Soft boxes came out with the idea being to reproduce a diffuse window light. The original light boxes in fact were hard shells with multiple lamps inside. Heavy, hard to move around and always used at a distance relatively far from the subject made for a convenient way to make a soft light for portraiture , and or fashion with use of speed lights.
With video becoming more popular and portable, the need for soft light weight rib mounted sewn fabric single source lightweight soft boxes ( rectangular and square) became the norm. The popular brands of the day were Photoflex, Chimera, and Plume.
The question that comes up often in forums is soft box or beauty dish?
The question should really be round or square?
Let’s look at what the differences are.
The diffuser,: it is placed between the light coming from the interior surfaces of the shell or reflector. Many have silver inserts, some have white added or painted white. Plume were the first to have interior baffles with a concentrated diffusion in the centre for even distribution towards the corners in the case of soft boxes.
Both soft boxes and beauty dishes are made to push the light in directions making use of the shape of the reflector. The light then is not only going forward from the flash if there is no baffle, but also at various angles with large amounts of scatter from the parabolic nature of the reflectors. An efficient reflector will be one that directs the light forward and the largest proportion of the light coming off the reflector is directed in an even but similar direction as the source. This is one reason why a true flash has a very different light quality than a small hot shoe flash inside a soft box or beauty dish.
When the light strikes the diffuser surface it will be reduced in intensity as well as redirect some of the light radiating outwards from the translucent fabric (or surface) to some degree. This redirection will have little consequence if not in very close proximity.
When the light source is large, and close relative to the subject this is what makes the shadow transitions gradual. It is the size of the source and distance to subject that appear soft as the transitions are gradual. Some confuse this with lower contrast which it is not. In fact the light if very close will be quite bright on the close side and possibly relatively dark in the shadows even though the transition is subtle between the two.
The effect of the size of the light relatively large compared to the subject is termed wrap or light wrapping. The speed at which the change happens is exactly what you want to watch for if you have modelling lights that represent the flash. The difference of only a few inches makes a huge difference. There is a point at which the light is too large, the skin texture is too filled thus lacks life. Moving the light back a few inches or turning it away can reveal the missing texture, and have more defined specular highlights.
The further you move the light away the less wrap you will have, as it’s size relation will become equal, and the light will fill less due to the collimation of the light.
Back to the question of round or rectangular diffusors.
When you are in close proximity, the geometry of the surface becomes the crucial factor when the light is used on beauty and portraits.
Since you know the diffusion effect of the surface is only significant when in very close range of the subject and the size is larger than the subject , the direction combined with the edge effect is what will determine the graduation of light and the shadow transitions.
While it is not obvious at first, think about the distance from a round source compared to a rectangular soft box. The nose shadows if front lit with a round source are equidistant. Square and rectangular lights have a variable that causes double shadows around the nose under the same light direction. Rectangular lights can be used from oblique angles where the distance will make the shadow shapes more or less equal, yet front or normal beauty light will almost always be questionable due to cross shadows.
There you have it, round for front or beauty lighting, rectangular for oblique side lighting or very high with some distance to subject.