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University of Wisconsin - Milwaukee

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Problem 45 Medium Difficulty

A vehicle with headlights separated by 2.00 m approaches an observer holding an infrared detector sensitive to radiation of wavelength 885 nm. What aperture diameter is required in the detector if the two headlights are to be resolved at a distance of 10.0 km?

Answer

0.00540 m

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Top Physics 103 Educators
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Video Transcript

So we have the separation between two headlights off ICO is two meter and this vehicle is approaching an observer who is using an infrared sensitive detector detector that is sensitive to web length 885 nanometer. Now, if the Observer wants to result those two headlights from the distance of 10 kilometer, we have to find the diameter of the oppressor of the sensor. So first used the fact that the angular separation of the headlight is that, uh and that's going to be ableto s over our where s is the separation between the two objects, Tim. So this is going to give us two over 10,000 and this is gonna be two times 10 to the negative for radiant. Now, if the headlights are to be just resolved, that means data is going to be approximately equal to that. I mean, right. But we also know that the limiting angle of resolution for circular preacher is that I mean equals 1.2 to Lambda over the diameter of the appraiser. So from sure we can actually write down D. He calls 1.22 lambda over there. I mean, which is gonna be 1.22 times 8 85 times, 10 to the negative, nine over two times, 10 to the negative four and this is going to give us 5.4 millimeter.

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

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Other Schools

Zachary M.

Hope College