CharleyL
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I think you are getting a bit "hung up" on precise measurements and F-Stops. You are over thinking this. It's best to test these modifiers in your own location, be it studio or other, to see the results. With experimenting you will learn what soft and hard lighting means, and how to work with it. Softer light means less sharp transition between bright and shadow. The softer the light source the more gradual the transition and more even the light on the model.
Some times you want this and sometimes you don't, Shiny jewelry looks flat in soft light, but sparkles in hard direct light. Skin looks best when evenly lit without shadow lines. The larger the size of the light source, the softer the light is, but it also will not be as bright as the smaller light source. The light is getting spread out over a larger surface. White umbrellas do reflect light some, but their translucent material makes them work better as diffusers where the light is passed through them to toward the model rather than reflected off of the inside surface.
I have one 45" translucent white umbrella, and true, the light passing through it will be about 1 F-stop less than not using it with the same light source, but the light quality for photography will be much softer and better, due to the size increase from the light source to the umbrella size, if your light source is spreading wide enough to light the entire umbrella. Using a Godox SK300 light (the smallest that I have), and using this size white translucent umbrella and light source in my white wall/ceiling studio I get very satisfactory soft light results when lighting a model about 5' from the umbrella.
When you add a diffuser to a light source, if your light source can illuminate the entire diffuser (umbrella) the diffuser then becomes your light source for measuring spacing between light source and model (inverse square law). A white translucent umbrella spreads light in all directions. If your studio is all white, some of the light will be reflecting off of all of the white surfaces and back on the model too. The light is spread well before it reaches the model, giving very soft, even light. But the light hitting the white walls and ceiling of my studio is also reflecting in all directions and making this umbrella light source effectively even larger, so very, very soft light reaches the model.
A silver umbrella is a reflector, not a diffuser. The distance from your light source into and then back out of the silver umbrella adds to the distance between your light source and model and allows spreading of the light based on this increased distance. With increased distance between light and model the Inverse Square Law causes less light to reach the model. Without a diffuser, it will be harder and more focused light too. There will be very little light reflecting off the ceiling and walls, even if they are white.
If you add a diffuser to the silver umbrella you will then get a better diffused and more even light from it on your model at slightly less brightness (1 F-Stop) because of the diffusion of this material. The result will be somewhere between the translucent and silver umbrella in use. Again, if the light source spreads sufficient to light the entire diffuser, your light source will be the diffuser surface, so 45" diameter, but it will be more directed toward the model with much less reflected off the white walls and ceiling, so a bit harder light than you get when using the white translucent umbrella in this white studio at the same light level settings. Putting math numbers on all of this gives me a headache. I just learned from testing what works well for me. Knowing what the inverse square law means is far better than trying to apply it mathematically to every situation. Again, a little experimenting with the light and subject spacing will give you what you need to know without the need to mathematically solve each situation.
I have a pair of 32" white translucent umbrellas, a pair of 32" silver reflector umbrellas, and a pair of
32" gold reflector umbrellas. I've had them for probably 25 years, because I bought them when I first became interested in portrait and studio photography, but had no studio. I tried them and they worked, but I never cared for the gold umbrellas because I didn't like the color change result that they gave me. I prefer 56-6200 K, so bright white. Silver works, but I like using the white translucent as diffusers.
Then one day a photographer friend said that 32" was too small and that I needed much larger. Well, about that time I was building my studio in my home with an 8' ceiling, which limited me to something less in diameter. I wanted 72", but wasn't successful at finding 72" easily at a reasonable price, so I went with the 54". On experimenting with it, I found that there is an improvement over the 32", but not as much as I had expected. For portrait work, the 32" are just fine in my white studio. I have pairs of many sizes of soft boxes that usually get used for my portraits in the studio now, but there isn't anything at all wrong with using umbrellas.
You need to learn by practice and testing what result each soft box, umbrella, diffuser, light source, etc. will do for you, so you can decide which will do the best job for you and your way of shooting. Don't get hung up on the math.
I learn by doing. I understand the math, but don't see the need for exact math measurements and math calculations. Learn how each works for you through some experimenting and test shots. Never mind trying to solve photography via math. Understand the basics through experimenting and enjoy the process. What is available, like umbrellas, soft boxes, speedlites, studio strobes, etc. all work, but learning what each does better, so you can choose the right one for the situation, is what makes great pictures and you a great photographer.
Charley
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