JEE Main 2025 Jan 24 Shift 2, Physics Q14: Magnification

The lens forms an image of the landscape on the film. Linear magnification:

$m=\frac{\text{image size}}{\text{object size}}=\frac{f}{u}$ (in magnitude, with the object far away so image distance $\approx f$)

Landscape area $=400{\text{km}}^2$, so its side length is $\sqrt{400}=20\text{km}=2\times 10^4\text{m}$.

Film side length $=2\text{cm}=2\times 10^{-2}\text{m}$.

Object distance $u=18\text{km}=18\times 10^3\text{m}$.

From $\frac{\text{film}}{\text{landscape}}=\frac{f}{u}$:

$\frac{2\times 10^{-2}}{2\times 10^4}=\frac{f}{18\times 10^3}$

$10^{-6}=\frac{f}{18\times 10^3}\Rightarrow f=18\times 10^{-3}\text{m}=18\text{mm}=1.8\text{cm}$

Correct option: (1)