The Appearance of a Rod Perpendicular to the Direction of Travel
Consider a straight rod AB of lengthat rest in an inertial frame O', with O' moving with speed v along the x axis of another inertial frame O.
A photograph of the rod is taken from the origin of the inertial frame O, at the instantwhen the origins of the inertial frames coincide.
To reach the origin of O at t=0 light must leave the points A, B and C (the ends and centre of the rod) at timesandThese are not the same, and in order to reach O at t=0, the light rays must leave before t=0.
Consider the light leaving from the centre of the rod C to reach the origin of O' atThe light must must travel a distanceand must leave C at
The Lorentz transformation gives
The equation above gives the apparent x coordinate of the mid point of the rod. Some illustrative examples are shown, with