{"id":87747,"date":"2025-06-01T06:53:24","date_gmt":"2025-06-01T06:53:24","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87747"},"modified":"2025-06-01T06:53:24","modified_gmt":"2025-06-01T06:53:24","slug":"according-to-the-new-cartesian-sign-convention-which-one-of-the-follo","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/according-to-the-new-cartesian-sign-convention-which-one-of-the-follo\/","title":{"rendered":"According to the New Cartesian Sign Convention, which one of the follo"},"content":{"rendered":"

According to the New Cartesian Sign Convention, which one of the following is correct in respect of the formula $\\frac{1}{f} = \\frac{1}{v} + \\frac{1}{u}$, where symbols have their usual meanings?<\/p>\n

[amp_mcq option1=”It applies only to spherical mirrors.” option2=”It applies only to spherical lenses.” option3=”It applies to spherical mirrors as well as spherical lenses.” option4=”It is an invalid formula.” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2021<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe formula $\\frac{1}{f} = \\frac{1}{v} + \\frac{1}{u}$ is the standard equation that applies to both spherical mirrors and spherical lenses when used with the New Cartesian Sign Convention.
\n<\/section>\n
\nFor spherical mirrors, this is known as the mirror formula. For spherical lenses, it is known as the thin lens formula. The New Cartesian Sign Convention provides a consistent set of rules for assigning positive or negative signs to object distance ($u$), image distance ($v$), and focal length ($f$), ensuring that the formula holds true for both real and virtual images\/objects and for both converging and diverging mirrors\/lenses.
\n<\/section>\n
\nWhile the formula form is the same, the application of the sign convention and the meaning of $f$ (positive for converging, negative for diverging) correctly distinguish between types of mirrors and lenses. Other related formulas, like the magnification formula ($m = \\frac{h’}{h} = -\\frac{v}{u}$ for mirrors and $m = \\frac{h’}{h} = \\frac{v}{u}$ for lenses, with the sign convention applied), are also used in conjunction with these fundamental formulas.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

According to the New Cartesian Sign Convention, which one of the following is correct in respect of the formula $\\frac{1}{f} = \\frac{1}{v} + \\frac{1}{u}$, where symbols have their usual meanings? [amp_mcq option1=”It applies only to spherical mirrors.” option2=”It applies only to spherical lenses.” option3=”It applies to spherical mirrors as well as spherical lenses.” option4=”It is … <\/p>\n

Detailed SolutionAccording to the New Cartesian Sign Convention, which one of the follo<\/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":[1110,1153,1128],"class_list":["post-87747","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1110","tag-optics","tag-physics","no-featured-image-padding"],"yoast_head":"\nAccording to the New Cartesian Sign Convention, which one of the follo<\/title>\n<meta name=\"description\" content=\"The formula $frac{1}{f} = frac{1}{v} + frac{1}{u}$ is the standard equation that applies to both spherical mirrors and spherical lenses when used with the New Cartesian Sign Convention. For spherical mirrors, this is known as the mirror formula. For spherical lenses, it is known as the thin lens formula. The New Cartesian Sign Convention provides a consistent set of rules for assigning positive or negative signs to object distance ($u$), image distance ($v$), and focal length ($f$), ensuring that the formula holds true for both real and virtual images\/objects and for both converging and diverging mirrors\/lenses.\" \/>\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\/according-to-the-new-cartesian-sign-convention-which-one-of-the-follo\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"According to the New Cartesian Sign Convention, which one of the follo\" \/>\n<meta property=\"og:description\" content=\"The formula $frac{1}{f} = frac{1}{v} + frac{1}{u}$ is the standard equation that applies to both spherical mirrors and spherical lenses when used with the New Cartesian Sign Convention. For spherical mirrors, this is known as the mirror formula. For spherical lenses, it is known as the thin lens formula. The New Cartesian Sign Convention provides a consistent set of rules for assigning positive or negative signs to object distance ($u$), image distance ($v$), and focal length ($f$), ensuring that the formula holds true for both real and virtual images\/objects and for both converging and diverging mirrors\/lenses.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/according-to-the-new-cartesian-sign-convention-which-one-of-the-follo\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:53:24+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":"According to the New Cartesian Sign Convention, which one of the follo","description":"The formula $frac{1}{f} = frac{1}{v} + frac{1}{u}$ is the standard equation that applies to both spherical mirrors and spherical lenses when used with the New Cartesian Sign Convention. 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For spherical lenses, it is known as the thin lens formula. 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