The distance between an object and a screen is $100\mathrm{c}\mathrm{m}$ . A lens can produce real image of the object on the screen for two different positions between the screen and the object.

The distance between these two positions is $40\mathrm{c}\mathrm{m}$ . If the power of the lens is close to $\left(\frac{\mathrm{N}}{100}\right)\mathrm{D}$ where $\mathrm{N}$ is an integer, the value of $\mathrm{N}$  is           

<p><strong>Sol.&nbsp;<math><mrow></mrow><mi>M</mi><mo>=</mo><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>f</mi></mrow></mrow><mrow><mrow><mi>o</mi></mrow></mrow></msub></mrow></mrow></mfrac><mfenced open=" [" close="]" separators="|"><mrow><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mrow><mi>D</mi></mrow></mrow><mrow><mrow><mi>F</mi><mi>e</mi></mrow></mrow></mfrac></mrow></mrow></mfenced></math></strong></p><p><strong><math><mo>⇒</mo><mn>100</mn><mo>=</mo><mfrac><mrow><mrow><mn>20</mn></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></mfrac><mfenced open=" [" close="]" separators="|"><mrow><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mrow><mn>25</mn></mrow></mrow><mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow></mrow></mfrac></mrow></mrow></mfenced></math></strong></p><p><strong><math><mo>⇒</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mrow><mn>25</mn></mrow></mrow><mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow></mrow></mfrac><mo>=</mo><mn>5</mn></math></strong></p><p><strong><math><mo>⇒</mo><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi><mo>=</mo><mfrac><mrow><mrow><mn>25</mn></mrow></mrow><mrow><mrow><mn>4</mn></mrow></mrow></mfrac><mo>=</mo><mn>6.25</mn><mtext></mtext><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math></strong></p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment