I was just thinking about shadows the other day.
If you look at photographs taken with a flash,
they often have really harsh, sharp edged shadows.
But,if the photographer decides to get the light
from other sources, the shadows have a nice large
penumbra, sometimes so much that the shadows
aren't visible. In these cases, the shadows
produced by the flash are from a small light
source, and the shadows that have large penumbras
are produced by very large light
So why does a large light source
make a larger penumbra? Let's try a"thought"
experiment. Let's take one object, and two very
small light sources that are separated. If we
just turn on one light , the object's shadows
should be well defined- no penumbra and all umbra.
Now, if we turn on the second light, there will
be two shadows, but the dark parts won't be as
dark as with one light. Why is this? One of the
lights is putting light into the other light's
shadow. In a way, we've made a well-defined
So how does this all apply
to your original question? You can think of the
large light source as have a bunch of small lights
at the opening. The more spread out the lights
are, the more spread out the penumbra is and the
smaller the umbra is, just like our thought
experiment. If you keep shrinking the distance
between the light sources, eventually you end up
with one tiny light source again, and the shadow
should be all umbra.
Another way to look at
this is with ray optics. You can look up
information about ray optics in many textbooks on
physics. Ask your teacher if you need help
finding information. Once you've looked at ray
optics, you can figure out how bright any point is
by seeing how much of the light source that point
"sees." Just as an example, in the umbra, those
points can't see the light, so that's why it's dark.
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