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The diameter of the moon is 3.5 xx 10^(3...

The diameter of the moon is `3.5 xx 10^(3) km` and its distance from the earth is `3.8 xx 10^(5)km`. It is seen through a telescope having focal lengths of objective and eye-piece as `4m` and `10 cm` respectively. Calculate (a) magnifying power of telescope (b) length of telescope tube and (c) anngular size of image of moon.

Text Solution

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For normal adjustment
a) `|M|=f_(0)/f_(e)=(4xx100)/10=40`
b) `L=f_(0) + f_(e)=400+10cm=4.10m`
c) As the angle subtended by moon on the objective of telescope `theta_(0)=(3.5xx10^(3))/(3.8xx10^(5))=3.5/3.8xx10^(-2)` rad and as `|M|=|theta/theta_(0)|`, the angular size of final image
`|theta|=|M|xxtheta_(0)=40xx3.5/3.8xx10^(-2)=0.3684` rad
ie `|theta|=.368xx180^@/pi=21^@`
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