The edges of a shadow are bright due to wave diffraction and interference effects of light.
the verdict
SUPPORTED
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refutedsupported
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Reference sources confirm that bright bands and intensity fluctuations at the edges of shadows are produced by the diffraction and interference of light waves.
But the assumption enabled him to establish the principle of interference,[6] one of the most fertile in the science of physical optics. The undulatory theory was also accepted by Fresnel who, perceiving the inadequacy of the researches of Huygens and Young, showed in 1818 by an analysis which, however, is not quite free from objection, that, by assuming that every element of a wave-surface could act as a source of secondary waves or wavelets, the diffraction bands were due to the interference of the secondary waves formed by each element of a primary wave falling upon the edge of an obstacle or aperture. One consequence of Fresnel’s theory was that the bands were independent of the nature of the diffracting edge—a fact confirmed by experiment and therefore invalidating Young’s theory that the bands were produced by the interference between the primary wave and the wave reflected from the edge of the obstacle. Another consequence, which was first mathematically deduced by Poisson and subsequently confirmed by experiment, is the paradoxical phenomenon that a small circular disk illuminated by a point source casts a shadow having a bright centre. § 12.
The law of diminution when V is moderately large is easily expressed with the aid of the series (16), (17) for G, H. We have ultimately G = 0, H = (πV)−1, so that
I2＝1/π2V2,
or the illumination is inversely as the square of the distance from the shadow of the edge. For a point Q outside the shadow the integration extends over more than half the primary wave. The intensity may be expressed by
and the maxima and minima occur when
whence
When V = 0, viz. at the edge of the shadow, I2 = 1/2; when V = ∞, I2 = 2, on the scale adopted. The latter is the intensity due to the uninterrupted wave. The quadrupling of the intensity in passing outwards from the edge of the shadow is, however, accompanied by fluctuations giving rise to bright and dark bands. The position of these bands determined by (23) may be very simply expressed when V is large, for then sensibly G = 0, and
n being an integer. In terms of δ, we have from (2)
The first maximum in fact occurs when δ = 3/8λ −·0046λ, and the first minimum when δ = 7/8λ −·0016λ, the corrections being readily obtainable from a table of G by substitution of the approximate value of V.
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