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Unformatted text preview: SOLUTIONS to Theory Question 2 Basic relations Position x shows up on the picture if light was emitted from there at an instant that is earlier than the instant of the picture taking by the light travel time T that is given by T = D 2 + x 2 slashBig c . During the lapse of T the respective segment of the rod has moved the dis- tance vT , so that its actual position x at the time of the picture taking is 2.1 x = x + D 2 + x 2 . Upon solving for x we find 2.2 x = 2 x- radicalBig D 2 + ( x ) 2 . Apparent length of the rod Owing to the Lorentz contraction, the actual length of the moving rod is L/ , so that the actual positions of the two ends of the rod are x = x L 2 for the braceleftBigg front end rear end bracerightBigg of the rod. The picture taken by the pinhole camera shows the images of the rod ends at x = parenleftbigg x L 2 parenrightbigg- radicalBigg D 2 + parenleftbigg x L 2 parenrightbigg 2 . The apparent length L ( x ) = x +- x- is therefore 2.3 L ( x ) = L + radicalBigg D 2 + parenleftbigg x- L 2 parenrightbigg 2- radicalBigg D 2 + parenleftbigg x + L 2 parenrightbigg 2 ....
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- Spring '11