First flashlights and now pizzas? How about instead you actually use the definition (https://en.m.wikipedia.org/wiki/F-number) and consider the concept that the luminance per area does not change. Better yet, perform the experiment I suggested. Have you actually tried using the same lens on a two different format cameras with the same exposure settings and compared the images? I actually have (using the same lightmeter measurements and exposure settings), and I KNOW the answer even if I didn’t believe the definition. You should try it.

Educate me, please! I was just reading some information on the Tamron 90mm f/2.8 Macro lens that I am thinking of buying, in which someone stated that on a DX camera, the effective field of view with a FX lens, would be ~ a 135mm equivalent, but the crop factor would also affect the f/stop, raising it to f/4.2.

Not saying this isn't true, but it is the first time I have heard that, and it doesn't seem correct to me. Despite the narrower field of view, the distance from the front element of the lens to the sensor doesn't change, and the light has no further to travel than before, so the f/stop should remain the same. (?)

Next, and I admit this is something I have never given much thought to, but lenses with internal focus do not change their physical length, therefore light has no further to travel from the lens' front element to the sensor, which I understand is the reason for non-internal focus macro F/2.8 lenses to have an actual rating of ~ f/4 at 1:1 distances, when their lens barrels are extended "waaay out yonder".

That's the reason my 70-300mm non-IF zoom is placarded at F4.5-5.6, and my 70-200 I F zoom is a fixed F/4 throughout their zoom ranges. So, providing my understanding is correct, there should need to be no "adjustment" of the f/stop at close focus distances for Internal Focus lenses. Or?

Do you have one of those flashlights that can zoom? The one in which you can adjust the light to be bigger or smaller in diameter? That can explain you dilema.
The flashlight throws out the same amount of light. Make the diameter small and it becomes bright. Make it big and it become dull.
In a camera lens, if everything stays the same except for the sensor size, if you view that in their natural state, there would not be any change in brightness in the image. you only get a cropped photo.

But if you print the image from the smaller sensor, to equal the bigger sensor, then your print will appear as if it was taken in a darker situation in comparison. Just like the small light from the torch spreading out to a bigger diameter.
In photography., we see the change as a higher f stop number equivalent.

The smaller sensor size is getting the same amount of light, but it is being distributed to a higher density smaller pixel wells. Much like a pizza sliced to share with 50 people (apsc) and 25 people (full frame). Its the same pizza, but they will not get the same size of slice. The 50 people will get a smaller bread to bite.

Do you have one of those flashlights that can zoom? The one in which you can adjust the light to be bigger or smaller in diameter? That can explain you dilema.
The flashlight throws out the same amount of light. Make the diameter small and it becomes bright. Make it big and it become dull.
In a camera lens, if everything stays the same except for the sensor size, if you view that in their natural state, there would not be any change in brightness in the image. you only get a cropped photo.

But if you print the image from the smaller sensor, to equal the bigger sensor, then your print will appear as if it was taken in a darker situation in comparison. Just like the small light from the torch spreading out to a bigger diameter.
In photography., we see the change as a higher f stop number equivalent.

The smaller sensor size is getting the same amount of light, but it is being distributed to a higher density smaller pixel wells. Much like a pizza sliced to share with 50 people (apsc) and 25 people (full frame). Its the same pizza, but they will not get the same size of slice. The 50 people will get a smaller bread to bite.

You are correct. An f2.8 is an f2.8 regardless of what format camera it’s used on. It’s the physical ratio of the focal length to the entrance pupil diameter and neither change regardless of what sensor the image is projected onto.

This debate surfaces periodically on UHH, and proponents of the idea that the f stop changes based on the sensor size refuse to believe otherwise despite the actual definition, the fact that the lens yields the same exposure on both FF and crop bodies, or the fact that light meters don’t have separate scales for various sensor sizes.

Nope. With the flash light analogy, you’re actually changing the luminance per area by concentrating the light, but that’s not what happens with a camera lens. In that case, unlike the flashlight, whose illuminated area gets smaller, the projected area for the lens remains the same, but only a percentage is used to illuminate the sensor - the luminance per area does not change.

You can easily prove this to yourself by using the same lens on a crop and a FF camera at the same exposure settings, and the resulting image will be the same brightness. Or you can use a lightmeter, meter the same scene, set the same settings and expose that same image on two different format cameras (film or digital) and look at the resulting brightness/density and they will be the same if the shutters are accurately calibrated.

Educate me, please! I was just reading some information on the Tamron 90mm f/2.8 Macro lens that I am thinking of buying, in which someone stated that on a DX camera, the effective field of view with a FX lens, would be ~ a 135mm equivalent, but the crop factor would also affect the f/stop, raising it to f/4.2.

Not saying this isn't true, but it is the first time I have heard that, and it doesn't seem correct to me. Despite the narrower field of view, the distance from the front element of the lens to the sensor doesn't change, and the light has no further to travel than before, so the f/stop should remain the same. (?)

Next, and I admit this is something I have never given much thought to, but lenses with internal focus do not change their physical length, therefore light has no further to travel from the lens' front element to the sensor, which I understand is the reason for non-internal focus macro F/2.8 lenses to have an actual rating of ~ f/4 at 1:1 distances, when their lens barrels are extended "waaay out yonder".

That's the reason my 70-300mm non-IF zoom is placarded at F4.5-5.6, and my 70-200 I F zoom is a fixed F/4 throughout their zoom ranges. So, providing my understanding is correct, there should need to be no "adjustment" of the f/stop at close focus distances for Internal Focus lenses. Or?