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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?

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#### Solution

Focal length of the objective lens, f_{o} = 140 cm

Focal length of the eyepiece, f_{e} = 5 cm

Height of the tower, h_{1} = 100 m

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

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

θ = `"h"_1/"u"`

= `100/3000`

= `1/30` rad

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

θ = `"h"_2/"f"_"o" = "h"_2/140 "rad"`

Where,

h_{2} = Height of the image of the tower formed by the objective lens

`1/30 = "h"_2/140`

∴ `"h"_2 = 140/30` = 4.7 cm

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

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