Why Is the Edge of a Shadow Often Blurred?

The edge of a shadow is often not a perfectly sharp line because everyday light sources usually have an area. A lamp’s glowing surface, and even the distant disc of the Sun, sends light towards the space behind an object from slightly different directions.

Hold a hand in front of a wall. The darkest region, where no part of the source is visible, is the umbra. Near its edge, the hand blocks only part of the glowing surface while the rest still illuminates the wall. This gradual transition is the penumbra. When the hand is close to the wall, the projections made by different parts of the source nearly overlap, so the penumbra is narrow. Move the hand farther away and those projections separate more, usually widening the blurred band. A smaller emitting surface also produces a sharper edge.

Blur therefore does not necessarily mean that the eye is out of focus, nor that light suddenly scatters at a shadow’s boundary. In this ordinary example, geometry is the main cause: rays leaving different points of the source draw slightly displaced shadows of the same object. NASA uses the same principle to explain eclipses: complete blockage of the Sun forms the umbra, while partial blockage forms the penumbra.

https://science.nasa.gov/eclipses/geometry/
https://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/shad.html