Visual Appearance of a Rod Moving Parallel to Itself

Consider a rod at rest in an inertial frame O', with O' moving at speedalong the x axis of an inertial frame O. If the length of the rod in O' isthen in the inertial frame O, an observer will measure the length of the rod to be

This is not the same as the length of the rod perceived by an observer in O.

A camera at rest at the origin of O takes a photograph of the rod atwhen the origins of O and O' coincide.

The light from the end A of the rod takes a timeto reach O so the light from A was actually emitted atsince it reaches the origin of O at

Applying the Lorentz transformation to the emission of the light pulse at A gives

Similarly the light from end B of the moving rod is emitted atso

Subtracting these gives

From the diagram aboveso