If we need a magnification of 375 from a compound microscope of tube length <math> <mn>150</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math> <math><mtext></mtext></math> and an objective of focal length <math> <mn>5</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math> <math><mtext></mtext></math> , the focal length of the eye piece should be close to

Case-I:If final image is at least distance of clear visionM.P. = L f 0 1 + D f e ; 375 = 150 5 1 + 25 f e 375 30 = 1 + 25 f e ; 345 30 = 25 f e f e = 750 345 = 2.17 c m ; f e ≈ 22 m m Case-II:In final image is at infinityM.P. = L f 0 D f e = 375 f e = 22 m m

If we need a magnification of 375 from a compound microscope of tube length <math> <mn>150</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math> <math><mtext></mtext></math>&nbsp;and an objective of focal length <math> <mn>5</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math> <math><mtext></mtext></math>&nbsp;, the focal length of the eye piece should be close to

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Physics Class 12th Physics Ray Optics and Optical Instruments

If we need a magnification of 375 from a compound microscope of tube length $150 m m$ and an objective of focal length $5 m m$ , the focal length of the eye piece should be close to

Option 1 -

$22 m m$

Option 2 -

$33 m$

Option 3 -

$12 m$

Option 4 -

$2 m m$

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Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

Case-I:

If final image is at least distance of clear vision

M.P. $= \frac{L}{f_{0}} (1 + \frac{D}{f_{e}}); 375 = \frac{150}{5} [1 + \frac{25}{f_{e}}]$ $\frac{}{_{}} (\frac{}{_{}}) \frac{}{} [\frac{}{_{}}]$

$\frac{375}{30} = 1 + \frac{25}{f_{e}}; \frac{345}{30} = \frac{25}{f_{e}}$

$f_{e} = \frac{750}{345} = 2.17 c m; f_{e} \approx 22 m m$

Case-II:

In final image is at infinity

M.P. $= \frac{L}{f_{0}} (\frac{D}{f_{e}}) = 375$ $f_{e} = 22 m m$ $\frac{}{_{}} (\frac{}{_{}})$

Case-I:If final image is at least distance of clear visionM.P. <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">L</mi> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mfenced separators="|"> <mrow> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">D</mi> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mo>;</mo> <mn>375</mn> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>150</mn> </mrow> </mrow> <mrow> <mrow> <mn>5</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> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> <math><mfrac><mrow><mrow></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac><mfenced separators="|"><mrow><mrow><mfrac><mrow><mrow></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mfenced><mfrac><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></mfrac><mfenced open="[" close="]" separators="|"><mrow><mrow><mfrac><mrow><mrow></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mfenced></math> <math> <mfrac> <mrow> <mrow> <mn>375</mn> </mrow> </mrow> <mrow> <mrow> <mn>30</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>25</mn> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mo>;</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mfrac> <mrow> <mrow> <mn>345</mn> </mrow> </mrow> <mrow> <mrow> <mn>30</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>25</mn> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> <math> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>750</mn> </mrow> </mrow> <mrow> <mrow> <mn>345</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>2.17</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> <mo>;</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>≈</mo> <mn>22</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math> Case-II:In final image is at infinityM.P. <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">L</mi> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi mathvariant="normal">D</mi> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mo>=</mo> <mn>375</mn> </math> <math> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>22</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </math> <math><mfrac><mrow><mrow></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac><mfenced separators="|"><mrow><mrow><mfrac><mrow><mrow></mrow></mrow><mrow><mrow><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mfenced></math>

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If we need a magnification of 375 from a compound microscope of tube length $150 m m$ and an objective of focal length $5 m m$ , the focal length of the eye piece should be close to

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If we need a magnification of 375 from a compound microscope of tube length $150 m m$ and an objective of focal length $5 m m$ , the focal length of the eye piece should be close to