Fresnel mirrors
This device uses a primary source combined with two reflecting plan mirrors that make a slight angle
between their planes. Their source is located at the distance
on the mirror's edge. Each mirror gives a virtual image of the primary source and both images act as secondary sources. In the intersection area of both beams we can observe interferences. Figure 2 presents the Fresnel mirrors device.
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We demonstrate geometrically that the secondary sources are used on a circle with center
and radius
. The screen is placed at the distance
from the secondary sources, parallel to the sources plane. The secondary sources are quantity
away . We recognize that we have to process the interferences between two spherical wavefronts emitted by both secondary sources. . In all point
, the interferences are written
And in the case of the parabolic approximation where
,
As the angle
is small, we have the triangle
:
So comes :
And the interfringe is :
To define the fringes's geometric shape, we will determine the place of the points for which the phase is constant, which leads to
, as the other magnitudes are set by the circuitry geometry. The fringes are vertical, perpendicular to the figure plane, and regularly spaced from the interfringe
.