Driving 30MPH. The light turned yellow when we were 100 feet from the intersection. If you are traveling straight through the intersection, you can be up to 154 feet away when the light turns yellow and make the light before it turns red.

As we decelerated to make the turn, I realized we might not make the light and had to decide whether to take the turn at an aggressive speed or heavily brake to a stop. Suddenly stopping would pose a significant risk to the passengers in my vehicle and in the vehicle behind me. I observed that the intersection was clear and committed to the turn.

This is the exact 'dilemma zone' described by Mats. If you are still having a hard time picturing it, there are plenty of diagrams in the ITE journal article that explains his calculations.

If the period of the yellow is too short, you can't safely stop in time.