A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of th camera film is 2 cm 2 cm and the area of the landscape photographed is 400 . The focal length of the lens in the drone camera is [2025]

Question

A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of the camera film is 2 cm $\times$ 2 cm and the area of the landscape photographed is 400 ${km}^{2}$ . The focal length of the lens in the drone camera is [2025]

Smart Achievers · Accepted Answer

(1)

Linear size of image = 2 cm

Linear size of object $= 20 \times 10^{5}$ cm

$m = \frac{2}{20 \times 10^{5}} = 10^{- 6}$

So, $v = \frac{u}{10^{6}}$

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{10^{6}}{u} + \frac{1}{u} = \frac{1}{f}$

$\Rightarrow \frac{(1 + 10^{6})}{u} = \frac{1}{f} \Rightarrow f \approx (\frac{u}{10^{6}})$

$\Rightarrow f = \frac{18000 \times 100}{10^{6}} cm = 1.8 cm$

Solution

Q.
A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of the camera film is 2 cm $\times$ 2 cm and the area of the landscape photographed is 400 ${km}^{2}$ . The focal length of the lens in the drone camera is [2025]

1 1.8 cm

2 2.8 cm

3 2.5 cm

4 0.9 cm

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