A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm . If a 50 m tall tower at a distance of 1 km is observed through this telescope in a normal setting, the a

Question

A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm . If a 50 m tall tower at a distance of 1 km is observed through this telescope in a normal setting, the angle formed by the image of the tower is θ , then θ is close to

TestHub · Accepted Answer

Angular magnification of a telescope in normal adjustment is

$m = \frac{β}{α} = \frac{f_{0}}{f_{e}} \Rightarrow β = \frac{f_{0}}{f_{e}} α$

According to the question

$α = \frac{y}{x} = \frac{50}{1000} = \frac{1}{20}$

$\Rightarrow α = \frac{1}{20}$

$\Rightarrow β = \frac{150}{5} \times \frac{1}{20} = 32 rad$

$= \frac{3}{2} \times \frac{180 °}{3.14} = 86 °$

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