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In the United States, traffic lights are in the category of "traffic control devices" (which also includes signs, pavement markings, etc). There is a US Federal Manual on Uniform Traffic Control Devices (MUTCD) which all states are supposed to follow so that traffic signs and signals are pretty much the same from state to state. The MUTCD contains formulas for calculating the duration of the yellow (sometimes called "amber") traffic light phase to minimize the frequency of collisions near, at, and in intersections. Factors include traffic speed approaching the light and speed of cross traffic, and seeing distance to the light (curves/hills, etc.). The yellow-light interval is supposed to be between 3 and 6 seconds.

However, adherence to the MUTCD is not rigorously enforced, and yellow light durations are sometimes set with goals other than minimizing collisions. It is well demonstrated that a relatively long yellow light drops red-light running to nearly zero, which is good for safety but bad for revenue from red-light ticket cameras; companies contracted to run red-light camera programs have often been caught colluding with the municipal or state agency in charge of the lights to shorten the yellow light time. This creates a "dilemma zone" where a non-speeding driver must choose between stopping short for a sudden red light after a quick yellow (and risk being rear-ended, with more money for the insurance company) or going through the suddenly-red light (and getting a ticket, with more money for the red-light camera operator and the city). Such is the influence of the red-light camera industry that the MUTCD protocols for yellow-light duration have been weakened to produce generally shorter yellows despite today's higher traffic speed and density. There is more information in the article(s) linked below.

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Q: Is there a legal length of time for a yellow light?
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