A Geometric Derivation of the Doppler Shift for Light

The Doppler effect for light is analyzed using a geometric description of light propagation in vacuum. By considering the actual displacement of the light source relative to the observer during the propagation time of the light signal, expressions for the change in wavelength for approaching and receding motion are derived. The analysis relies solely on the speed of light and the relative velocity between the source and the observer and leads to the classical expressions for the Doppler shift. Figure-based reasoning is used to clarify the geometric relationships.