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Classical Mechanics Level 3

Recently there have been technological advances that allow for 3-d imaging up to kilometers away of an object. This can be done by using laser light that bounces off an object. By measuring the time it takes the laser light to get to the object and back, one can construct a detailed 3-d image of the object. The obstruction has been to get enough of the light back to actually make an image, but new detectors are sensitive enough to overcome this limitation.

If I want to measure a 3-d object down to millimeter accuracy, to what accuracy in seconds must my detector be able to measure the time of arrival of the light that bounced off the object?

Remember... the light has to bounce there and back.

Details and assumptions

  • The speed of light is \(3 \times 10^8~\mbox{m/s}\).

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