Diffuser size vs distance - any formula available?

Is there a formula one can use to calculate at what distance a modifier with area "A" will be no different from a point source of light?
And the reverse (even though this one is more subjective): at what distance a modifier with area "A" will provide a "soft" light?

Its not a "formula" but generally, its considered that the modifier has to have twice the long dimension measurement as the distance from the subject to be a truly soft source that delivers a wrapping light.

As for point source, if a modifier is far enough away from the subject so the transition from shadow to highlight area is a sharp edge, then the source is effectively a point source. The most extreme example is the sun.

Also it depends on how even the light comes out from that modifiers from edge to edge. If we use very large softbox but the hotspot in the center is too bright, it will gives less wrapping effects, etc.

And also how paralel the light comes out from the modifiers. If we use perfect parabolic shape modifiers and the strobe head in the focus position and without any diffusers, even if it has very large size and very close, it will gives a hard shadow

nixland wrote in post #17923775
Also it depends on how even the light comes out from that modifiers from edge to edge. If we use very large softbox but the hotspot in the center is too bright, it will gives less wrapping effects, etc.

Which is why I like deflectors ala beauty dish in my soft boxes. Or, having the flash tube pointing toward the back.

Another option is to feather the softbox to control how the light falls on the subject.

The sun is quite close to a point source, but shadow edges do soften progressively with distance. My hardest light, being a projector, is even harder. An interesting modifier is the silk (either plastic or real "china" silk) which combines both diffuser and scrim qualities: edged shadows and your choice of fill ratio.

RicoTudor wrote in post #17923805
The sun is quite close to a point source, but shadow edges do soften progressively with distance.

Care to elaborate on this statement in blue?

Wilt wrote in post #17924364
Care to elaborate on this statement in blue?

If you hold your hand just in front of a wall, the shadow cast in sunlight will look like a hand. As you move your hand farther from the wall, the shadow become softer, then indistinct, then disappears entirely. This progression doesn't happen with a true point source. At Earth distances, the sun looks like a disk.

RicoTudor wrote in post #17924375
If you hold your hand just in front of a wall, the shadow cast in sunlight will look like a hand. As you move your hand farther from the wall, the shadow become softer, then indistinct, then disappears entirely. This progression doesn't happen with a true point source. At Earth distances, the sun looks like a disk.

I'm not a scientist but I think the phenomenon you are describing is caused by the bending of the light particles around the subject (hand).

A similar phenomenon I've noticed when looking out an aircraft window at altitude is the aircraft's shadow on the ground encircled by a bright halo.

The umbra, penumbra are two parts of a shadow, created by any light source after impinging on an opaque object.
For a point source only the umbra is cast; and the region of diffuse shadow created by a somewhat broad source is called the penumbra, which is at the edges of the umbra.

Not sure why the umbra seems to disappear with long distances to the wall, but some enhanced scatter of light particles due to atmospheric moisture and dust could account for it, more than simply penumbra due to relative size of the source.

dmward wrote in post #17924477
I'm not a scientist but I think the phenomenon you are describing is caused by the bending of the light particles around the subject (hand).

A similar phenomenon I've noticed when looking out an aircraft window at altitude is the aircraft's shadow on the ground encircled by a bright halo.

I thought the only thing that can bend light is a black hole. Light particles travel in a strait line but can bounce off a surface and change direction.

digital paradise wrote in post #17924717
I thought the only thing that can bend light is a black hole. Light particles travel in a strait line but can bounce off a surface and change direction.

Light can be bent many ways. Light is definitely being bent by the various elements in your lenses. Light is bent when going through water at an angle. Light can be bent when going through pockets of air that are more moist than surrounding air.

SkipD wrote in post #17924731
Light can be bent many ways. Light is definitely being bent by the various elements in your lenses. Light is bent when going through water at an angle. Light can be bent when going through pockets of air that are more moist than surrounding air.

That I'm OK with. Makes perfect sense for lenses because that is what they do. I just thought it won't bend around something a brick.

digital paradise wrote in post #17924717
I thought the only thing that can bend light is a black hole. Light particles travel in a strait line but can bounce off a surface and change direction.

SkipD wrote in post #17924731
Light can be bent many ways. Light is definitely being bent by the various elements in your lenses. Light is bent when going through water at an angle. Light can be bent when going through pockets of air that are more moist than surrounding air.

I agree with DP, basically. (Massive objects like galaxies also bend light.)

Light is refracted at surfaces, not "bent". If you like, we can say light is bent in air and liquids with varying properties, but that is also refraction.

So if you like, we can speak of "bending" of sunlight to affect the form of shadows, but this effect is almost always very small. The shadow would look essentially the same if there was no such "bending". The umbra and penumbra of a shadow are the result of straight line propagation and simple geometry.

The angular angle of the sun from the earth is 0.5 degree.
Using angular size calculator on the internet:

if the object is 1 inch from the wall, the fuzzy area of penumbra is about 0.2 mm (sharp edge shadow)

At 5 feet it will have 1.3 cm fuzzy area.