From Speed of Light

The fact that all observers measure the same speed for any light signal (passing through a vacuum) can be used to derive the Lorentz transformation rules in various ways.

The Ship’s Mast

Consider a flashlight or laser pointer shining from the crow’s nest at the top of a ship’s mast down to a point on the deck right at the base of the mast

The Light Clock

If each observer measures time using a clock whose ticks are triggered by the reflection of a light pulse back and forth between two reflecting plates

The Wave Front Formula

The condition that the position of the light signal is given by the same formula in terms of either observer’s coordinates