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A spy satellite circles the Earth at an altitude of 212 km and carries out surveillance with a special high-resolution telescopic camera having a lens diameter of 20 cm. If the angular resolution of this camera is limited by diffraction, estimate the separation of two small objects on the Earth's surface that are just resolved in yellow-green light (????=550 nm). Use the small-angle approximation for this problem.

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Answer:

0.71126 m

Explanation:

[tex]\lambda[/tex] = Wavelength = 550 nm

D = Lens diameter = 20 cm

L = Distance from object = 212 km

Angular resolution is given by

[tex]sin\theta=1.22\frac{\lambda}{D}[/tex]

[tex]sin\theta=\frac{d}{L}[/tex]

[tex]\frac{d}{L}=1.22\frac{\lambda}{D}\\\Rightarrow d=1.22\frac{\lambda\times L}{D} \\\Rightarrow d=1.22\times \frac{550\times 10^{-9}\times 212000}{20\times 10^{-2}}\\\Rightarrow d=0.71126\ m[/tex]

The separation of the two object on the Earth's surface is 0.71126 m

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