{"id":333364,"date":"2023-01-06T02:36:03","date_gmt":"2023-01-05T21:06:03","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/an-object-is-placed-at-a-distance-of-30-cm-from-a-convex-mirror-the-magnification-produced-is-12-what-should-be-the-position-of-the-object-to-get-the-magnification-of-13\/"},"modified":"2025-06-26T18:13:38","modified_gmt":"2025-06-26T12:43:38","slug":"an-object-is-placed-at-a-distance-of-30-cm-from-a-convex-mirror-the-magnification-produced-is-12-what-should-be-the-position-of-the-object-to-get-the-magnification-of-13","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/an-object-is-placed-at-a-distance-of-30cm-from-a-convex-mir\/","title":{"rendered":"An object is placed at a distance of 30\u00a0cm from a convex mirror. The magnification produced is 12. What should be the position of the object to get the magnification of 13?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"An object is placed at a distance of 30\u00a0cm from a convex mirror. The magnification produced is 12. What should be the position of the object to get the magnification of 13?","custom_permalink":"question\/physics\/an-object-is-placed-at-a-distance-of-30cm-from-a-convex-mir\/"},"categories":[],"acf":{"question":"

An object is placed at a distance of <\/span>30<\/mn> cm<\/mi><\/math> from a convex mirror. The magnification produced is <\/span>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac><\/math>. What should be the position of the object to get the magnification of <\/span>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/math>? <\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:normal;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:normal;font-size:12pt\">","options":[{"option":"60<\/mn> cm<\/mi><\/math>","correct":false},{"option":"15<\/mn> cm<\/mi><\/math>","correct":false},{"option":"90<\/mn> cm<\/mi><\/math>","correct":false},{"option":"120<\/mn> cm<\/mi><\/math> <\/span>","correct":true}],"solution":"The object should be placed <\/span>60<\/mn> cm<\/mi><\/math> from the convex mirror to get a magnification of <\/span>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac><\/math>.<\/span>
Given, <\/span>
u<\/mi><\/mrow>1<\/mn><\/mrow><\/msub> <\/mi>=<\/mo> <\/mi>-<\/mo>30<\/mn> cm<\/mi><\/math>
 m <\/mi>=<\/mo> <\/mi>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac><\/math>
The formula of magnification is given as<\/span>
   <\/span>m<\/mi>=<\/mo> <\/mi>-<\/mo>v<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow>u<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>=<\/mo> <\/mi>-<\/mo>v<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow>-<\/mo>30<\/mn><\/mrow><\/mfrac><\/math>             <\/span>\u21d2<\/mo>v<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>=<\/mo> <\/mi>+<\/mo>15<\/mn> cm<\/mi><\/math>     <\/span>Using mirror formula <\/span>
   <\/span>1<\/mn><\/mrow>f<\/mi><\/mrow><\/mfrac>=<\/mo> <\/mi>1<\/mn><\/mrow>u<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>v<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>f<\/mi><\/mrow><\/mfrac>=<\/mo> <\/mi>1<\/mn><\/mrow>-<\/mo>30<\/mn><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>15<\/mn><\/mrow><\/mfrac><\/math>         <\/span>\u21d2<\/mo><\/math> <\/span>f<\/mi>=<\/mo> <\/mi>+<\/mo>30<\/mn> cm <\/mi><\/math>     <\/span>\u2026\u2026\u2026..(1)<\/span>
Again,<\/span>                                       <\/span>    <\/span>m<\/mi>'<\/mo>=<\/mo> <\/mi>-<\/mo>v<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow>u<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>3<\/mn><\/mrow><\/mfrac> <\/mi>=<\/mo> <\/mi>-<\/mo>v<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow>u<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac> <\/mi><\/math>
\u21d2<\/mo>v<\/mi><\/mrow>2<\/mn><\/mrow><\/msub> <\/mi>=<\/mo> <\/mi>-<\/mo>u<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow>3<\/mn><\/mrow><\/mfrac> <\/mi><\/math>       <\/span>\u2026\u2026\u2026\u2026.(2)<\/span>
Using mirror formula again<\/span>
1<\/mn><\/mrow>f<\/mi><\/mrow><\/mfrac>=<\/mo> <\/mi>1<\/mn><\/mrow>u<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>v<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math>
Using equations (1) and (2)<\/span>
   <\/span>1<\/mn><\/mrow>30<\/mn><\/mrow><\/mfrac>=<\/mo> <\/mi>1<\/mn><\/mrow>u<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>-<\/mo>3<\/mn><\/mrow>u<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>30<\/mn><\/mrow><\/mfrac>=<\/mo> <\/mi>-<\/mo>2<\/mn><\/mrow>u<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math>
\u21d2<\/mo><\/math>  <\/span>u<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>=<\/mo> <\/mi>-<\/mo>60<\/mn> cm<\/mi><\/math>
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