Don,
Just to clarify: Using a longer lens to get the same print size will not result in a longer exposure time. The same portion of light is hitting the paper at the same intensity with both the short and the long lens. It's just that the shorter lens has a wider angle of projection and the longer has a narrower angle. Since the light is focused and directed, the inverse square law does not apply here. If the image size (read magnification) is the same, and the f-stop is the same, and the enlarger-light intensity the same, the exposure time will remain the same too.
Best,
Doremus
Actually, the inverse square law always applies no matter what. There are no exceptions in physics.
You have a finite number of photons that get emitted by the lamp.
When you use a longer lens, the light cone is bigger than when you use a short lens at a given distance.
What makes the image size the same is the negative holder itself which absorbs all the photons that fall outside of the negative place.
To focus a longer lens, you need to put it further away from the negative than with a short lens.
Since you project a smaller negative, you need to rise the head more to get the same size image. That means that more photons get absorbed by the negative carrier and the internals of the enlarger.
I really like an analogy I once heard in College. Light is like peanut butter. If you spread a teaspoon of it on a slice of bread, you'll have a pretty thick coating. But if you double the size of surface to coat, increasing it to four slices, you'll have only enough peanut butter to lightly cover them.
Cropping an image at it's source doesn't condense light in a smaller area.
I just measured it using my enlargers.
6x6 negative focused to a 10x10 with a 135mm: 27 inches from lens to baseboard.
6x6 negative focused to a 10x10 with a 75mm: 16 inches from lens to baseboard.
If it didn't have any effect, the projectors in movie theaters wouldn't need such powerful bulbs.