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?


Given:


Focal length of the objective lens, f0 = 140 cm


Focal length of the eyepiece, fe = 5 cm


Height of the tower, h1 = 100 m


Distance of the tower (object) from the telescope, u = 3Km = 3000 m


The angle subtended by the tower at the telescope is given as:


θ = h1/ u


θ = 100/3000


θ = 1/30 rad


The angle subtended by the image produced by the objective lens is given as:


θ = h2/ fo


θ = h2 /140 rad


Where, h2 = height of the image of the tower formed by the objective lens


1/30 = h2 /140


Therefore,


h2 = 140/30


h2 = 4.7 cm


Therefore, the objective lens forms a 4.7 cm tall image of the tower.


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