(a) For the telescope described what is the separation between the objective lens and eye piece ?
(b) If this telescope is used to view a `100 m` tall tower `3 km` away, what is the height of the image of the tower formed by the objective lens ?
(c ) What is the height of the final image of the tower if it is formed at 25 cm` ?

Explanation

(a) Here, in normal adjustment,
Separation between objective lens and eye lens `= f_(0) + f_(e) = 140 + 5 = 145 cm`
(b) Angle subtended by tower `100 m` tall at `3 km`
`alpha = (100)/(3 xx 100) = (1)/(30)` radian
If `h` is the height of image formed by the objective, then `alpha = (h)/(f_(0)) = (h)/(140)`
`:. (h)/(140) = (1)/(30)` or `h = (140)/(30)cm. = 4.7 cm`
( c) Magnifying produced by eye piece `= (1 + (d)/(f_(e))) = 1 + (25)/(5) = 6`
`:.` Height of final image `= 4.7 xx 6 = 28.2 cm`