[paul.fr]

THIS topic reminded me of this question:

You have fours incandescent light bulbs in a row, there is only a 2cm gap fromone bulb to the next. From the centre point of the four bulbs move away 18 inches and place a pencil stood upright there. You have four shadows of the pencil, but why?
why does the light from the 4 bulbs not act as one, cancelling the individual lights out and just give one shadow?

Hope I explained that OK.

[JP]

I'd explain this by setting up a diagram of the situation.  Each bulb can be thought to emit light rays in all directions.  Any place the light rays reach ends up being lit up by the bulb.  Now, draw a bunch of light rays heading from the bulb towards the pencil.  Any rays blocked by the pencil don't reach the other side, so that bulb casts a shadow there.  The size of the shadow depends on the distances you specified and the size of the pencil.  When you repeat this for all four bulbs, you can see how the shadows overlap and where they're separated.  In order to see four shadows, the four shadow regions need to be separated from each other.  I haven't done the math for your numbers, but if you see four distinct shadows, that must be the case.   

[JP]

[diagram=371_0]

^here's the ray diagram to go with my explanation.  Yellow circles = bulbs, orange hexagon = pencil, black lines = rays.  The shadow is the region behind the pencil with no rays.

[lyner]

there are several 'penumbras' but no total shdow.

[LeeE]

You get multiple shadows because the wavelength of the light you are using is much smaller than the gap between the sources, so each source acts as a discrete emitter.  If you were to use long enough wavelength radiation i.e. microwaves, the four 'light' bulbs would act as a single source.

[paul.fr]

  The size of the shadow depends on the distances you specified and the size of the pencil. 

Don't quote me on the distance, JP, it was a long time ago!

there are several 'penumbras' but no total shdow.

Umbras and Penumbras, eh. Care to explain what they are?

[lyner]

You're into the realm of UHF wavelengths, at least.

Umbra is the full shadow - like in a total eclipse when you can't see any part of the Sun.
Penumbra is the partial shadow - when the light source is large / of the same order as the  obscuring object. Some of the light gets round the edge of the obstacle. This is the effect when the Moon partially covers the Sun and the sky gets dimmer but there's still a bit of Sun visible.

[LeeE]

I figured microwaves (generally up to 10cm) because of the 2cm spacing.  Even then though, and assuming the effective emitting surface is flat, and not curved, there will always be at least a tiny region of total shadow (assuming no ambient illumination) behind the pencil.  As the emitting surface gets bigger the region of total shadow will extend less far away from the pencil (actually, with a hexagonal x-section pencil this won't always be the case, depending upon the orientation of the pencil).

[lyner]

My thinking was that total aperture width counts - so a bit longer than your estimate. That's all. No real disagreement.
There is, of course, a major difference in principle between  incoherent sources (hot filaments) and coherent sources (microwave source).