +10 cm = +0.1 m, R\u2082 = -20 cm = -0.2 m (negative because the center of curvature is on the same side as the incoming light for the second surface of a double convex lens), and n = 1.5.
\nUsing the lensmaker’s formula:
\n1\/f = (1.5 – 1) * (1\/0.1 – 1\/(-0.2))
\n1\/f = 0.5 * (1\/0.1 + 1\/0.2)
\n1\/f = 0.5 * (10 + 5)
\n1\/f = 0.5 * 15
\n1\/f = 7.5 m\u207b\u00b9
\nPower P = 1\/f = 7.5 Dioptre (D). Since the focal length is positive (1\/7.5 m), it is a converging lens, which is expected for a double convex lens in air.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The radii of curvature of the faces of a double convex lens are 10 cm and 20 cm. The refractive index of the glass is 1.5. What is the power of this lens (in units of dioptre) ? [amp_mcq option1=”+7\u00b75 D” option2=”\u20137\u00b75 D” option3=”+2\u00b75 D” option4=”+5\u00b70 D” correct=”option1″] This question was previously asked in UPSC … <\/p>\n

Detailed SolutionThe radii of curvature of the faces of a double convex lens are 10 cm<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1093],"tags":[1101,1153,1128],"class_list":["post-87493","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1101","tag-optics","tag-physics","no-featured-image-padding"],"yoast_head":"\nThe radii of curvature of the faces of a double convex lens are 10 cm<\/title>\n<meta name=\"description\" content=\"The correct answer is +7.5 D. For a thin lens, the power (P) is given by the reciprocal of the focal length (f) in meters, P = 1\/f. The focal length of a lens in air can be calculated using the lensmaker's formula: 1\/f = (n - 1) * (1\/R\u2081 - 1\/R\u2082), where n is the refractive index of the lens material, and R\u2081 and R\u2082 are the radii of curvature of the two surfaces. For a double convex lens, assuming light comes from the left, the first surface is convex (R\u2081 > 0) and the second surface is also convex but faces the opposite direction (R\u2082 < 0).\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-radii-of-curvature-of-the-faces-of-a-double-convex-lens-are-10-cm\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The radii of curvature of the faces of a double convex lens are 10 cm\" \/>\n<meta property=\"og:description\" content=\"The correct answer is +7.5 D. For a thin lens, the power (P) is given by the reciprocal of the focal length (f) in meters, P = 1\/f. The focal length of a lens in air can be calculated using the lensmaker's formula: 1\/f = (n - 1) * (1\/R\u2081 - 1\/R\u2082), where n is the refractive index of the lens material, and R\u2081 and R\u2082 are the radii of curvature of the two surfaces. For a double convex lens, assuming light comes from the left, the first surface is convex (R\u2081 > 0) and the second surface is also convex but faces the opposite direction (R\u2082 < 0).\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-radii-of-curvature-of-the-faces-of-a-double-convex-lens-are-10-cm\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:45:23+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The radii of curvature of the faces of a double convex lens are 10 cm","description":"The correct answer is +7.5 D. For a thin lens, the power (P) is given by the reciprocal of the focal length (f) in meters, P = 1\/f. The focal length of a lens in air can be calculated using the lensmaker's formula: 1\/f = (n - 1) * (1\/R\u2081 - 1\/R\u2082), where n is the refractive index of the lens material, and R\u2081 and R\u2082 are the radii of curvature of the two surfaces. 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The focal length of a lens in air can be calculated using the lensmaker's formula: 1\/f = (n - 1) * (1\/R\u2081 - 1\/R\u2082), where n is the refractive index of the lens material, and R\u2081 and R\u2082 are the radii of curvature of the two surfaces. 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For a thin lens, the power (P) is given by the reciprocal of the focal length (f) in meters, P = 1\/f. The focal length of a lens in air can be calculated using the lensmaker's formula: 1\/f = (n - 1) * (1\/R\u2081 - 1\/R\u2082), where n is the refractive index of the lens material, and R\u2081 and R\u2082 are the radii of curvature of the two surfaces. 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