I’ve noticed a number of photography instructors who dance around the inverse square law of light without really discussing it. Basically they know that when you move the source of light ways from the subject you need a brighter light to illuminate the subject to the same brightness. They just don’t seem to explain why.
It’s because of the inverse square law of light. The Inverse Square Law states that if the light is moved twice as far from the subject it only shines with one quarter of the brightness.
Say you have a light source 1 foot from your subject and you move it to two feet away, you will end up with only one fourth the amount of light at your subject. If you move the light four feet away you will only have one sixteenth the light falling on the subject.
My crude attempt at drawing a diagram of the inverse square law. The light falling two feet from the source has to cover four times the area of the light one foot from the source.