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The black kettle with chrome represents the extreme in tonal ranges one is likely to encounter, one that exceeds the DR of the camera sensor. Thus it's a given that fill will be needed. It's an afterthought in that tutorial, resulting from bounce off the white walls surrounding the subject rather than a dedicated fill source that was controlled.
Lighting is like cooking in that one can make a lot of variations with 2-4 basic ingredients combined different ways. The most basic ingredients are fill to reveal the shadow detail and key to define the shape. In a situation like the tea kettle a simple strategy for fill is to bounce it down off the ceiling near the camera or a white wall or panel behind and above the camera to create an "over cast day" effect. Joe Zeltsman, the mentor of my mentor Monte Zucker mounted his fill lights permanently to the ceiling aimed backwards at the white wall in his studio to create that type of omni-directional fill effect, so that's not an original idea of mine.
With fill bounced that way to become omni-directional it won't create a distinct catchlight on the shiny black or chrome parts so it would just be a matter of selecting the f/stop needed for DOF then raising the fill level until the darkest parts of the kettle are in the 20,20,20 range. Better to overfill at capture and then darken in PP than under fill and and wind up with nothing but noise in the shadows.
On lighter objects the more noticeable clues to shape come from the shadows. For example when depicting mountain relief on maps the cartographic artist simply draws the shadows the mountalns would cast at 2PM when the sun is hitting them at a 45° angle. The brain, used to seeing objects illuminated at that angle sees the shape of the drawn shadow and infers the 3D shape of the relief, longer shadows being higher peaks. The highlight clues are also important but the reaction to them is more subliminal. If not placed naturally on the top of objects from downward sources the lighting doesn't look "right" for reasons that aren't obvious. A good example of that is flash on camera. It looks fake because the reflections wind up unnaturally low on the cheeks. Take the same flash and raise it so it hits at a 45° angle and the reflections are the same, but positioned where natural light would put them..
The difference with a black object vs a lighter one is that all the clues to 3D shape come from the placement of the highlights and the gradient in the shadows created with the fall off and feathering of the fill source. The object will look "normal" when the reflections of the "key" source are seen in the upper quadrants....
... rather than below the equator, in part because the sun is never seen below the equator...
Getting back to the setting of lights. If the fill is raised to the point the blackest part of the kettle is reading 20 with the 8-bit eye dropper on a scale of 0-255 the highlights in the chrome will nearly always be underexposed because the camera sensor can't handle the extreme tonal range. So a key light is needed. Where to place it?
Above the object so it hits at a natural angle, if that is the goal for the look of the shot. That might not be for a tea kettle. Where are kettles used? On a stove. Were does the heat come from? Below. So for creative purposes one might want to deviate from the "normal" downward angle. The goals for the look of should guide the lighting strategy rather than having a playbook strategy applied to every situation.
In my "normal" black-on-black illustration the small highlight at 2 PM creates the strongest clue to the overall shape of the object, that it is a sphere vs a flat disk, but the more subtle gradient similar to what you might get with a reflector adds more subtle clues about the shape.
A technique I've used on occasion to create that effect with a minimum of gear is a single bare bulb flash in a small white room. The bare bulb creates both a specular "key" highlight on the object and at the same time bounces light 360° off the walls and ceiling and background to create an "overcast" day effect, not unlike how the sky on an overcast day is uniform, but still directional from the spot in the sky where the sun is hiding.
I few years ago a furniture maker e-mailed me wanting suggestions for lighting catalog photos on white backgrounds with only the two Alien Bee 800s they had. It's a similar problem of needing to avoid reflections from the sources except where desired to create the illusion of 3D modeling. This are not the epitome of furniture shots, I just grabbed a table I had handy and in about 15 min. knocked out these examples to illustrate the bare flash / overcast day approach, using the second flash from behind as rim lighting to help the person understand the cause and effect of filling for shadow detail without reflection from the source and modeling shape with the highlight placement.
This was the set-up I used. The rim light with the grid is what I use as hair light for portraits and was already in place.
Not visible in that shot is that there is a black sheet covering the wall on the right. I didn't put it there for the shot, it's always there to cover a huge mirror the previous owner of the house put on that wall. But here is worked to create a "subtractive" lighting effect and shade the reflected light from the right
... this was the result SOOC...
.... and after some basic PP with adjustment layers...
For comparison here is what it looked like with just the bare bulb flash SOOC and with PP:
The strategy was driven by the need to get a foundation of even fill bright enough to reveal the shadow detail without any highlight clues revealing a directional source of the lighting. The single bare bulb flash in the small white room did most of what was needed, the rim light just added a accent.
Mind you I'm not saying that same approach would work for the kettle shot, only that the problem should be approached the same way by first tackling the task of getting detail in the shadows with a non-reflective fill strategy then finding the best strategy to create the illusion of 3D shape on the object with placement of a reflection of the key source (direct from a SB or bounced off a white panel) and nuancing of the shadow gradient by spacing from the white surround and using either reflectors or black flags to make the other parts appear higher or lower relative to each other and define the shape in a way that seems "natural" in that it would mimic the appearance of the object on the same background if taken outdoors at 2PM.