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Q.

A telescope has an objective lens of focal length 200 cm and an eyepiece with focal length 2 cm. If this telescope is used to see a 50 m tall building at a distance of 2 km, what is the height of the image of the building formed by the objective lens?

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a

5 cm

b

10 cm

c

1 cm

d

2 cm

answer is A.

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Detailed Solution

$m = \frac{f_{0}}{f_{e}} = \frac{200}{2} = 100$
$Angle made by object = θ_{0} = \frac{50}{2000} = \frac{1}{40} rad$
$Angle made by image at eye = \frac{1}{40} (100) = 2.5 rad$
$\frac{height of image}{dis tance of image} = 2.5$
Height of image = 2.5 x 2cm = 5cm

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A telescope has an objective lens of focal length 200 cm and an eyepiece with focal length 2 cm. If this telescope is used to see a 50 m tall building at a distance of 2 km, what is the height of the image of the building formed by the objective lens?