Tomsk State University. Physical Department.
Laboratory of training physics experiment

Phase Shift upon Passing through the Focal Point     Обратно     

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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).


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A laser can be conveniently used to demonstrate this. The expanded and collimated beam of the laser is directed to a Mach-Zender interferometer (or a Michelson interferometer), as shown in figure. A lens L with a focal length of 2 m is placed in one arm of the interferometer. Interference rings are produced by the interference between the waves passing through the lens and those going along the second arm.


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The center of the interference rings changes from light to dark on going through the focus, which confirms the phase change of π.

This phenomenon was studied by Gouey, Fabry, Zeeman, and Sagnac, using rather complicated apparatus requiring a large space with a length of over 7 m.