{"id":336916,"date":"2023-01-06T09:34:21","date_gmt":"2023-01-06T04:04:21","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-diverging-lens-has-focal-length-20-cm-an-object-of-height-4-cm-is-placed-20-cm-from-the-optical-centre-in-front-of-the-lens-the-image-is-formed-at-10-cm-away-from-it-the-size\/"},"modified":"2025-06-26T17:59:27","modified_gmt":"2025-06-26T12:29:27","slug":"a-diverging-lens-has-focal-length-20-cm-an-object-of-height-4-cm-is-placed-20-cm-from-the-optical-centre-in-front-of-the-lens-the-image-is-formed-at-10-cm-away-from-it-the-size","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-diverging-lens-has-focal-length-20cm-an-object-of-height\/","title":{"rendered":"A diverging lens has focal length 20\u00a0cm. An object of height 4\u00a0cm is placed 20\u00a0cm from the optical centre, in front of the lens. The image is formed at 10\u00a0cm away from it. The size of the image formed is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A diverging lens has focal length 20\u00a0cm. An object of height 4\u00a0cm is placed 20\u00a0cm from the optical centre, in front of the lens. The image is formed at 10\u00a0cm away from it. The size of the image formed is","custom_permalink":"question\/physics\/a-diverging-lens-has-focal-length-20cm-an-object-of-height\/"},"categories":[],"acf":{"question":"

A diverging lens has focal length <\/span>20<\/mn> cm<\/mi><\/math>. An object of height <\/span>4<\/mn> cm<\/mi><\/math> is placed <\/span>20<\/mn> cm<\/mi><\/math> from the optical centre, in front of the lens. The image is formed at <\/span>10<\/mn> cm<\/mi><\/math> away from it. The size of the image formed is <\/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":"2<\/mn> cm<\/mi><\/math>","correct":false},{"option":"4<\/mn> cm <\/mi><\/math>","correct":true},{"option":"1<\/mn> cm <\/mi><\/math> <\/span>","correct":false},{"option":"3<\/mn> cm <\/mi><\/math> <\/span>","correct":false}],"solution":"A diverging lens has focal length <\/span>20<\/mn> cm<\/mi><\/math>. An object of height <\/span>4<\/mn> cm<\/mi><\/math> is placed <\/span>20<\/mn> cm<\/mi><\/math> from the optical centre, in front of the lens. The image is formed at <\/span>10<\/mn> cm<\/mi><\/math> away from it. The size of the image formed is<\/span>  <\/span>2<\/mn> cm<\/mi><\/math>.<\/span>
A diverging lens is also called a concave lens. It has a negative focal length.<\/span>
Given<\/span>
 Focal length<\/mi>,<\/mo> f<\/mi>=<\/mo> <\/mi>-<\/mo>20<\/mn> cm<\/mi>,<\/mo><\/math>
Height of object<\/mi>,<\/mo> <\/mi>h<\/mi><\/mrow>1<\/mn><\/mrow><\/msub>=<\/mo>4<\/mn> cm<\/mi><\/math>
Object distance<\/mi>,<\/mo> u <\/mi>=<\/mo> <\/mi>-<\/mo>20<\/mn> cm<\/mi><\/math>
Image distance<\/mi>,<\/mo> v<\/mi>=<\/mo> <\/mi>-<\/mo>10<\/mn> cm<\/mi><\/math>
To find <\/span>image height<\/mi>,<\/mo> <\/mi>h<\/mi><\/mrow>2<\/mn><\/mrow><\/msub>=<\/mo> <\/mi>?<\/mo><\/math>
By magnification formula, we know<\/span>
   <\/mi>h<\/mi><\/mrow>i<\/mi><\/mrow><\/msub><\/mrow>h<\/mi><\/mrow>o<\/mi><\/mrow><\/msub><\/mrow><\/mfrac>=<\/mo>v<\/mi><\/mrow>u<\/mi><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>h<\/mi><\/mrow>i<\/mi><\/mrow><\/msub>=<\/mo>v<\/mi><\/mrow>u<\/mi><\/mrow><\/mfrac>\u00d7<\/mo>h<\/mi><\/mrow>o<\/mi><\/mrow><\/msub><\/math>
\u21d2<\/mo>h<\/mi><\/mrow>i<\/mi><\/mrow><\/msub>=<\/mo> <\/mi>-<\/mo>10<\/mn><\/mrow>-<\/mo>20<\/mn><\/mrow><\/mfrac>\u00d7<\/mo>4<\/mn><\/math>
 <\/mi>h<\/mi><\/mrow>i<\/mi><\/mrow><\/msub>=<\/mo>2<\/mn> cm<\/mi><\/math>
\"\" <\/span> <\/span>","subject":""},"yoast_head":"\nA diverging lens has focal length 20\u00a0cm. An object of height 4\u00a0cm is placed 20\u00a0cm from the optical centre, in front of the lens. The image is formed at 10\u00a0cm away from it. The size of the image formed is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A diverging lens has focal length 20\u00a0cm. An object of height 4\u00a0cm is placed 20\u00a0cm from the optical centre, in front of the lens. The image is formed at 10\u00a0cm away from it. 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