Another thought experiment in special relativity

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We present a simple thought experiment in which a beam of light of a finite length (a light-pulse) enters a detection device that consists of a wave detector and a light bulb. We examine the experiment from the reference frame where the device is stationary and from the reference frame where it moves at a constant velocity along the axis of the beam. We use basic special relativity to derive the formulas that show how the length of the light beam is transformed between the reference frames. We further show that the uncommon formulas for length transformation of a light beam do not contradict the usual relativistic result that a uniformly moving non-light object will be Lorentz contracted along the direction of its motion.