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Question

An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance of-

A
37.3 cm
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B
46.0 cm
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C
50.0 cm
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D
53.4 cm
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Solution

The correct option is D 53.4 cm
Given, f0=40 cm ; fe=4 cmu0=200 cmL=|v0|+|ue|=?

Using lens formula, for the objective lens,

1f0=1v01u0

140=1v01200

v0=50 cm

Using lens formula, for the eyepiece lens,

1fe=1ve1ue

14=1251ue [ ve=25 cm]

1ue=(125+14)=29100

ue=10029=3.4cm

The separation between lenses,

L=|v0|+|ue|=50+3.4=53.4 cm

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (D) is the correct answer.

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