Reciprocal Diffraction Relations between Circular and Elliptical Plates

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Abstract
Diffraction Patterns inside Elliptical Shadows Due to a Point Source of Light.—When a circular disc with its plane originally tangent to the light wave is rotated about an axis in its plane, the Arago spot changes to a figure with four cusps which move out along the axes of the elliptical shadow, two approaching the foci as limits and the other two going outside the shadow. These changes are shown by a set of photographs obtained with a disc 1.6 cm. diameter placed 2 meters from a pinhole 0.3 mm. in diameter and 5 meters from the photographic plate. The diffraction pattern was found to depend only on the ellipticity of the shadow whether produced by an ellipse or by an inclined disc. Each quadrant of the diffraction pattern was found to be associated with the quadrant of the shadow adjacent to it but on the opposite side of the major axis. Careful measurements of the photographs proves that in each case the diffraction pattern is the evolute of the geometrical shadow. The effect is as though each element of the edge of the shadow contributed a spot along its normal, the result being a caustic curve of diffraction.

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