An object viewed from a near point distance of 25 cm, using a… | JEE Main 2021 (20 Jul, Shift 1)

Q26JEE Main 2021 · 20 JUL · SHIFT 1Difficult

Optical Instruments & the Eye

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to __________ cm.

Numerical answer type. Work it out, then open the answer.

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Answer: 25

Simple microscope, image at near point: $6 = 1 + \dfrac{25}{f} \Rightarrow f = 5$ cm (this lens becomes the objective).
Compound microscope, image at infinity: $M = \dfrac{L}{f_o} \cdot \dfrac{D}{f_e} = 12$ .
$12 = \dfrac{60}{5} \times \dfrac{25}{f_e} \Rightarrow f_e = 25$ cm.

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