
A Demonstration of the 180°
Phase Shift of a Wave
upon Passing through the
Focal Point of a Lens.
The 180° shift in the phase of a wave
which occurs when the wave passes through a focal point can easily be
demonstrated by using the following argument. A concave wave front
becomes convex after passing through the focus. Using the arguments
generally employed in constructing the Fresnel zones of the wave front Ф1, it can be shown that the
phase of the resultant electric vector in the vector diagram
corresponds to the vertically upward direction (Fig. 1). The situation
is different in the case of the wave front Ф2 converging to the focus. In this
case, all points on the wave front are of course equally distant from
the focal point, but from the point of observation A which is at the
maximum distance from the vertex B, the rest of the points on the wave
front are located closer to A. When the vector diagram is constructed,
taking into account the fact that waves arriving at A from points on
the wave front which are different from В are leading in phase, one obtains a
resultant electric vector whose phase corresponds to the vertically
downward direction, which also confirms the presence of a phase shift
by π radians (Fig. 2).
