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 ?

Explanation

If angle made at top of tower of 100 m height at 3 km distance is `alpha`, then

`therefore tan alpha = (100)/(3000) = 1/30` rad
For smaller angle,
` tan alpha = alpha`
`therefore alpha = 1/30` rad
`rArr` If image height by objecgtive is h, then angle made by image will also be `alpha`
`therefore alpha = (h)/(f_0) = (h)/(140)`
`therefore (1)/(30) = (h)/(140)`
`therefore h= (140)/(30) = 4.67` cm