A compound microscope consists of an objective lens of focal length 1… | JEE Main 2020 (5 Sep, Shift 1)

Q32JEE Main 2020 · 5 SEP · SHIFT 1Medium

Optical Instruments & the Eye

A compound microscope consists of an objective lens of focal length 1 cm and an eyepiece of focal length 5 cm with a separation of 10 cm.

The distance between an object and the objective lens, at which the strain on the eye is minimum is $\frac{n}{40}$ cm. The value of n is _____.

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

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Answer: 50

Minimum strain: final image at infinity, so the objective's image is at $f_e = 5$ cm from the eyepiece.
Objective image distance $v = 10 - 5 = 5$ cm.
$\dfrac{1}{u} = \dfrac{1}{v} - \dfrac{1}{f} = \dfrac{1}{5} - 1 = -\dfrac{4}{5} \Rightarrow |u| = \dfrac{5}{4}$ cm $= \dfrac{50}{40}$ cm.
So $n = 50$ .

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