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(C) To obtain the final image at infinity,the intermediate image formed by the objective lens must be at the focal point of the eyepiece. Using the le

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$120$

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(C) To obtain the final image at infinity,the intermediate image formed by the objective lens must be at the focal point of the eyepiece. Using the lens formula for the objective lens: $\frac{1}{v_{0}} - \frac{1}{u_{0}} = \frac{1}{f_{0}}$ Given: $u_{0} = -25\, mm$ and $f_{0} = 20\, mm$. Substituting the values: $\frac{1}{v_{0}} - \frac{1}{-25} = \frac{1}{20}$ $\frac{1}{v_{0}} + \frac{1}{25} = \frac{1}{20}$ $\frac{1}{v_{0}} = \frac{1}{20} - \frac{1}{25} = \frac{5 - 4}{100} = \frac{1}{100}$ $v_{0} = 100\, mm$ For the final image to be at infinity,the intermediate image must lie at the focal point of the eyepiece $(f_{e} = 20\, mm)$. Therefore,the distance between the lenses is $L = v_{0} + f_{e} = 100\, mm + 20\, mm = 120\, mm$.

We wish to make a microscope with the help of two positive lenses,both with a focal length of $20\, mm$ each,and the object is positioned $25\, mm$ from the objective lens. How far apart should the lenses be so that the final image is formed at infinity?......$mm$

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