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Question

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


A
5 cm
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B
10 cm
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C
1 cm
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D
2 cm
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Solution

The correct option is A 5 cm
Given, $$u = -2000m, \,v=?, \,f=200 cm = 2 m$$

From lens formula, $$\displaystyle \frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}+\frac{1}{2000}=\frac{1}{2}$$

$$\displaystyle \frac{1}{v}=\frac{1}{2}-\frac{1}{2000}=\frac{1000-1}{2000}=\frac{999}{2000}$$

$$\displaystyle v=\frac{2000}{999}$$

Magnification, $$ \dfrac{v}{u} = m = \dfrac{2000}{999\times 2000}=\dfrac{1}{999}$$ 

Size of image $$\displaystyle = \frac{1}{999}\times 50\times 100 cm \approx 5 cm$$

Physics
NCERT
Standard XII

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