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We can see diffraction of light if we allow light to pass through a slit, but why doesn't diffraction occur if we obstruct light using some other object, say a block? Why are shadows formed? Why doesn't light diffract around the obstruction as it does around the slit?

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"Why doesn't light diffract around the obstruction as it does around the slit?". But it does. See for instance Babinet's principle –  Trimok Aug 13 '13 at 11:07

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Light will diffract around anything, including a block. We simply don't observe this diffraction because most blocks are very large compared to the wavelength of light. One historically-famous example of diffraction around an object is Poisson's spot, in which diffraction around a circular disk is easily observed.

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Good question. Actually, early 19th century this question was put forward as an argument against diffraction theory.

The below is from http://minerva.union.edu/jonesc/scientific_photos%202010.htm :

enter image description here

"In 1818, Fresnel presented his theory explaining diffraction of light. Poisson denied the truth of the theory, and argued that a consequence of the theory would be that there would be a bright spot right in the middle of the shadow of a circular object. The spot, shown above of the shadow of a ball bearing suspended on a needle, was promptly discovered by Arago. This was a lot harder to do before lasers were invented!"

Note: observation of such diffraction patterns are best done in (nearly) monochromatic light. Hence the remark about using lasers. The bright spot at the center of a circular shadow is known as an Arago spot.

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