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University of Wisconsin - Milwaukee

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Problem 48 Medium Difficulty

A spy satellite circles Earth at an altitude of 200. km and carries out surveillance with a special high-resolution telescopic camera having a lens diameter of 35 cm. If the angular resolution of this camera is limited by diffraction, estimate the separation of two small objects on Earth's surface that are just resolved in yellow-green light $(\lambda=550 \mathrm{nm})$

Answer

0.383 m

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

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Video Transcript

So we have the distance between Earth and the satellite is 200 kilometer, which is our I'm gonna convert this to meter, which is two times 2 95 meter. The diameter of the lens of the camera used by this satellite to spy and earth is de course 35 centimeter, which is 0.35 meters. And the web link of the light uses 550. Narrator which is 5 50 times to do negative nine meter. So when the two objects are just resolved, just like in problem number 47 then it is going to be data. It goes that I mean, because 1.2 to Lambda over tea, all right? And we know that data is all toe also s over our. So from these two guys here, we can actually write down s it calls 1.2 to lambda over D. Times are and plug in all the values here. You're going to get sirrah 0.38 meter, which is 30 ace inhibitors.

University of Wisconsin - Milwaukee
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Aspen F.

University of Sheffield

Meghan M.

McMaster University