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Question

A telescope has an objective of focal length 30 cm and an eyepiece of focal length 3.0 cm. It is focussed on a scale present at a distance of 2.0 m. For seeing with relaxed eye, calculate the separation between the objective and the eyepiece.

A
38.3 cm
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B
42.3 cm
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C
35.3 cm
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D
49 cm
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Solution

The correct option is A 38.3 cm
For seeing with relaxed eye, the final image should be formed at infinity.

For this, the image formed by the objective should fall at the focus of the eyepiece.

Let v0 be the distance of the image formed by the objective.

Then, from the lens formula,

1v01u0=1f0

Here u0=2.0 m=200 cm,f0=30 cm

1v01200=130

1v0=1301200=203600=17600

v0=60017=35.3 cm

distance between the objective and the eyepiece,

d=v0+fe=35.3+3.0=38.3 cm

Hence, option (A) is correct.
Why this question?
Key Note:For seeing with relaxed eye, the final image should be formed at infinity. For this, the image formed by the objective should fall at the focus of the eyepiece.

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