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Question

The angle subtended by the moon, at the objective lens of an astronomical telescope, is 0.5 rad. The focal length of the objective lens and the eyepiece of the telescope are 30 cm and 10 cm respectively. Find the angle subtended by the final image, at the eyepiece, in case of the least strain on the eye.

A
1.1 rad
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B
1.5 rad
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C
1.7 rad
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D
1.9 rad
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Solution

The correct option is B 1.5 rad

Given:
α=0.5 rad
fo=30 cm
fe=10 cm

In case of the least strain on the eye, the final image is formed at infinity.

So, ve=

On using lens formula for eyepiece,

1ve1ue=1fe

1()1ue=110

ue=10 cm
Also, from geometry
tanα=hfo,
for small angle α,tanαα
h=αfo
So,

β=|h||ue|

β=αfo|ue|

β=0.5×3010=1.5 rad

Hence, option (B) is the correct answer.

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