{"id":335096,"date":"2023-01-06T08:37:34","date_gmt":"2023-01-06T03:07:34","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/an-object-of-size-7-cm-is-placed-27-cm-in-front-of-a-concave-mirror-of-a-focal-length-of-18-cm-at-what-distance-from-the-mirror-should-a-screen-be-placed-so-that-a-sharp-focused-image\/"},"modified":"2025-06-26T18:14:55","modified_gmt":"2025-06-26T12:44:55","slug":"an-object-of-size-7-cm-is-placed-27-cm-in-front-of-a-concave-mirror-of-a-focal-length-of-18-cm-at-what-distance-from-the-mirror-should-a-screen-be-placed-so-that-a-sharp-focused-image","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/an-object-of-size-7cm-is-placed-27cm-in-front-of-a-concave\/","title":{"rendered":"An object of size 7\u00a0cm is placed 27\u00a0cm in front of a concave mirror of a focal length of 18\u00a0cm. At what distance from the mirror should a screen be placed so that a sharp, focused image can be obtained?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"An object of size 7\u00a0cm is placed 27\u00a0cm in front of a concave mirror of a focal length of 18\u00a0cm. At what distance from the mirror should a screen be placed so that a sharp, focused image can be obtained?","custom_permalink":"question\/physics\/an-object-of-size-7cm-is-placed-27cm-in-front-of-a-concave\/"},"categories":[],"acf":{"question":"

An object of size <\/span>7<\/mn> cm<\/mi><\/math> is placed <\/span>27<\/mn> cm<\/mi><\/math> in front of a concave mirror of a focal length of <\/span>18<\/mn> cm<\/mi><\/math>. At what distance from the mirror should a screen be placed so that a sharp, focused image can be obtained?<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\">","options":[{"option":"52<\/mn> cm <\/mi><\/math>","correct":false},{"option":"\u2013<\/mi>54<\/mn> cm <\/mi><\/math>","correct":true},{"option":"20<\/mn> cm<\/mi><\/math>","correct":false},{"option":"55<\/mn> cm<\/mi><\/math> <\/span>","correct":false}],"solution":"An object of size <\/span>7<\/mn> cm<\/mi><\/math> is placed <\/span>27<\/mn> cm<\/mi><\/math> in front of a concave mirror of a focal length of <\/span>18<\/mn> cm<\/mi><\/math>. The screen can be placed <\/span>54<\/mn> cm<\/mi><\/math> to the left of the mirror so that a sharp, focused image can be obtained.<\/span>
Given,<\/span>
Object distance, <\/span>(<\/mo> u <\/mi>)<\/mo>=<\/mo> <\/mi>-<\/mo>27<\/mn>cm<\/mi><\/math>
Focal length,<\/span>     <\/span>(<\/mo> f <\/mi>)<\/mo>=<\/mo> <\/mi>-<\/mo>18<\/mn> cm<\/mi><\/math>
Object height,<\/span>    <\/span>(<\/mo>h<\/mi>)<\/mo> <\/mi>=<\/mo> <\/mi>7<\/mn> cm<\/mi><\/math>
Applying mirror formula,<\/span>
           <\/span>1<\/mn><\/mrow>f<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/mrow>v<\/mi><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>u<\/mi><\/mrow><\/mfrac><\/math>
By substituting given values, we get<\/span>
\u21d2<\/mo>   <\/mi>1<\/mn><\/mrow>-<\/mo>18<\/mn><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/mrow>v<\/mi><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>-<\/mo>27<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo><\/math>        <\/span>1<\/mn><\/mrow>v<\/mi><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/mrow>27<\/mn><\/mrow><\/mfrac>-<\/mo>1<\/mn><\/mrow>18<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo><\/math>        <\/span>1<\/mn><\/mrow>v<\/mi><\/mrow><\/mfrac>=<\/mo>2<\/mn>-<\/mo>3<\/mn><\/mrow>54<\/mn><\/mrow><\/mfrac><\/math>
\u21d2<\/mo><\/math>     <\/span>  v   <\/mi>=<\/mo> <\/mi>-<\/mo>54<\/mn> cm<\/mi><\/math>
-ve sign indicates that the image forms in the front of the concave mirror and on the same side of the object. <\/span>
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