There are two effects involved here. One is that as the bulb moves away from the observer (in the observer's frame) the last light emitted takes longer to get to the observer. The other is that the bulb's clock appear slow to the observer. The net effect is that the light is seen for a time of 4 min*sqrt(1.99/0.01) or about 4 min*14 = 56 min. If the light blinks on and off, the apparent blinking rate is reduced by that factor of sqrt(199), the relativistic Doppler shift factor.
Mike W.
(published on 03/28/2015)
