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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 + β √ D 2 + ˜ x 2 . Upon solving for ˜ x we find 2.2 ˜ x = γ 2 x βγ radicalBig D 2 + ( γx ) 2 . Apparent length of the rod Owing to the Lorentz contraction, the actual length of the moving rod is L/γ , so that the actual positions of the two ends of the rod are x ± = x ± L 2 γ 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 ± = γ parenleftbigg γx ± L 2 parenrightbigg βγ radicalBigg D 2 + parenleftbigg γx ± L 2 parenrightbigg 2 . The apparent length ˜ L ( x ) = ˜ x + ˜ x is therefore 2.3 ˜ L ( x ) = γL + βγ radicalBigg D 2 + parenleftbigg γx L 2 parenrightbigg 2 βγ radicalBigg D 2 + parenleftbigg γx + L 2 parenrightbigg 2 ....
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 Spring '11
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 Light, ........., Learly Llate, Learly − Llate

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