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, f_e = 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.