A bell in the middle of a carriage rings if its associated detector observes light pulses from the two lamps at either end of the carriage arriving simultaneously. At time t=100 ns on a clock in the carriage the bell rings. i) What time did the left and right lamps each emit their light pulses, according to the carriage clock? ii) An observer, Anna, is sitting on a bench outside the carriage while the carriage travels past at a velocity of v = 0:99c. According to Anna's very precise wristwatch the bell to rings at 200 ns past mid-day (i.e. 12:00pm + 200 ns). At what time did the lamps switch on according to Anna's watch? (you do not need to consider the transit time of any light or sound to reach Anna; she is a good experimental physicist and has corrected for these delays) iii) When the bell rang, the detector was just passing a post at a position labeled 0 meters. Where were the lamps, measured from this post, when they emitted their pulses of light? Show that the velocity of light from each lamp as it headed towards the detector is consistent with expectations of special relativity. iv) From inside the carriage the lamps are 18m apart. From Anna's observation frame (the bench), what is the distance between lamps.
A bell in the middle of a carriage rings if its associated detector observes light pulses from the two lamps at either end of the carriage arriving simultaneously. At time t=100 ns on a clock in the carriage the bell rings.
i) What time did the left and right lamps each emit their light pulses, according to the carriage clock?
ii) An observer, Anna, is sitting on a bench outside the carriage while the carriage travels past at a velocity of v = 0:99c. According to Anna's very precise wristwatch the bell to rings at 200 ns past mid-day (i.e. 12:00pm + 200 ns). At what time did the lamps switch on according to Anna's watch? (you do not need to consider the transit time of any light or sound to reach Anna; she is a good experimental physicist and has corrected for these delays)
iii) When the bell rang, the detector was just passing a post at a position labeled 0 meters. Where were the lamps, measured from this post, when they emitted their pulses of light?
Show that the velocity of light from each lamp as it headed towards the detector is consistent with expectations of
iv) From inside the carriage the lamps are 18m apart. From Anna's observation frame (the bench), what is the distance between lamps.
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