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If the focal lengths of the objective an...

If the focal lengths of the objective and the eyepiece of an astronomical telescope be 100 cm and 20 cm respectively , calculate the angular magnification of the instrument . If a house of height 60 m situated at a distance of 1 km be observed by the instrument determine the height of the image formed by the objective.

Text Solution

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Angular magnification of the telescope ,
`m=(f_o)/(f_e)=(100)/(20)=5`
For the objective,
`f_o=100cm, u=-1km =-10^5cm`
According to the equation of lens we have ,
`1/v+1/(10^5)=1/(100) or, 1/v=-1/(10^5)+1/(100) or, v=100.1 cm `
Magnification `=v/u=(100.1)/(10^5)=1/(10^3)=(" size of the image")/("size of the object") or, 1/(10^3)=("size of the image")/(60xx100)`
`therefore` Size of the image `=(6000)/(1000)=6 cm`
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